centre for business mathematics and … · mr rk maxwell tel : (018) 299 ... the mission of the...

POTCHEFSTROOM CAMPUSPrivate Bag X6001, Potchefstroom, South Africa, 2520

Tel: (018) 299-1111 • Fax: (018) 299-2799 Internet: http://www.nwu.ac.za

CENTRE FOR BUSINESS MATHEMATICS

AND INFORMATICS®

INFORMATION BROCHURE 2011 BMI & ACTUARIAL STUDY PROGRAMMES

Updated: September 2010

Web page: http://www.nwu.ac.za/bmi

E-mail: [email protected]

Contact Persons:

Prof PJ de Jongh Tel: (018) 299-2585

Fax: (018) 299-2584


Nominated Accreditation Actuary:

Mr RK Maxwell Tel : (018) 299 2502

Fax : (018) 299 2584

E-mail : [email protected]

Mrs M Geldenhuys Tel: (018) 299-2581

Fax: (018) 299-2584


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a Centre of Expertise in

Financial Risk Management

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VISION

“To be a recognised player in the South African Industry and the international academic world, and to obtain, develop and disseminate financial risk

management expertise in close collaboration with the industry and public sector.”

GOALS

The Centre aims to:

1. Train innovative-thinking undergraduate, post-graduate and non-degree students in financial risk management and related areas, with emphasis on integrating the theoretical knowledge in the workplace.

2. Conduct applicable and internationally acknowledged research on aspects of financial risk management, and to promote the publication of such results.

3. Promote co-operation and interaction between the industry and the University and to cultivate specialised expertise in the implementation of practical, training-related research projects in the industry.

4. To improve the general level of expertise in the industry by developing and presenting practical training courses.

5. To extend and develop appropriate and well-equipped facilities to an outstanding level.

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BMI Business Concept

The mission of the Centre for Business Mathematics and Informatics® (Centre for BMI) is to assist the financial industry in South Africa in managing the different types of risks they encounter in the execution of their daily functions, by correctly identifying, quantifying, and hedging against such risks.

This is done through the provision of consultation and research services, and the training of students as Risk Managers, Financial Engineers, Financial Mathematicians, Investment Analysts, Actuaries and Business Intelligence Analysts or Data Geologists.

The training methodology is an integrated approach between the Economic, Mathematical and Informatics disciplines, with a strong practical focus to remain relevant in the industry.

The driving force of the Centre is technology/know-how, with the focus on obtaining, developing, and disseminating risk management expertise, and achieving international recognition in the process.

In pursuing its mission the Centre will actively build international knowledge networks with other suitable institutions and experts, and will also obtain appropriate infrastructure and technology in the form of supporting systems.

a Centre of Expertise in Financial Risk Management Solutions

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LANGUAGE POLICY OF THE NORTH-WEST UNIVERSITY

All the undergraduate training programmes of the Centre for BMI are presented at the Potchefstroom and Vaal Triangle campuses. For the sake of background information, it is important to state that although Afrikaans is used as primary tuition language at undergraduate level at the Potchefstroom Campus, educational interpreting services are available in certain niche programmes, while both English and Afrikaans are used as tuition languages at the Vaal Triangle Campus. For the BMI programme, the language arrangement is as follows: while the undergraduate programme at the Vaal Triangle Campus is offered in English only , interpreting facilities (into English) are available for the actuarial programme at the Potchefstroom Campus.

All BMI post-graduate training programmes are presented at the Potchefstroom Campus. In order to prepare students for their professional careers in business and industry, the primary tuition language is English.

Please note that the North-West University has adopted a functionally multilingual language policy, which in practice means the following:

(a) Correspondence with the University may be conducted in Afrikaans, English or Setswana.

(b) If undergraduate lectures are presented in Afrikaans, students are free to interact with the lecturer in English. Similarly, if lectures (undergraduate or postgraduate) are presented in English, students are free to interact with the lecturer in Afrikaans.

(c) Tests and examinations are set in both Afrikaans and English, and may be answered in either language.

(d) The University has made considerable progress in making study guides throughout available in both English and Afrikaans.

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TABEL OF CONTENTS

1. PURPOSE AND SCOPE OF DOCUMENT 2. ABBREVIATIONS 3. BACKGROUND: ESTABLISHMENT OF THE CENTRE 4. RISK MANAGEMENT AND FINANCIAL ENGINEERING 5. WHAT IS RISK? 6. WHAT DOES BUSINESS MATHEMATICS AND INFORMATICS

ENTAIL? 7. PROFESSIONAL QUALIFICATIONS 8. ADMISSION REQUIREMENTS 9. WHAT SCHOOL SUBJECTS DO YOU NEED? 10. WHAT CAREER OPPORTUNITIES DO THESE PROGRAMMES

OFFER TO THE STUDENT? 11. WHERE ARE YOU GOING TO WORK? 12. MORE ON THE BMI STUDY PROGAMME 13. THE UNDERGRADUATE B.Sc. TRAINING PROGRAMME 14. THE POST-GRADUATE HONS. B.Sc. AND MSc. (BMI)

PROGRAMME 15. THE ACTUARIAL TRAINING PROGRAMME 16. BMI RESEARCH PROGRAMME (MSc. AND Ph.D) 17. BURSARIES APPENDICES A. SCHEMATIC OF THE BMI PROGRAMME B. SCHEMATIC OF THE ACTUARIAL PROGRAMME C. SYLLABI FOR THE B.Sc. PROGRAMMES D. SYLLABI FOR THE Hons. B.Sc. AND M.Sc. PROGRAMMES

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1. PURPOSE AND SCOPE OF THE DOCUMENT

The aim of this document is to provide a detailed exposition of the Centre and the structure of the Business Mathematics and Informatics (BMI) and Actuarial (Act) training programmes. Although all possible steps have been taken to ensure that the information is correct, it should be emphasised that the University year-book with the regulations set out therein is the final authority in this regard.

2. ABBREVIATIONS

ABSA Amalgamated Banks of SA Ltd. APS Achievement Point Score

BMI Business Mathematics and Informatics BWI "Bedryfswiskunde en Informatika" Centre The Centre for BMI

FSB Financial Support Bureau (at the PUK) RM Risk Management

PU for CHE Potchefstroom University for Christian Higher Education (Potchefstroom Campus of the North-West University before the amalgamation on the 1st of January 2004)

PUK Potchefstroom Campus (of the North-West University)

SCSM School for Computer, Statistical and Mathematical Sciences

VU "Vrije University at Amsterdam" VTC Vaal Triangle campus (of the North-West

University) 3. BACKGROUND: ESTABLISHMENT OF THE CENTRE

In the late nineties ABSA adopted a strategy to acquire expertise in risk management. At the same time the erstwhile PU for CHE accepted as a strategy the establishment of expert focus areas by means of which the University could concentrate its resources and expertise on a few fields in order to obtain the highest degree of quality and relevance in its training and research. Subsequently ABSA decided to support the erstwhile PU for CHE in the establishment of a Centre for BMI where expertise in the field of risk management could be established. Because the PU for CHE already had qualified mathematicians and statistical experts at its disposal, it was decided to focus on this field in collaboration with ABSA.

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The idea of co-operation between a bank and a university is not a new concept. In the Netherlands a similar partnership exists between the Vrije University at Amsterdam and the RABO bank. Because the PU for CHE has had a long relationship with the VU, this university was more than willing to make its expertise available to the PUK. The current programme has been structured with inputs from various experts from the VU. Full access to the VU's subject and lecturing material was also made available to the PUK, with the result that the PUK's programme started off with a well-established international baseline.

4. RISK MANAGEMENT AND FINANCIAL ENGINEERING

The financial services sector is, like the other business sectors, currently increasingly confronted with the dynamically changing environment, to mention only the impact of the Internet, the digital economy and supermarkets planning to sell traditionally financial type of products. Traditionally financial institutions had a product focus, meaning that they endeavoured to sell existing products to clients, with thorough covering of the bank's risk in the transaction. The new approach is to take the client's risk appetite into consideration, and if necessary, to design new products that will consider both parties’ interests. This necessitates that all the underlying risk elements in the transaction should be identified, measured, quantified and incorporated into a model that can be used to analyse it, and ultimately assist in managing it. To design such new products, a sound knowledge of Financial Engineering is required, as one of the basic building blocks in the process.

The importance of risk management up to the highest levels of an organisation is widely recognised today, where it is commonly known as ERM, or Enterprise Wide Risk Management in its widest form. The sophisticated level of development that we have reached today really started in 1989, and was caused by a range of factors, such as changes in the economy, competition, new legislation, market requirements (such as the capital requirements emanating from the Basel II accord), and the availability of new technology. The development of ERM started with concepts such as Asset and Liability Management to the current concepts of Value at Risk and Earnings at Risk. Some of the newer methodologies include concepts such as Economic Capital, Risk-adjusted Performance Measurement, and Risk and Control Self-Assessment. The presence of risk is seen as an opportunity. The overriding purpose is to establish an integrated, consistent and effective risk management framework wherein all risks can be identified, quantified, and managed in such a way to achieve the best risk-reward profile.

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During the risk identification process, risks are classified as one of market-, credit, underwriting-, or operational risk. In the risk measurement or evaluation phase, a quantitative or qualitative risk profile is developed to assess the risk level – a process that makes extensive use of quantitative analysis. Both these profiles have an impact on the final optimal risk-reward profile.

The integrated ERM framework takes all aspects of risk management into account, and includes aspects such as policies and procedures, quantitative and qualitative risk measurement, risk monitoring and control, bottom-up and top-down approaches, as well as compliance with regulations and laws.

5. WHAT IS RISK?

Since all four BMI training programmes focus primarily on risk and the measurement and management thereof, it is necessary to explain the basics of risk. Risk comes in many forms. Every person and organization faces risk. As experts in measuring and managing risk, actuaries and risk managers fulfil a significant need in our society. Their contribution to society’s psychological, physical and economic well-being is immense. If the risk management programmes that actuaries and risk managers develop did not exist, our economy would not be able to grow as it does.

Consider the following:

Would as many people be willing to own a home if fire insurance did

not exist? Would a company build a factory that could be destroyed in an

earthquake if it were not protected by insurance? Would people spend money today and still be confident about their

future if there were no retirement programmes? Would the cars people drive be safe if the parts were not rigorously

tested using mathematical techniques actuaries and risk managers routinely use?

Would parents enjoy risky and adventurous recreational activities such as rock climbing or skiing if their children faced financial disaster in the event of an accident?

Would the banks (and the money deposited in them) be safe if their assets and liabilities were not carefully managed to control financial risk?

Would the returns on our investments be high if financial institutions such as mutual funds, banks and insurance companies did not use sophisticated techniques to improve returns without increasing risk too much?

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6. WHAT DOES BUSINESS MATHEMATICS AND INFORMATICS ENTAIL?

One might wonder, if the focus of the BMI training programmes is on risk management and related fields, why the name Business Mathematics and Informatics? Initially the BMI programme was designed on the basis of the VU BMI training programmes, hence the name Business Mathematics and Informatics. The reason behind the VU’s choice could be motivated as follows. Business Mathematics and Informatics (BMI) is a multi-disciplinary study that focus on the integration of Business Economics, Mathematical and Informatics principles with the aim of solving management and operational problems in the industry with a quantitative thrust. Nowadays, BMI is regarded not as a ‘field of study’, but rather a training philosophy that is used in BMI training programmes to prepare students for professional careers in business and industry. This philosophy comes to fruition in the BMI master’s degree where students receive on-the-job training on how to solve real problems in business and industry. Four specialisation directions are currently offered that all form part of the so-called BMI-programmes. These are: Quantitative Risk Management (also referred to as the B-leg) Financial Mathematics (also referred to as the M-leg) Business Intelligence / Data Mining (also referred to as the I-leg) Actuarial Science (also referred to as the A-leg) All these programmes are offered up to honours level and all BSc and Hons BSc degrees carry the names of these specialisation areas. At master’s level students may enroll for the MSc-degree in Business Mathematics and Informatics in each of these specialisation areas.

Within this broad focus, the Centre concentrates on quantitative financial risk management expertise to address problems in the financial industry. The sectors that are specifically targeted are: Financial services Investment services Insurance industry Other companies, such as Eskom, Telkom and the mining houses,

that are exposed to financial risks as part of their normal daily operations.

Note that the actuarial training programme forms an intergral part of the BMI training philosophy. The Actuarial programme has been designed to conform to the requirements of the Actuarial Society of South Africa (AS) and the Institute and Faculty of Actuaries (IFA), and is structured such that maximum exemption can be obtained from the AS level A1 and A2 subjects and the IFA’s CT-subjects.

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The focus of actuarial training at the NWU is on enterprise-wide risk management (ERM) and investments and not so much on pensions, life and general insurance. From 2011, the Centre for BMI position itself to present an associate level actuarial training programme that will offer specialist training in ERM and investments.

7. PROFESSIONAL QUALIFICATIONS

Professional Actuarial Qualifications: o FFA - Fellow of the Faculty of Actuaries o FIA – Fellow of the Institute of Actuaries o FASSA – Fellow of the Actuarial Society of South Africa

Professional Risk Qualifications: o FRM (Financial Risk Manager) certification from the Global

Association of Risk Professionals (GARP) o PRM (Professional Risk Manager) certification of the

Professional Risk Manager’s international Association (PRMIA)

Accreditation of BMI programmes by Professional bodies:

o The Hons BSc. in Quantitative Risk Management is accredited by PRMIA for Level I and II of the PRM (Professional Risk Manager) certification see website [http://www.prmia.org].

o The B.Sc. Hons. in Actuarial Science is accredited by the Institute and Faculty of Actuaries (UK) see website [http://www.actuaries.org.uk] for CT1-CT8 and interim accreditation was received from AS for their level A1 and A2 subjects. We are currently awaiting feedback from AS for our 2010 full accreditation application.

o The BMI risk training and research programmes are accredited by ERMII (the Enterprise Risk Management International Institute) see website [http://www.ermii.org].

After completing the Hons. BSc degree, BMI students are well-prepared to attempt the FRM and CFA (Chartered Financial Analysts) exams as well.

8. ADMISSION REQUIREMENTS Mathematics above 70% (Level 6) and an APS Score of at least 32. The higher the Mathematics mark, the better the chances of the prospective student to successfully complete the BMI programme. For more detail visit the website: http://www.puk.ac.za/akawww/Toelatingsvereistes_2011.pdf

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Students who did not have Accountancy as a subject at school, must successfully complete the short course in Basic Accounting at the Potchefstroom Campus. Should the short course not be passed with a minimum of 65% the student should register for ACCS111. Students who achieved at least 65% in ACCF111 at the end of the first semester will be allowed to continue with ACCC121 in the second semester. If a student achieves at least 65% in ACCF121 he/she can write the second opportunity examination in ACCC121 and if the result is at least 55% admission to the second year CA-Accounting can be obtained. A foundation programme currently run at the Vaal Triangle Campus of the North-West University. Admission requirements: Mathematics above 50% (Level 4) and an APS of 28. For more detail on this programme contact prof Philip Pretorius (016 910 3262). 9. WHAT SCHOOL SUBJECTS DO YOU NEED? All programmes require at least grade 12 Mathematics (Level 6, 70%). Although not a strict requirement, all learners are advised to do Computer Studies, and learners who want to follow the A- and B-legs, are advised to study Accounting.

10. WHAT CAREER OPPORTUNITIES DO THESE PROGRAMMES OFFER TO THE STUDENT? After completion of the study, students will be thoroughly prepared for a variety of careers in the financial, commercial or industrial sectors where the emphasis is on the modelling, analysis and management of risk-related problems. If one specialise in the B-leg of the BMI programme (Quantitative Risk Management), typical jobs in the financial sector would be the following:

Market- or Credit Risk Analyst/Manager Commercial Banker Corporate Banker Treasury Analyst Risk Analyst/Manager Decision Support Analyst Investment Analyst Financial Engineer

If one specialise in the M-leg of the BMI programme (called Financial Mathematics), typical jobs in the financial sector would be the following:

Financial Product Developer Structured Financing Specialist Financial Instrument Pricing Specialist

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Mathematical Finance Specialist Financial Engineer Financial Mathematician

If one specialise in the I-leg of the BMI programme (called Data Mining), a typical job in the financial sector would be the following:

Quantitative Strategist Business Intelligence Specialist Business Analytic Specialist Data Geologist Decision Support Analyst Financial Statistician

If one specialise in the A-leg of the BMI programme (called Actuarial), a typical job in the financial sector would be the following:

Actuary

11. WERE ARE YOU GOING TO WORK?

Mostly in large companies in the financial services sector (e.g. Absa, SAS, Barclays, Nedbank, Transunion ITC, Standard Bank, KPMG, Ernst & Young and Pricewaterhouse Coopers). Currently BMI students are spread all over the world. A list of companies where BMI alumni currently are employed appear below: Absa Advantage Asset Managers African Bank Anglo Platinum Auto & General Barclays Bank, London Brait Clark McKay and Walpole Credit Suisse Deloitte Ernst & Young First Rand Bank FNB Free State Maize Galileo Capital Grain Africa Investec IQ Business Group JDG Trading Financial Services Kagiso Securities KPMG Liberty

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Lloyds TSB, London Momentum Munnik Basson and DaGama Nedbank PIC Solutions Price Waterhouse Coopers Rand Merchant Bank Rennies Bank Royal Bank of Scotland SA Reserve Bank Sanlam SAS Senwes Sigma Synergy Standard Bank Stanlib Swiss Re Capital Telkom Transunion West Bank XDS Analytics

12. MORE ON THE BMI STUDY PROGRAMME

The full course has been designed for a period of five years, during which time students obtain a B.Sc. degree after three years, followed by a full time one year Hons. B.Sc degree and a full time one year M.Sc. degree. What is the global structure of the programme? The undergraduate course is a B.Sc. degree in one of the four specialisation areas. In this course students will receive thorough training in Mathematics, Statistics, Informatics, Economics and Bank Risk Management, with specific attention paid to the integration of the disciplines to solve business problems in the field of specialisation. For each specialisation area, the specific undergraduate degree programme will provide admission to the corresponding post-graduate Honours degree programme, (See training roadmap in Appendix A.) Note that it is possible for students to switch between specialisation areas and that the first semester of the first year of all four programmes are very similar. More on this in the next subsection. As stated previously, thorough attention is paid to the integration of the different disciplines in terms of creative problem solving in especially the M.Sc. programme.

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This programme is concluded with a final semester during which the student will be placed in the industry on a 60% full-time basis and where he/she will be expected to solve a practical problem and to document the result in the form of a report.

How do the undergraduate B.Sc. fit into the post-graduate programme? After the successful completion of the B.Sc degree in Quantitative Risk Management the student will be able to register for the Hons. B.Sc in Quantitative Risk Management. After the successful completion of the B.Sc. degree in Financial Mathematics the student will be able to register for the Hons. B.Sc. in Financial Mathematics or Hons B.Sc. in Quantitative Risk Management (accreditation for levels I and II of the PRM not guaranteed).

After the successful completion of the B.Sc. degree in Business Intelligence/Data Mining the student will be able to register for the Hons. B.Sc. in Business Intelligence/Data Mining or Hons. B.Sc. in Quantitative Risk Management (accreditation for levels I and II of the PRM not guaranteed).

After the successful completion of the B.Sc. Actuarial degree the student will be able to register for the Hons. B.Sc. in Actuarial Science or the Hons. B.Sc in Quantitative Risk Management (accreditation for levels I and II of the PRM not guaranteed). Students who wish to change specialisation fields should obtain approval from the BMI Centre Director.

After the successful completion of the B.Sc. Hons. in the specific specialisation field students can continue with the full time Masters degree (Business Mathematics and Informatics) in the same specialisation field. In 2010, Actuarial Science students may register for the MSc BMI (Quantitative Risk Management) and from 2011 Actuarial Students can register for the MSc BMI (Actuarial Science) subject to the approval of the Higher Education Department. Students who find it difficult to cope with the mathematical content of the BMI programmes may consider switching to the B.Com. Risk Management programmes (see Yearbook of the Faculty of Economic Sciences). Note that these programmes are presented by the School of Economics and has significant less mathematical content. Career options should be discussed with the Director: School for Economics.

How does the Vaal Triangle Campus fit into the programme?

As stated previously, all BMI undergraduate programmes are presented at the Vaal Triangle Campus in English, except the Actuarial programme.

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Integrated Assessment

Integrated assessment of the various undergraduate and post-graduate BMI programmes takes place as follows:

For the undergraduate B.Sc. programmes by means of the BWIN321

module;

For the Hons B.Sc. in Quantitative Risk Management by means of the BWIN623 and ECON623 modules; For the Hons B.Sc. programme in Financial Mathematics by means of the BWIN623 module; For the Hons B.Sc. programme in Business Intelligence / Data Mining by means of the ITRI626 module; For the Hons B.Sc. programme in Actuarial Science by means of the BWIA672 and BWIN623 modules. For the M.Sc. programmes by means of the BWIN826 module. Students from other universities Undergraduate studies: Students from other universities will be allowed to register for the BMI study programmes provided they meet the individual prerequisites per subject module. This will be considered on an individual basis, though it may be expected of them to follow additional prescribed courses so as to ensure the appropriate background knowledge.

Post graduate studies: Students from other universities will be allowed to register for post graduate studies provided they meet the requirements for the specific specialisation area. This will be considered on an individual basis. For the honours programme, this will require as a minimum statistics (at 3rd year level), risk economics (3rd year level), mathematics (2nd year level), computer science (1st year level) and accounting (1st year level). Also note that accreditation arrangements with professional bodies are not automatically guaranteed. For the master’s programme, students from other universities must formally apply before the end of July to the Director: Centre for BMI. The BMI examination and selection committee will make the final decision on such an application in August of the year preceding the year of application.

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How do the University's course codes work? Subjects are presented according to modules stretching over a semester, and each module has to be passed. Modules have been arranged according to levels of advancement, which will typically be related to the study year in which the module is taken (providing the degree is completed over the minimum period). Each module has a code and a name (e.g. BWIN613) is the code, with the name of the module "Financial Engineering". The first four letters ABCD of the code ABCD123 indicate the subject, while the first figure (1) indicates the level (year), and the second figure (2) the semester in which the module is presented. The third figure (3) distinguishes between modules for which the first six characters are the same.

13. THE UNDERGRADUATE B.Sc.(BMI) TRAINING PROGRAMME

The programme is set out schematically in the training roadmap in Appendix A, with specific module codes and credits in the undergraduate curriculum, in the same appendix. The specific module contents can be obtained by using the module code and looking it up in the syllabi in Appendix C. Undergraduate students who are unsure about which specialisation (B, M, I or A) to choose are advised to enrol for either the B or the A leg. These students may keep their options open until the end of the first semester of the first year (in which case a choice has to be made for the I-specialisation field) or until the end of the first year of study when the choice has to be made for the other specialisations fields (B, M or A).

14. THE POST-GRADUATE Hons. B.Sc. and M.Sc.(BMI) TRAINING PROGRAMME

Admission to the Hons. B.Sc. is subject to a consistent, good academic performance throughout the Baccalareus study, culminating in a final mark of at least 60% for each subject in the 2nd and 3rd year of study. Candidates must take note that they may be refused admission to the postgraduate programme should this not be the case. In addition, admission to the Hons. B.Sc. (Actuarial Science-programme) will be dependent on the number of undergraduate exemptions students achieve. Admission to the M.Sc. is subject to the availability of academic supervisors and the demand for students from industry. Students will be screened for selection for the M.Sc. programme in the second semester of the Hons. B.Sc.

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The Masters degree in Quantitative Risk Management/ Financial Mathematics and Data Mining give admission to the PhD in Risk Analysis. Students can also obtain admission to the PhD in Statistics, Mathematics and Economics, but could be required to take some extra subjects, depending on the area of specialisation of their PhD thesis.

15. THE ACTUARIAL TRAINING PROGRAMME

The PUK offers an actuarial training programme structured in accordance with the requirements of the Institute and Faculty of Actuaries(IFA) and the Actuarial Society of South Africa (AS). AS in 2010 launched a local internationally recognised actuarial qualification. The PUK in May 2010 lodged its application for full accreditation with AS. From 2011, the PUK is positioning itself to present an actuarial training programme up to associate level with specialisation in Enterprise-wide Risk Management (ERM) in accordance with the learning objectives of the new ERM Global Syllabus of the International Actuarial Association. A schematic exposition of the programme is given in Appendix B, which is similarly structured to the BMI programme in Appendix A. Exemption for a subject from the Level A1 subjects (unspecified) of AS may be granted if a student passes the appropriate university modules with certain final marks (see page B6). Exemption for a subject from the Level A2 subjects (specified) of AS may be granted if a student fulfils the requirements for external evaluation in the appropriate university modules (see page B6). Actuarial students should note that subjects such as A403/CT9 (Business Awareness), A402/CA2 (Model Documentation Analysis and Reporting) and A302/CA3 (Communications) are short modules or courses that need to be done through AS. These modules or courses are typically very expensive and might require relevant work experience. Please note that in order to qualify for exemption, a higher mark than the 50% university requirement is needed (see section B; Actuarial Information B5).

Specialised actuarial degree courses are currently presented up to a fifth-year level. It consists of a three year B.Sc.(Actuarial) degree course which currently may give exemption for all three level A1 subjects and three level A2 subjects (see Appendix B). The undergraduate curriculum is shown in Appendix B, where the specific module content can be obtained by using the module code and the syllabi in Appendix C.

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Students can also complete a postgraduate Hons. B.Sc.(Actuarial) degree to obtain a further two exemptions for the level A2 subjects (Appendix B). The structure of this programme is shown in Appendix B.

Integrated assessment of the undergraduate B.Sc. programme (N137P) takes place by means of the BWIN321 module and the postgraduate Hons B.Sc. programme (N609P) by means of the BWIA672 and BWIN623 modules. There is a strong degree of communality between the undergraduate B.Sc.(BMI) and the B.Sc.(Actuarial) programs. More specific, the modules for the above mentioned programmes are essentially the same in the first year, which gives a student the option to change from one programme to another after finishing the first year. Thereafter each course is structured in such a way as to bring about specialisation in a specific field. The B.Sc.(Actuarial) modules are structured in such a way as to give a student the maximum number of exemptions for the AS Level A1 and A2-series (IFA CT-series) after successful completion of the programme. Students who complete the other BMI programmes may also obtain exemption for a number of the AS Levels A1 and A2-series subjects provided they convey their attention of doing so to the Nominated Accreditation Actuary at the beginning of their second year of study. The possible exemptions per curriculum are given in Appendix B, (Actuarial Subject Exemptions).

How do I qualify as an Associate and as a Fellow AS presents two professional qualifications: Associate (AMASSA) and fellow (FASSA). Subjects required for completion of Associateship (The corresponding subjects of the Institute and Faculty of Actuaries are show in brackets): Part A1 (Foundation Technical) Pass all 3 subjects A101 (CT3) – Probability & Mathematical Statistics A102 (CT7) – Economics A103 (CT2) – Finance & Financial Reporting

Part A2 (Intermediate Technical) Pass all 5 subjects A201 (CT1) – Financial Mathematics A202 (CT4) – Models A203 (CT5) – Contingencies A204 (CT6) – Statistical Methods A205 (CT8) – Financial Economics

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Part A3 (Core Principles) Pass both subjects A301 (CA1) – Actuarial Risk Management A302 (CA3) – Communications Part A4 (Associateship Professionalism Skills) Pass both modules A401 (CT9) – Business Awareness Module A402 (CA2) – Model Documentation, Analysis and Reporting

Module and fulfil A403 – Associateship Work-based Skills Requirements and attend A404 – Associateship Professionalism Course. Further subjects required for completion of fellowship Part F1 (Fellow Principles) Pass 2 of the following subjects F101 (ST1) – Health & Care Principles F102 (ST2) – Life Insurance Principles F103 (ST3) – General Insurance Principles F104 (ST4) – Pension & Other Benefits Principles F105 (ST5) – Finance and Investments Principles F106 (ST9) – Enterprise-wide Risk Management Principles* *F106 can only be taken in conjunction with one of F101, F102, F103 and F104. Part F2 (Fellowship Applications) Pass 1 of the following subjects F200 (SA0) – Research Option (on the level of a Masters degree

research dissertation) F201 (SA1) – Health and Care Applications F202 (SA2) – Life Insurance Applications F203 (SA3) – General Insurance Applications F204 (SA4) – Pension and Other Benefits Applications F205 (SA5) – Investment Applications and pass 1 of the following modules: F211 (P1) – Health and Care Practice Module F212 (P2) – Life Insurance Practice Module F213 (P3) – General insurance Practice Module F214 (P4) – Pension and Other Benefits Practice Module F215 (P5) – Investment Practice Module

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Part F4 (Fellowship Professionalism Skills) Pass both modules (if not done as part of Associateship) A401 (CT9) – Business Awareness Module A402 (CA2) – Model Documentation, Analysis and Reporting)

Module and fulfil F403 – Fellowship Work-based Skills Requirements and attend F404 – Fellowship Professionalism Course. Summary

Students who passed the Hons. B.Sc. Actuarial degree could qualify for exemption for A101-A103 and A201-A205 (IFA CT1-CT8). A301/CA1, F105/ST5 and F106/ST9 are presented to prepare students for the AS exams.

External Examining: Students should note that it is required by the AS (and IFA) that exam papers and scripts for certain subjects (A201/CT1, A202/CT4, A203/CT5, A204/CT6, A205/CT8) be moderated by an approved independent examiner. This is of course subject to the payment of the applicable moderator fees. Also, when the student eventually wishes to apply for exemptions from AS and IFA, it becomes advisable to only join the local organisation (AS), where further fees as stipulated by the AS will become payable. It is important to note that all such extra costs (including prescribed text books and/or course material) will be for the students’ account, and is not covered by the standard academic fees. Generally, your future employers will cover these costs. Actuarial Study Options at other universities: Students who successfully passed their Hons BSc degree in Actuarial Science AND who has obtained exemptions for A101-A103 and A201-A205 may consider enrolling for the Postgraduate Diploma in Actuarial Science presented by the University of Stellenbosch (US) in collaboration with the University of Cape Town. This present the student with the opportunity of obtaining an extra 3 exemptions from AS. Note that this option is only recommended to students who do not want to follow the ERM and Investment specialisation as offered at the PUK. The US diploma is presented to full time or to part time students and the minimum time of completion is 18 months.

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A student will be required to pass modules totalling at least 120 credits selected from the Core Applications, Specialist Technical and Specialist Applications subjects of AS (IFA) (from those which the University of Stellenbosch may offer from time to time). The following modules are currently available: Actuarial Risk Management (A301/CA1), Life Insurance Technical (F102/ST2), Pensions Technical (F104/ST4), Health and Care Applications (F201/SA1), Life Insurance Applications (F202/SA2) and Pensions Applications (F204/SA4). The last three subjects will be for non-exemption purposes as these university subjects only serve as preparation for the relevant Specialist Applications subject from AS or IFA. More information can be obtained from the Nominated Accreditation Actuary (018) 299 2502. Since the NWU has established a close liaison with US it is advised that students apply for this diploma via the Centre for BMI.

16. BMI RESEARCH PROGRAMME (M.Sc. and Ph.D)

Successful completion of the M.Sc. BMI will allow a student to register for the Ph.D in Risk Analysis (Curriculum N905P). Please note that students who complete the honours programmes have the option to enrol for a thesis based M.Sc. in Risk Analysis (Curriculum N865P). Please refer to the Yearbook of the Faculty of Natural Sciences for more information.

17. BURSARIES

NWU ACADEMIC BURSARIES First-year Academic Bursaries These bursaries are awarded AUTOMATICALLY to all full-time first-year students who: Completed Grade 12 in the previous year. Register at the NWU for the first time after completing Grade 12, for

a first, undergraduate qualification. Obtained an average of 75% or higher (calculated by using FSD

regulations) during the Grade 12 final examination. The bursary is awarded on account of the student’s true average

obtained. You can calculate it as follows: 10% is deducted from the subject’s percentage for Any/Every Non-Designated subject and Life Orientation is disregarded.

22

Then add the percentages of the six subjects with the highest marks and divide by six to calculate the true average. No marks will be rounded off.

Student’s average

% Merits bursary

90% 110% of tuition fees 85% 100% of tuition fees 80% 75% of tuition fees 75% 40% of tuition fees

For more detail visit the website: http://www.nwu.ac.za/export/sites/default/nwu/p-fsd/p_fsd_doc_2011/1-Voorgraads/Kitsinligting_VG_Potch_2011.pdf Or contact: Elsabe Bosman (018) 299 2045, e-mail: [email protected]

ABSA BURSARIES FOR BMI AND B.Com RISK MANAGEMENT STUDENTS

Visit the Centre for BMI website [http://www.nwu.ac.za/bmi] or contact Mr. Cronjé (018 299 2577). Absa Bursary (BMI) Programme process: The Absa/ BMI Bursary Scheme is managed by the Absa/ BMI

Bursary Committee. Students who wish to enrol for

any one of the BMI programmes, the Actuarial programme, the B.Com Economics and Risk Management programme or the B.Com Economics, Risk Management and Investment

Management programme, could be considered for an Absa bursary.

Advertising for first year bursaries are done by the BMI Student Marketer, BMI Website and the NWU Marketing Department until the end of September of each year.

Successful applicants who meet the requirements are awarded a conditional Absa BMI bursary pending their acceptance by the NWU and the quality of their final Grade 12 results. The top 15 students are invited for an interview in January at the Vaal Triangle Campus and the bursaries are finally awarded after the results of the interview are taken into account.

Requests for applications for bursaries for students already in the above programmes from the second year on are advertised on the bulletin boards of the Centre for BMI at the Potchefstroom Campus and The School for IT at the Vaal Triangle Campus during February of every year. Bursaries are awarded in March of the same year.

23

Each successful student will have to sign a formal contract with

Absa in order to secure funding. Awarded bursaries will be re-evaluated each year based on academic performance.

The amount of the bursary that is awarded will depend on which campus of the NWU the student is enrolled at and differs for undergraduate and post graduate students. The amount awarded is sufficient to cover the normal expenses with regards to tuition and books, residential fees and meals.

APPENDIX A: SCHEMATIC OF THE BMI PROGRAMME 2011

Training Roadmap – Potchefstroom Campus A1 Undergraduate Programme – Quantitative Risk Management (N134P) A2 Undergraduate Programme – Financial Mathematics (N135P) A3 Undergraduate Programme – Data Mining (N136P) A4 Hons. B.Sc Programme – Quantitative Risk Management (N610P) A5 Hons. B.Sc Programme – Financial Mathematics (N611P) A6 Hons. B.Sc Programme – Data Mining (Business Analytics) (N612P) A7 Hons. B.Sc Programme – Data Mining (Business Intelligence) (N612P) A8 M.Sc. Programme – Business Mathematics and Informatics (Quantitative Risk Management) (N809P) A9 M.Sc. Programme – Business Mathematics and Informatics (Financial Mathematics) (N810P) A10 M.Sc. Programme – Business Mathematics and Informatics (Data Mining) (N811P) A11 M.Sc. Programme – Risk Analysis (N865P) A12

Industrie-gerigte Navorsings-projekBedryfsintegrasieprojek

Praktiese Risikoanalise SAS RDKeusemodule x 4

M.Sc. : N809PKwantitatiewe Risikobestuur

Kwantitatiewe Risikoanalise IFinansiële Ingenieurswese I IIBeleggingsteorie IStatistiese Data-Analise I IIRisikobestuurMeerveranderlike StatistiekKeusemodule x 2

Hons. B.Sc. : N610P Kwantitatiewe Risikobestuur

BWI OPLEIDINGSPADKAART 2011 - Potchefstroom Kampus

Jaar 4

Jaar 5 Jaar 5

Jaar 4

A1Weergawe: September 2010

Finansiële Ingenieurswese I IIStatistiese Data-Analise I IIStogastiese Prosesse I IITopologie van Metriese en Normeerde RuimtesMaat- en Integrasieteorie I IIDifferensiaalvergelykingsPrysing van Afgeleides A

Hons. B.Sc. : N611PFinansiële Wiskunde


Prysing van Afgeleides BPraktiese Risikoanalise SAS RDKeusemodule x 3

M.Sc. : N810PFinansiële Wiskunde

Kunsmatige Intelligensie I IIStatistiese Data-Analise I IIMeerveranderlike StatistiekKeusemodules x 5


Praktiese Data-ontginningKeusemodule x 4

Hons. B.Sc. : N612PData-Ontginning

M.Sc. : N811PData-Ontginning

Inleidende Algebra & Analise I II (a) (b)Beskrywende Statistiek (a)Inleidende Statistiese Inferensie (b)Inleiding tot Rekenaars en Programmering (a)Grafiese Koppelvlakprogrammering I (b)Inleiding tot Ekonomie (a)Basiese Mikro en Makro Ekonomie (b)Finansiële Rekeningkunde (a) (b)Finansiële Wiskunde (b)Besigheidsbestuur (a)

Analise III (a)Lineêre Algebra I II (a) (b)Waarskynlikheidsleer (a)Makro Ekonomie (a)

Finansiële Wiskunde (A201/CT1)(a) (b)Steekproeftoerie & Statistiese Interferensie (b)Numeriese Analise (b)Inleiding tot Risikobestuur (a)Moderne Portefeulje Teorie (A205/CT8) (b)

Finansiële Wiskunde (A201/CT1) (a) (b)Statistiese Inferensie (a)Finansiële Bestuur (a) Bankrisikobestuur (a)Effektebeurs Modellering en analise (b)Lineêre Modelle (b)Statistiek Projek (b)Finansiële Markte (b)

B.Sc. : N134P Kwantitatiewe Risikobestuur

(B-Been)

B.Sc. : N135PFinansiële Wiskunde

(W-Been)

B.Sc. : N136P Data-Ontginning

(I-Been)

Studente wat baie onseker is betreffende hulle keuse van spesialisasierigting word aanbeveel om vir N136P (Data-Ontginning) te registreer en dan aan die einde van die tweede jaar 'n keuse te maak tussen die Finansiële Wiskunde en die Data-Ontginning spesialisasierigtings. Let op dat beide N135P (Finansiële Wiskunde) en N136P (Data-Ontginning) toegang verleen tot N610P (Kwantitatiewe Risikobestuur). Al hierdie bene word ook op Vaaldriehoek Kampus in Engels aangebied.

LW: a = Eerste Semester vakb = Tweede Semester vak

Inleidende Algebra & Analise I II (a) (b)Beskrywende Statistiek (a)Inleidende Statistiese Inferensie (b)Inleiding tot Rekenaars en Programmering (a)Grafiese Koppelvlakprogrammering I (b)Inleiding tot Ekonomie (a)Basiese Mikro en Makro Ekonomie (b)Finansiële Rekeningkunde (a) (b)Finansiële Wiskunde (b)

Inleidende Algebra & Analise I II (a) (b)Beskrywende Statistiek (a)Inleidende Statistiese Inferensie (b)Inleiding tot Rekenaars en Programmering (a)Programmering I (a)Inleiding tot Ekonomie (a)Basiese Mikro en Makro Ekonomie (b)Finansiële Rekeningkunde (a) (b)Finansiële Wiskunde (b)

Analise III IV (a) (b)Lineêre Algebra I II (a) (b)Waarskynlikheidsleer (a)Makro Ekonomie (a)Besluitsteunstelsels I (a)Finansiële Wiskunde (A201/CT1)(a) (b)Steekproeftoerie & Statistiese Interferensie (b)Numeriese Analise (b)

Moderne Portefeulje Teorie (A205/CT8)

Analise III (a)Lineêre Algebra I II (a) (b)Waarskynlikheidsleer (a)Makro Ekonomie (a)Programmering II (a)Finansiële Wiskunde (A201/CT1)(a) (b)Steekproeftoerie & Statistiese Interferensie (b)Numeriese Analise (b)

Datastrukture en Algoritmes (b)

Finansiële Wiskunde (A201/CT1) (a) (b)Statistiese Inferensie (a)Reële Analise I II (a) (b)Bankrisikobestuur (a)Effektebeurs Modellering en analise (b)Lineêre Modelle (b)Statistiek Projek (b)

Finansiële Wiskunde (A201/CT1) (a) (b)Statistiese Inferensie (a)Databasusse I II (a) (b)Bankrisikobestuur (a)Effektebeurs Modellering en analise (b)Lineêre Modelle (b)Statistiek Projek (b)

Jaa

r 1

Jaar

2Ja

ar 3

Version: September 2010 A2

UNDERGRADUATE CURRICULUMS:

Curriculum N134P: Quantitative Risk Management (B-Leg)

Qualification code: 200166

This curriculum is compiled as follows:

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 First semester First semester First semester Module code Core Cr Module code Core Cr Module code Core Cr WISN111 X 12 WISN211 X 8 STTN311 H 32 STTN111 H 12 WISN212 X 8 EKRP311 H 16 ITRW112 X 12 STTK211 H 16 FINM211 H 16 ECON111 H 12 ECON211 H 16 ACCF111 or ACCC111

H 16 EKRP211 H 16

BMAN111 X 12 WVES311 X 12 Total 1st semester

76 Total 1st semester


64

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 Second semester Second semester Second semester Module code Core Cr Module code Core Cr Module code Core Cr BWIN123 H 12 WISN222 X 8 BWIN321 H 16 WISN121 X 12 STTN221 H 16 STTK321 H 24 STTN121 H 12 TGWN222 X 8 STTK322 H 8 ITRW123 X 12 WVES221 X 12 EKRP321 H 16 ECON121 H 12 BWIA221 H 16 ACCF121 or ACCC121

H 16

AGLA121 or AGLE121

X 12

Total 2nd semester

88 Total 2nd semester


64

Year Module Year Module BWIA271 H 32 BWIA271 H 32 Total year level 1

164 Total year level 2


160

Total of curriculum credits 492

*Student enrolled for the curricula N134P, N135P, N136P and N137P, must report for a compulsory test of skills in academic literacy in order that their ability to function in an academic environment may be evaluated.

*Students who are identified as borderline cases must register for module AGLA111 [Afrikaans]/AGLE111 [English], depending on the language in which they have taken the compulsory skills test. The credits earned for these modules do not contribute to the number of credits required by a curriculum, but are regarded as additional credits.


Curriculum N135P: Financial Mathematics (M-Leg)


This curriculum is compiled as follows:

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 First semester First semester First semester Module code Core Cr Module code Core Cr Module code Core Cr WISN111 X 12 WISN211 X 8 STTN311 H 32 STTN111 H 12 WISN212 X 8 WISN311 H 16 ITRW112 X 12 STTK211 H 16 EKRP311 H 16 ECON111 H 12 ITRW214 X 16 ACCS111 or ACCF111

H 16 ECON211 H 16

WVES311 X 12 Total 1st semester



64

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 Second semester Second semester Second semester Module code Core Cr Module code Core Cr Module code Core Cr BWIN123 H 12 WISN221 X 8 BWIN321 H 16 WISN121 X 12 WISN222 X 8 WISN321 H 16 STTN121 H 12 STTN221 H 16 STTK321 H 24 ITRW123 X 12 BWIA221 H 16 STTK322 H 8 ECON121 H 12 TGWN222 X 8 ACCS121 or ACCF121

H 16 WVES221 X 12

AGLA121 or AGLE121

X 12

Total 2nd semester



64




160





Curriculum N136P: Data Mining (I-Leg)


The curriculum is compiled as follows:

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 First semester First semester First semester Module code Core Cr Module code Core Cr Module code Core Cr WISN111 X 12 WISN211 X 8 STTN311 H 32 STTN111 H 12 WISN212 X 8 ITRW311 H 16 ITRW112 X 12 STTK211 H 16 EKRP311 H 16 ECON111 H 12 ITRW212 H 16 ACCS111 or ACCF111

H 16 ECON211 H 16

WVES311 X 12 Total 1st semester



64

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 Second semester Second semester Second semester Module code Core Cr Module code Core Cr Module code Core Cr BWIN123 H 12 WISN222 X 8 BWIN321 H 16 WISN121 X 12 STTN221 H 16 STTK321 H 24 STTN121 H 12 ITRW222 H 16 STTK322 H 8 ITRW124 H 12 TGWN222 X 8 ITRW321 H 16 ECON121 H 12 WVES221 X 12 ACCS121 or ACCF121

H 16

AGLA121 or AGLE121

X 12

Total 2nd semester



64




160





POST GRADUATE HONS CURRICULUMS:

Curriculum N610P: Quantitative Risk Management (after B.Sc. N134P, N135P, N136P, N137P) (B-Leg)


This curriculum consists of the following modules divided into two semesters:

Module code Descriptive name Credits

First semester

BWIN611 Quantitative Risk Analysis I 16

BWIN613 Financial Engineering I 16

BWIN614 Investment Theory I 16

STTN612 Statistical Data-analysis I: Models 12

Elective Module (BWIN615) 12/16

Second semester

BWIN623 Financial Engineering II 16

ECON623 Risk Management 16

STTN622 Statistical Data-analysis II: Time Series 12 STTN623 Multivariate Statistics 12

Elective Module# (BWIN621) 12/16

Total number of credits 140/148

#The elective module in the first semester is chosen from the modules in the following table.


BWIN615 Financial Modelling I 16

ECON617 Econometrics 16

STTN613 Re-sampling Methods 12

STTN616 Nonparametric estimation methods 12

#The elective modules in the second semester are chosen from the modules in the following table.


BWIN625 Financial Modelling II 16

BWIN621 Quantitative Risk Analysis 16

ECON622 Fiscal and monetary policy 16

STTN624 Discrete Data analysis 12

The integrated assessment of this curriculum takes place during the assessment of the modules BWIN623 and ECON623.


Curriculum N611P: Financial Mathematics (after B.Sc. N135P) (M-Leg)



Module code Descriptive name Credits First semester

BWIN613 Financial Engineering I 16 STTN612 Statistical Data-analysis I:

Models 12

STTN615 Stochastic Processes I 12 WISK613 Topology of Metric and Normed

Spaces 8

WISK614 Measure and Integration Theory I 8 WISK615 Differential Equations 16

Second semester BWIN622 Pricing of Derivatives A 16 BWIN623 Financial Engineering II 16 STTN622 Statistical Data-analysis II: Time

Series 12

STTN625 Stochastic Processes II 12 WISK624 Measure and Integration Theory II 16

Total number of credits 144

The integrated assessment of this curriculum takes place during the assessment of the modules BWIN623.


Curriculum N612P: Data Mining [Business Analytics] (after B.Sc.

N134P, N135P, N136P, N137P ) (I-Leg)




First semester

ITRI616 Artificial Intelligence I 12


Elective Module (BWIN614) 16

Elective Module (STTN613/ECON617) 12/16

Elective Module (ITRI618) 12/16

Second semester

ITRI626 Artificial Intelligence II 12

STTN622 Statistical Data-analysis II: Time Series 12

STTN623 Multivariate Statistics 12

Elective Module (STTN624) 12/16



#The elective modules in the first semester are chosen from the modules in the following table.


BWIN615 Financial Modelling 16

ITRI613 Databases I 12


ITRI618 Decision Support Systems I 12



ITRI611 Data Warehouses I 12

ITRI614 Information Systems Engineering I 12






ITRI623 Databases II 12

ITRI628 Decision Support Systems II 12


ITRI621 Data Warehouses II 12

ITRI624 Information System Engineering II 12

STTN624 Discrete Data Analysis 12

The integrated assessment of this curriculum takes place during the assessment of the modules ITRI626.


Curriculum N612P: Data Mining [Business Intelligence] (after B.Sc.

N136P ) (I-Leg)




First semester

ITRI616 Artificial Intelligence I 12


Elective Module (BWIN614/ECON617) 16



Second semester

ITRI626 Artificial Intelligence II 12

STTN622 Statistical Data-analysis II: Time Series 12







BWIN615 Financial Modelling 16

ITRI613 Databases I 12





ITRI611 Data Warehouses I 12

ITRI614 Information Systems Engineering I 12






ITRI623 Databases II 12



ITRI621 Data Warehouses II 12

ITRI624 Information System Engineering II 12


The integrated assessment of this curriculum takes place during the assessment of the modules ITRI626.


POST GRADUATE MSc CURRICULUMS:

Curriculum N809P: BMI [Quantitative Risk Management] (after Hons.B.Sc. N609P or N610P) (B-Leg)


This curriculum consists of the following modules that are divided into two semesters:


First semester

BWIN811 Practical Risk Management SAS RD 16

BWIN815 Industry Integration Project 32

Elective Module #NQF level 9 (BWIN817)

16

Elective Module # (BWIN818) 16

Elective Module# (BWIA811/BWIA812)

12/16/24

Second semester

BWIN826 Industry Directed Research Project 80

Elective Module # (BWIA821) 12/16

Total number of credits 184/188/200


At least one of the elective modules must be on NQF level 9.



ITRI612 Linear Programming I 12

BWIN816 Modern Portfolio Theory 16

BWIN817 Retail Credit Risk 16

BWIN813 Practical Data Mining 16

BWIN818 Topical research issues in risk analysis

16

BWIA811* Enterprise-wide Risk Management 16

BWIA812* Enterprise-wide Risk Management I 24

BWIA813 Finance and Investments (F105/ST5)

24

STTN616 Nonparametric Methods of Estimation

12

STTN613 Resampling Methods 12

#The elective module in the second semester is chosen from the modules in the following table.



BWIN621 Quantitative Risk Analysis II 16

ITRI622 Linear Programming II 12

BWIA821 Enterprise-wide Risk Management 16

The integrated assessment of this curriculum takes lace during the assessment of the module BWIN826. At least one of the elective modules must be on NQF level 9.

* Students must choose between BWIA811 or BWIA812.

*Actuarial students are advised to take BWIA812.

*An NQF level 9 translates into a BWIN subject with an 8 prefix.

*Note: That at least 120 credits must be on level 9.


Curriculum N810P: BMI [Financial Mathematics] (after Hons. B.Sc. N611P) (M-Leg)




First semester

BWIN812 Pricing of Derivatives B 16

BWIN811 Practical Risk Analysis 16


Elective Module# NQF level 9 (BWIA811) 16

Elective Module # (BWIN818) 12/16

Second semester


Elective Module # (BWIA821) 12/16







BWIN818 Topical research issues in Risk Analysis

16




STTN616 Nonparametric Methods of Estimation 12


#The elective module in the second semester is chosen from the modules in the following table. At least one of the elective modules must be on NQF level 9.







The integrated assessment of this curriculum takes lace during the assessment of the modules BWIN826. At least one of the elective modules must be on NQF level 9.

*An NQF level 9 translates into a BWIN subject with an 8 prefix



Curriculum N811P: BMI [Data Mining] (after Hons. B.Sc. N612P) (I-Leg)




First semester



Elective Module #NQF level 9 (BWIN817) 16

Elective Module # (BWIN615) 16

Elective Module # (ITRI618) 12/16

Second semester

Elective Module # (BWIN625) 12/16













STTN616 Nonparametric Methods of Estimation

12


BWIN819* Advanced Business Analytics 16

#The elective module in the second semester is chosen from the modules in the following table. At least one of the elective modules must be on NQF level 9.







ITRI624 Information Systems Engineering II 12

BWIA821 Enterprise-wide Risk Management II 16

The integrated assessment of this curriculum takes place during the assessment of the module BWIN826. At least one of the elective modules must be on NQF level 9.

*Please note: BWIN819 will not be presented in 2011.

*An NQF level 9 translates into a BWIN subject with an 8 prefix



Curriculum N865P in Risk Analysis


The curriculum consists of a dissertation and an examination paper on topics that are supportive of the research done for the dissertation. The study leader decides together with the research director and the school/centre director on appropriate topics.

Module code Descriptive Name Credits

First Semester

BWIN872 Dissertation 132

RSWW811 Research Methodology 8

Select in consultation with the research director and director of the Centre for BMI one of the following modules:





BWIN812 Pricing of Derivatives B 16




BWIN818 Topical Research issues in Risk Analysis

16

BWIA811 Enterprise wide Risk Management I 16

Semester 2

BWIN872 Dissertation (continue)

RSWW821 Research Communication 8

Select in consultation with the research director and director of the Centre for BMI one of the following modules:

BWIN621 Quantitative Risk Analysis II 16

BWIN622 Pricing of Derivatives A 16



BWIA821 Enterprise wide Risk Management II 16

Total number of credits 180

APPENDIX B: SCHEMATIC OF THE ACTUARIAL PROGRAMME

2011

Actuarial Training Roadmap B1 Actuarial Curricula B2 NWU Actuarial Exemption Policy B5

ACTUARIAL TRAINING ROADMAP 2011

B1Version: September 2010

Practical Risk Management SAS RD (a)Industry Integration Project (a)Enterprise-wide Risk Management (F106/ST9) (a) (b)Finance and Investment (F105/ST5) (a)Industry Directed Research Project (b)

B.Sc. M.Sc. : NxxxPActuarial Science

Year 5

Year 2

Year 3

Year 1

Accounting (a) (b)Financial Mathematics (b)Economics (a)Micro-and Macro Economics (b)Statistics (a) (b)Introductory to Computers and Programming (a)Graphical Interface programming I (b)Algebra and Analysis (a) (b)Business Management (a)

Financial Mathematics (A201/CT1) (a) (b)Models: Survival Models and Stochastic Processes (A202/CT4) (a)Actuarial Statistical Models (A204/CT6) (a) (b)Capital Markets Modelling and Analysis (b)Statistical Inference (a)Linear Models (b)Statistics Project (b)

B.Sc. (Act) : N137PActuarial Science

Financial Engineering I II (a) (b)Investment Theory I (a)Contingencies (A203/CT5) I II (a) (b)Models: Survival Models and Stochastic Processes (A202/CT4) (a)Actuarial Risk Management (A301/CA1) (a) (b)

B.Sc. Hons. : N609PActuarial Science

Year 4

2012

Modern Portfolio Theory (A205/CT8) (b)Financial Mathematics (A201/CT1) (a) (b)Macro Economics (a)Financial Management (a)Probability Theory (a)Sampling Theory and Statistical Inference (b)Numerical Analysis (b)Analysis III (a)Linear Algebra I II (a) (b)

Version: September 2010 B2

UNDERGRADUATE CURRICULUMS:

Curriculum N137P: Actuarial Science (A-Leg)


YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 First semester First semester First semester Module code Core Cr Module code Core Cr Module code Core Cr WISN111 X 12 WISN211 X 8 BWIA311 H 24 STTN111 H 12 WISN212 X 8 BWIA312 H 16 ITRW112 X 12 STTK211 H 16 STTN311 H 32 ECON111 H 12 ECON211 H 16 ACCF111 or ACCC111

H 16 FINM211 H 16

BMAN111 H 12 WVES311 X 12 Total 1st semester



72

YEAR LEVEL 1 YEAR LEVEL 2 YEAR LEVEL 3 Second semester Second semester Second semester Module code Core Cr Module code Core Cr Module code Core Cr BWIN123 H 12 WISN222 X 8 BWIA321 H 16 WISN121 X 12 STTN221 H 16 STTK321 H 24 STTN121 H 12 TGWN222 X 8 STTK322 H 8 ITRW123 X 12 BWIA221 H 16 BWIN321 H 16 ECON121 H 12 WVES221 X 12 ACCC121

H 16

AGLA121 or AGLE121

X 12

Total 2nd semester



64




168





POST GRADUATE HONS CURRICULUMS:

Curriculum N609P: Actuarial Science (after B.Sc. N137P) (A-Leg)


This curriculum is compiled from the following modules:


First semester



BWIA612 Models: Survival Models and Stochastic Processes (A202/CT4)

24

Second semester


Year Module

BWIA672 Actuarial Risk Management (A301/CA1) 56

BWIA673 Contingencies (A203/CT5) 32

Total number of credits of this curriculum 160

The integrated assessment of this curriculum takes place during the assessment of the modules BWIN623.


POST GRADUATE MSc CURRICULUMS:

Curriculum NxxxP: BMI [Actuarial Science] (after Hons. B.Sc. N609P) (A-Leg)

Qualification code: xxxxxx

**Still waiting for approval of the HEQC



First semester



BWIA812 Enterprise-wide Risk Management I 24

BWIA813 Finance and Investment (F105/ST5) 24

Elective Module# (BWIN611) 16

Second semester


BWIA821 Enterprise-wide Risk Management II 16

Total credits 208

# The elective module in the first semester is chosen from the modules in the following table.





BWIN813 Practical Data Mining: SAS EM 16

BWIN818 Topical research issues in risk analysis 16


The integrated assessment of this curriculum takes place during the assessment of the module BWIN826.


POTCHEFSTROOM CAMPUS

Private Bag X6001, Potchefstroom, South Africa, 2520 Tel: (018) 299-1111 • Fax: (018) 299-2799

Internet: http://www.nwu.ac.za

B5

Dear Actuarial Student Actuarial Information 2011

We would like to bring following under you attention: 1. Actuarial Society of South Africa (AS) and Institute and Faculty of Actuaries (IFA) exemption

recognition agreements The University has exemption recognition agreements with AS and the IFA. With these agreements the University may recommend a student for exemption from the AS Foundation and Intermediate Technical subjects A101-A103 and A201-A205 and the IFA Core Technical subjects CT1 to CT8 if the student performs well in the relevant subjects. In the post graduate programme the University offers education for subjects A301/CA1, F105/ST5 and F106/ST9. Note that the University does not offer exemption for these subjects. You can however write these subjects at AS or the IFA the year following your graduation at the University (see attached table).

2. Examination policy For specified subjects (see attached table) in the actuarial curriculum, students may only make use of the first examination opportunity, in order to be eligible for exemption recommendation. All students may write the second exam to improve their marks for degree purposes. Students who do not qualify for exemption or for some reason cannot write the first exam (e.g. due to sickness) have two choices.

Rewrite the exam of AS or the IFA. Reregister for the module.

Note that re-registration will only be allowed if the student is registered for a degree. Re-registration for non-degree purposes will not be allowed. For non-specified subjects (see attached table), students may take advantage of any of the two examination opportunities. This policy is in accordance with the guidelines of AS (Actuarial Society of South Africa).

3. Exemptions and external examination You can be recommended for exemption for a non-specified subject by the University if you receive an annual average mark of above 60% for the specific university modules covering the subject with a sub-minimum of 55% an 60% applied to certain university modules. The non-specified subjects are A103/CT2, A101/CT3 and A102/CT7 (see attached table). You can be recommended for exemption for a specified subject by the University if you receive a mark above what is specified by the external examiner for the specific university modules covering the subject. The non-specified subjects are A201/CT1, A202/CT4, A203/CT5, A204/CT6 and A205/CT8 (see attached table). As soon as you complete your degree the University will send recommendation letters to AS and the IFA.

4. ActEd study material The following subjects make use of the ActEd study material prescribed by the IFA: A201/CT1, A202/CT4, A203/CT5, A204/CT6 an, A205/CT8, A301/CA1, F105/ST5 and F106/ST9. AS and IFA require that students purchase these course notes. Students can order these course notes through the university. The course notes are ordered by the University at the beginning of the year and are sold to the students. The price of the notes will be given to the students as soon as it is set, since the notes are purchased in Pounds.

CENTRE FOR BUSINESS MATHEMATICS AND INFORMATICS Tel: +27 18 299-2575 Fax: +27 18 299-2584 E-mail: [email protected]



B6

Actuarial Exemptions 2011

AS IFA Name of Module Modules B.Sc. N137P

Hons. B.Sc. N609P

Specified / Unspecified

Exemption Recommendation

A201 CT1 Financial Mathematics BWIA271 x Specified Determined by external examiner A103 CT2 Finance and Financial

Reporting ACCC121 x Unspecified 60% minimum

FINM211 60% minimum A101 CT3 Probability and

Mathematical Statistics STTN111 STTN121 x Unspecified minimum 60% average for STTN111 and STTN121 with

minimum 55% per module STTK211 STTN221 minimum 60% average for STTK211 and STTN221 with

minimum 55% per module STTN311 60% minimum

A202 CT4 Models: Survival Models and Stochastic Processes

BWIA311 BWIA612 x x Specified BWIA311 and BWIA612 students in 2011 will write the same examination for exemption purposes

A203 CT5 Contingencies BWIA673 x Specified Determined by external examiner A204 CT6 Actuarial Statistical Models BWIA312 BWIA321 x x Specified Determined by external examiner A102 CT7 Economics ECON111 ECON121 x Unspecified minimum 60% average for ECON111 and ECON121 with

minimum 55% per module ECON211 60% minimum

A205 CT8 Financial Engineering I, Investment Theory I/Modern Portfolio Theory

BWIN613 BWIN614/BWIA221

x x Specified Determined by external examiner

A301 CA1 Actuarial Risk Management BWIA672 x No

Exemption Awaiting feedback from 2010 application

F105 ST5 Finance and Investments BWIA813 M.Sc No Exemption

Awaiting feedback from 2010 application

F106 ST9 Enterprise-wide Risk Management I/II

BWIA812 BWIA821 M.Sc No Exemption

Awaiting feedback from 2010 application



B7

Actuarial Exemptions 2010

IFA AS Name of Module Modules B.Sc. N137P

Hons. B.Sc. N609P

Specified / Unspecified

Exemption Recommendation

CT1 A201 Financial Mathematics BWIN313 x Specified Determined by external examiner CT2 A103 Finance and Financial

Reporting ACCF211 ACCF221 x Unspecified minimum 60% average for ACCF211 and ACCF221 with

minimum 55% per module FINM211 60% minimum

CT3 A101 Probability and Mathematical Statistics

STTN111 STTN121 x Unspecified minimum 60% average for STTN111 and STTN121 with minimum 55% per module

STTK211 STTN221 minimum 60% average for STTK211 and STTN221 with minimum 55% per module

STTN311 60% minimum CT4 A202 Models STTK615 STTK616 x Specified Determined by external examiner CT5 A203 Contingencies BWIA611 BWIA621 x Specified Determined by external examiner CT6 A204 Statistical Methods BWIN324 STTK622 x Specified Determined by external examiner CT7 A102 Economics ECON111 ECON121 x Unspecified minimum 60% average for ECON111 and ECON121 with

minimum 55% per module ECON211 60% minimum

CT8 A205 Financial Economics BWIN613 BWIN614 x Specified Determined by external examiner

CA1 A301 Actuarial Risk Management BWIN629 BWIN627 x No Exemption

Application in 2010

ST5 F105 Finance and investments BWIN628 x No Exemption

Application in 2010

ST9 Enterprise risk management BWIA811 BWIA821 M.Sc No Exemption

Application in 2010

Version: September 2010 C1

APPENDIX C: SYLLABI FOR THE B.Sc. PROGRAMMES

2011 LIST OF MODULES ACADEMIC LITERACY

AGLE111 AGLE121 WVES221 WVES311

BUSINESS MANAGEMENT BMAN111

BUSINESS MATHEMATICS BWIN123 BWIN321 BWIA221 BWIA271 BWIA311 BWIA312 BWIA321

ECONOMICS, RISK MANAGENT AND INTERNATIONAL TRADE

ECON111 ECON121 ECON211 EKRP211 EKRP311 EKRP321

FINANCIAL ACCOUNTANCY

ACCS111 ACCS121 ACCF111 ACCF121 ACCC111 ACCC121 FINM211


COMPUTER SCIENCE AND INFORMATION SYSTEMS

ITRW112 ITRW123 ITRW124 ITRW212 ITRW214 ITRW222 ITRW311 ITRW321

STATISTICS AND OPERATIONAL RESEARCH

STTN111 STTN121 STTK211 STTN221 STTN311 STTK321 STTK322

APPLIED MATHEMATICS

TGWN222 MATHEMATICS

WISN111 WISN121 WISN211 WISN212 WISN221 WISN222 WISN311 WISN321

NOTE: In some instances titles of textbooks related to course syllabi are indicated. The purpose thereof is to give prospective learners an indication of the type of textbooks that can be used for the course. These are not necessarily the prescribed textbooks. Before the start of the relevant course learners should confirm with the lecturer concerned which textbooks(s) is (are) prescribed.


ACADEMIC LITERACY AGLE111 Module code: AGLE111 Semester 1 NQF: 5 Title: Introduction to Academic Literacy Module outcomes: On completion of this module the student should be able to demonstrate basic knowledge of learning strategies, academic vocabulary and register as well as the reading and writing of academic texts in order to function effectively in the academic environment; communicate effectively orally and in writing in an appropriate manner in an academic environment; understand, interpret, and evaluate basic academic texts and write appropriate academic genres in a coherent manner by making use of accurate and appropriate academic conventions; listen, speak, read and write accurately, fluently and appropriately in an ethical framework.

Method of delivery: Full-time Assessment methods: Tests and assignments — weight: 60% Semester exam 1x2 hours — weight: 40% AGLE121 Module code: AGLE121 Semester 2 NQF: 5 Title: Academic Literacy Module outcomes: On completion of this module, students should be able to demonstrate fundamental knowledge of appropriate computer programs, as well as apply learning, listening, reading and writing strategies, use academic language register and read and write academic texts, in order to function effectively in the academic environment; as an individual and a member of a group communicate effectively orally and in writing in an ethically responsible and acceptable manner in an academic environment; as an individual and a member of a group find and collect scientific knowledge in a variety of study fields, analyse, interpret, and evaluate texts, and in a coherent manner synthesise and propose solutions in appropriate academic genres by making use of linguistic conventions used in formal language registers. Method of delivery: Full-time Assessment methods: Tests and assignments — weight: 60% Semester exam 1x2 hours — weight: 40%


WVES221 Module code: WVES221 Semester 2 Title: Understanding the economic world Module outcomes: Upon completion of this module, you should be able to: have a fundamental knowledge base of a selection of world views and ideologies; demonstrate their critical understanding through an ability to compare the nature and function, as well as different contemporary manifestations of these world views and ideologies; have the ability to understand the interrelatedness of phenomena such as occurs in natural and social systems, and from this vantage point, analyse and evaluate real life problems or case studies based on core issues of our time, such as poverty, constant change, human rights, HIV-AIDS, power abuse, corruption, racism, xenophobia, etc.; be able to articulate their personal world view and use it as a point of departure for arguing and communicating feasible solutions to core issues and problems of our time in a typical academic manner.

WVES311 Module code: WVES311 Semester 1 Title: Business ethics Module outcomes: After completion of this module you should: Possess knowledge of o selected ethical theories o moral decision-making strategies o selected socio-economic ethical issues o selected issues and approaches with regard to business ethics o the nature of organizations and management from an ethical perspective Possess the ability and skills to apply the above knowledge to case studies Possess the ability and skills to analyse and evaluate the abovementioned theories and issues from different philosophical and ideological perspectives.

BUSINESS MANAGEMENT BMAN111 Module code: BMAN111 Semester 1 Title: Introduction to business management Module outcomes: Upon completion of this module, you should be able to demonstrate: a complete and systematic knowledge of the nature of business management,establishment issues of a new business, the different business functions and the basic elements of a business plan; skills, based upon an informed comprehension of theories and concepts, to identify established issues of a new business, identify the different business functions and to draw up a basic SWOT analysis and business plan; and the ability to undertake a literature and environmental review, prepare a basic report as individual or as a member of a team and to communicate in writing as well as verbally he report to an audience.


BUSINESS MATHEMATICS BWIN123

Module code: BWIN123 Semester 2

Title: BMI Project: Financial Mathematics Module outcomes: At the end of this module, the student will have acquired knowledge and insight into the calculation of interests, time value of money, present and future values, nominal and effective interest rates and annuities and loans. The concepts are presented in the form of a self-created project. In this module, the student acquires skills to handle vaguely defined problems and to integrate concepts from the financial-economic world that can be quantified with the aid of mathematical models and solved by means of computer spreadsheet-based implementation. Specific attention is given to playing off simulation versus the analytical, as well as to discrete versus stochastic modelling of such problems.

BWIN321

Module code: BWIN321 Semester 2

Title: BMI Project: Capital Markets Modelling and Analysis Module outcomes: After completion of the module the student should: demonstrate a well-rounded and systematic knowledge and coherent and critical understanding

of and insight into the mathematical modelling and analysis of financial instruments; be able to derive and apply mathematical formulas to price and hedge linear claims such as

futures contracts and swaps as well as derive and apply binomial pricing of options; be able to use the MS Excel software package (or SAS/IML) to practically implement basic

numerical procedures to price vanilla options using binomial trees; as an individual or as a member of a group demonstrate the ability to plan and conduct research

according to standard protocol and to employ appropriate processes, procedures and techniques to solve problems in the field of capital markets modelling and analyses, communicate results effectively, orally and in writing, and to make use of appropriate technologies in all communications. Act ethically sound in dealing with issues and people.

BWIA221

Module code: BWIA221 Semester 2

Title: Modern Portfolio Theory (A205/CT8) Module outcomes: On completion of the module the student will demonstrate a sound knowledge and understanding of:

(i) the meaning of the term “utility function”. (ii) the advantages and disadvantages of different measures of investment risk. (iii) the assumptions of mean-variance portfolio theory and its principal results. (iv) the properties of single and multifactor models of asset returns. (v) asset pricing models through discussing the principal results and assumptions and

limitations of such models. (vi) the various forms of the Efficient Markets Hypothesis and discuss the evidence for and

against the hypothesis.


The student will also as an individual or as a member of a group demonstrate the ability to: (a) solve well-defined but unfamiliar problems using correct procedures and appropriate

evidence (b) perform a critical analysis and synthesis of information (c) present information using basic information technology (d) present and communicate information reliably and coherently, using

academic/professional discourse conventions and formats appropriately through integrated assessment of objectives (i) to (vi) in the form of project(s).

BWIA271

Module code: BWIA271 Year module

Title: Financial Mathematics (A201/CT1)

Module outcomes: On completion of the module the student will demonstrate a sound knowledge and understanding of:

(i) using a generalised cashflow model to describe financial transactions. (ii) taking into account the time value of money using the concepts of compound interest

and discounting. (iii) showing how interest rates or discount rates may be expressed in terms of different

time periods. (iv) real and money interest rates. (v) calculating the present value and the accumulated value of a stream of equal or

unequal payments using specified rates of interest and the net present value at a real rate of interest, assuming a constant rate of inflation.

(vi) the definitions and use of more important compound interest functions including annuities certain.

(vii) the definition of an equation of value. (viii) describing how a loan may be repaid by regular instalments of interest and capital. (ix) using discounted cashflow techniques in investment project appraisal. (x) describing the investment and risk characteristics of the following types of asset

available for investment purposes: (a) fixed interest government borrowings (b) fixed interest borrowing by other bodies (c) shares and other equity-type finance (d) derivatives

(xi) analysing elementary compound interest problems. (xii) calculating the delivery price and the value of a forward contract using arbitrage free

pricing methods. (xiii) the term structure of interest rates. (xiv) simple stochastic models for investment returns.

The student will also as an individual or as a member of a group demonstrate the ability to:

(a) solve well-defined but unfamiliar problems using correct procedures and appropriate evidence

(b) perform a critical analysis and synthesis of information (c) present information using basic information technology (d) present and communicate information reliably and coherently, using

academic/professional discourse conventions and formats appropriately through integrated assessment of objectives (i) to (xiv) in the form of project(s).


BWIA311

Module code: BWIA311 Semester 1 Title: Models: Survival Models and Stochastic Processes (A202/CT4) Module outcomes: On completion of the module the student will demonstrate a well-rounded and systematic knowledge and coherent and critical understanding of:

(i) the principles of actuarial modelling. (ii) the general principles of stochastic processes, and their classification into different

types. (iii) the definition and application of a Markov chain. (iv) the definition and application of a Markov process. (v) the concept of survival models. (vi) the estimation procedures for lifetime distributions. (vii) the derivation of maximum likelihood estimators for the transition intensities in models

of transfers between states with piecewise constant transition intensities. (viii) the Binomial model of mortality inclusive of the derivation of a maximum likelihood

estimator for the probability of death and the comparison of the Binomial model with the multiple state models.

(ix) how to estimate transition intensities depending on age, exactly or using the census approximation.

(x) how to test crude estimates for consistency with a standard table or a set of graduated estimates.

(xi) the process of graduation. The student will also as an individual or as a member of a group demonstrate the ability to:

(a) deal with unfamiliar concrete and abstract problems and issues using evidence-based solutions and theory-driven arguments

(b) use well-developed information retrieval skills (c) perform a critical analysis and synthesis of quantitative and/or qualitative data (d) use appropriate IT skills to present results using prescribed formats (e) present and communicate information and their own ideas and opinions in well-

structured arguments (f) show an awareness of audience and using academic/professional discourse

appropriately through integrated assessment of objectives (i) to (xi) in the form of project(s).

BWIA312

Module code: BWIA312 Semester 1 Title: Actuarial Statistical Models (A204/CT6) Module outcomes: On completion of the module the student will demonstrate a well-rounded and systematic knowledge and coherent and critical understanding of:

(i) the concepts of decision theory and the application of them. (ii) the calculation of probabilities and moments of loss distributions both with and without

limits and risk-sharing arrangements. (iii) the construction of risk models involving frequency and severity distributions and the

calculation of the moment generating function and the moments for the risk models both with and without simple reinsurance arrangements.

(iv) the concept of ruin for a risk model. This will include the calculation of the adjustment coefficient and being able to state Lundberg’s inequality. This also include the effect on the probability of ruin of changing parameter values and of simple reinsurance arrangements.

(v) the fundamental concepts of Bayesian statistics and using these concepts to calculate Bayesian estimators.

(vi) techniques for analysing a delay (or run-off) triangle and projecting the ultimate


position through applying the techniques.

(vii) the fundamental concepts of a generalised linear model (GLM) and describing how a GLM may be applied.

The student will also as an individual or as a member of a group demonstrate the ability to:

(a) deal with unfamiliar concrete and abstract problems and issues using evidence-based solutions and theory-driven arguments

(b) use well-developed information retrieval skills (c) perform a critical analysis and synthesis of quantitative and/or qualitative data (d) use appropriate IT skills to present results using prescribed formats (e) present and communicate information and their own ideas and opinions in well-


appropriately through integrated assessment of objectives (i) to (vii) in the form of project(s).

BWIA321

Module code: BWIA321 Semester 2 Title: Actuarial Statistical Models: Time Series (A204/CT6) Module outcomes: On completion of the module the student will demonstrate a well-rounded and systematic knowledge and coherent and critical understanding of:

(i) the concept and general properties of stationary, I(0), and integrated, I(1), univariate time series.

(ii) the concept of a stationary random series. (iii) the concept of a filter applied to a stationary random series. (iv) the notation for backwards shift operator, backwards difference operator, and the

concept of roots of the characteristic equation of time series. (v) the concepts and basic properties of autoregressive (AR), moving average (MA),

autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) time series.

(vi) the concept and properties of discrete random walks and random walks with normally distributed increments, both with and without drift.

(vii) the basic concept of a multivariate autoregressive model. (viii) the concept of cointegrated time series. (ix) certain univariate time series models having the Markov property and how to

rearrange a univariate time series model as a multivariate Markov model. (x) the processes of identification, estimation and diagnosis of a time series, the criteria

for choosing between models and the diagnostic tests that might be applied to the residuals of a time series after estimation.

(xi) other non-stationary, non-linear time series models. (xii) simple applications of a time series model, including random walk, autoregressive and

cointegrated models as applied to investment variables. (xiii) the development of deterministic forecasts from time series data, using simple

extrapolation and moving average models, applying smoothing techniques and seasonal adjustment when appropriate.

(xiv) the concepts of “Monte Carlo” simulation using a series of pseudorandom numbers.


The student will also as an individual or as a member of a group demonstrate the ability to: (a) deal with unfamiliar concrete and abstract problems and issues using evidence-based

solutions and theory-driven arguments (b) use well-developed information retrieval skills (c) perform a critical analysis and synthesis of quantitative and/or qualitative data (d) use appropriate IT skills to present results using prescribed formats (e) present and communicate information and their own ideas and opinions in well-


appropriately through integrated assessment of objectives (i) to (xiv) in the form of project(s).

ECONOMICS, RISK MANAGENT AND INTERNATIONAL TRADE ECON111

Module code: ECON111 Semester 1

Title: Introduction to Economics Module outcomes: On completing this module you should: be able to demonstrate fundamental knowledge and insight into the basic functioning of the

economy and its different components, the economic problem of scarcity, limited resources and unlimited needs, the way in which the different economic systems try to solve this problem and the ways in which fiscal, monetary and other policy measures are applied to reach specific economic objectives;

have skills as an individual and/or as a member of a group to interpret and analyse the behaviour of the most important economic agents, such as consumers and producers;

have skills as an individual and as a member of a group to interpret and analyse the economic data of the fiscal, monetary and other types of policy in South Africa;

have the ability to identify, evaluate and solve clear-cut routines and new economic problems (such as unemployment and high inflation rates) in the South African context by means of proven methods, procedures and techniques;

have the ability to collect information from given sources, to select information suitable to the task, to analyse, synthesise and evaluate that information, and to communicate the results and/or proposals in an ethically healthy manner in writing and in an oral demonstration by means of appropriate information technology.


ECON121

Module code: ECON121 Semester 2 Title: Basic Micro- and Macroeconomics Module outcomes: On completing this module you should be able to demonstrate: fundamental knowledge and insight into the principles and theories on which microeconomics,

macroeconomics and the Simple Macroeconomic Model are based and also have the ability to apply concepts and terminology in answering well-defined problems and case studies;

fundamental knowledge of the interaction between and interdependence of economic participants and economic indicators;

skills to analyse and evaluate case studies, examples and problems of certain macro- and microeconomic phenomena, with reference to demand, supply, equilibrium, consumption, production, price elasticity and various forms of competition;

fundamental understanding of the causes of inflation, unemployment and economic growth and knowledge to recommend policies in this regard;

skills to apply the Simple Macroeconomic Model in economic analyses and predictions; information gathering and processing skills for writing assignments within the context of micro-

and macroeconomics, individually and in groups;

ECON211

Module code: ECON211 Semester 1 Title: Macroeconomics Module outcomes: On completing this module you should be able: to analyse the interrelationships in macroeconomics between different economic variables in

an open economy; to evaluate the effect of various policy steps on the functioning of the economy in the long and

short run; to identify different policy measures to identify macroeconomic problems; to explain how these measures may be applied.

EKRP211

Module code: EKRP211 Semester 1 NQF level: 5 b (6) Title: Introduction to risk management Module outcomes: After completion of this module, the student should be able to: demonstrate a clear understanding of what risk entails and how to manage risk strategically in

a corporate environment in South Africa; explain why risk management plays an important role in the business environment; identify and distinguish between various types of risks; demonstrate both theoretical knowledge and practical application of the risk management

process, i.e. the identification, evaluation and control of risk in a variety of scenarios; and demonstrate a clear understanding of the various forms of risk financing strategies, the cost

associated with the different strategies and the appropriateness thereof for different risks.


EKRP311

Module code: EKRP311 Semester 1

Title: Bank Risk Management Module outcomes: On completing this module you should be able: to demonstrate a sound and systematic knowledge and understanding of how the Assets and

Liabilities Committee (ALCO) manage their assets and liabilities to address banking risks, the role that the management of these financial assets and liabilities play in the South African economy, as well as to address the financial and other related risks in a financial institution;

to demonstrate well developed skills to solve problems by strategic management of the process of minimising financial risks; of maximising the interest income and equity of financial institutions, and show thorough understanding of the regulatory environment in which banks operate;

to use individual and group methods to communicate information effectively, coherently and in appropriate format.

EKRP321

Module code: EKRP321 Semester 2

Title: Financial Markets Module outcomes: On completing this module you should be able: to demonstrate a well-rounded and systematic knowledge and understanding of the

mechanics of the South African Money and Capital Markets, including SAFEX and the Bond Exchange (the Johannesburg Stock Exchange and shares were covered in EKRP211), and demonstrate an understanding of and the ability to use the mechanics of the products and instruments, including derivatives used in these markets and the regulatory environment;

to demonstrate the ability to work as an analyst, a market dealer, stock broker and back office official in the banking and treasury environment;

in unfamiliar concrete and abstract scenarios, to apply basic portfolio management using the products and instruments of the above mentioned markets;

to work in groups and/or as an individual and to communicate information effectively in an ethically sound manner, using appropriate information technology.

FINANCIAL ACCOUNTANCY ACCS111

Module code: ACCS111 Semester 2

Title: Financial Accounting (Special) – Basic Concepts, Accounting Cycle and Accounting Systems Module outcomes: On completing the module the student should be able: to explain the purpose and function of accounting; to record transactions in journals, ledger accounts and control accounts; to design an accounting system for a specific enterprise; to compile financial statements for a sole proprietor of an enterprise.


ACCS121

Module code: ACCS121 Semester 2 Title: Financial Accounting (Special) – Bank Reconciliation, Elementary Financial Reporting and Analysis and Interpretation of Financial StatementsModule outcomes: On completing the module the student should be able: to record transactions in the cash receipts and payment journal and to compile a bank

reconciliation statement; to compile the statement of comprehensive income (income statement), statement of financial

position (balance sheet) and statement of change in equity for a sole trader in a generally accepted format;

to identify financial ratios and to be able to explain and apply their purpose in analysing and interpreting the liquidity, profitability and solvency of a sole trader.

ACCF111

Module code: ACCF111 Semester 2 Title: Financial Accounting – Basic Concepts, Accounting Systems and Elementary Financial Reporting Module outcomes: On completing the module the student should be able: to explain the purpose and function of accounting; to demonstrate a clear insight into the accounting equation; to compile journals, ledgers, subsidiary ledgers and control account to design a accounting system that will comply with the requirements of a specific entity; to prepare bank reconciliations; to calculate claims against insurers for inventory losses; to record transactions and compile financial statements for sole traders and departmental

accounts. ACCF121

Module code: ACCF121 Semester 2 Title: Financial Accounting – Elementary Financial Reporting, Partnerships, Close Corporations and Companies Module outcomes: On completing the module the student should be able: to record transactions in the accounting records; to record transactions in the statement of receipt and payments; to compile a statement of comprehensive income (income statement) and a statement of the

financial position (balance sheet) for non-trading enterprises; to compile annual financial statements of partnerships and to compile annual financial

statements for close corporations according to the requirements of Generally Accepted Accountancy Practice (GAAP);

to demonstrate a clear insight into the different types of company shares, record transactions for issuing and redeeming shares and compile elementary financial statements for companies.


ACCC111

Module code: ACCC111 Semester 1 Title: Framework, foundations, cycle and financial reporting Module outcomes: On completion of the module, the student should be able to: demonstrate a basic knowledge of the principles of the accounting cycle, including the

recording of transactions and adjustments from source documents in the subsidiary journals/ledgers and general ledger of an entity;

understand the accounting framework and the basic elements of financial statements, including their recognition and measurement criteria;

prepare a set of basic financial statements, in the correct format, based on the information in a trial balance or general ledger, including basic disclosure in the notes to the financial statements; and record transactions incurred by clubs and other non-profit enterprises in the subsidiary ledgers, general ledger and financial statements.

ACCC121

Module code: ACCC121 Semester 2 Title: Accounting for different entities Module outcomes: On completion of the module, the student should be able to: apply the definitions, recognition and measurement criteria of the different elements of

financial statements, as well as the principles regarding the presentation of financial statements to a given situation;

distinguish between different entity forms, including sole proprietors, partnerships, companies and closed corporations, and account for transactions in the records of each of these entity forms;

effectively use information technology in the recording of transactions in the records of an entity; and effectively work together with others as part of a team or group.


FINM211

Module code: FINM211 Semester 2 Title: Financial Management Module outcomes: On completing this module you should be able: Understand the role of financial management and the financial manager in a business

organisation and identify the primary goal of financial management Understand the concept of the time value of money and perform calculations Understand the relationship between risk and return and evaluate the risk and return of

organisations based on the necessary calculations. Understand the basic accounting statements and concepts and perform an evaluation of

financial performance, using financial statement analysis to assess the current financial condition of the firm.

Demonstrate a knowledge of the characteristics of the principle forms of finance used by companies and the ways in which they may be issued

Demonstrate a basic knowledge of the characteristics of financial instruments and how they can be applied by companies to hedge against risk.

Demonstrate a complete and systematic knowledge of the factors to be considered by a company when deciding on its capital structure

Demonstrate the skills to calculate the cost of the different sources of finance and the weighted average cost of capital of a company.

Understand and apply the various techniques in evaluating capital investment projects. COMPUTER SCIENCE AND INFORMATION SYSTEMS ITRW112

Module code: ITRW112 Semester 1 Title: Introduction to Computers and Programming Module outcomes: On completing this module, the students should be able to demonstrate fundamental knowledge of the different components of a computer and an information system, as well as programming languages and their uses. Furthermore, the student should be able to demonstrate the manipulation of spreadsheets by applying knowledge of tables, computations, transfer of data between different applications, functions and graphic presentations; to demonstrate the ability to solve problems by designing and implementing structured programming, by using data manipulation and data presentations and applying ‘GUI’ event-driven approaches in the development environment of a spreadsheet; to demonstrate insight into ethical issues related to the wider IT business and an awareness of the risks and dangers that threaten the business; to demonstrate the ability to communicate in writing by compiling a report after having completed a project.


ITRW123

Module code: ITRW123 Semester 2 Title: Graphic Interface Programming I Module outcomes: On completing the module, the student should demonstrate knowledge to be able to write a computer program that requires certain fundamental theoretical prescience have been mastered; demonstrate the ability to solve simple problems by applying fundamental theoretical prescience; demonstrate sufficient fundamental knowledge of and insight into the graphic interface environment to develop computerised systems in a visual object-based computer language; demonstrate the ability to implement repetitive, conditional and sequential structures, as well as aspects like graphic interface design, event-driven programming, procedural and object-based programming.

ITRW124

Module code: ITRW124 Semester 2 Title: Programming I Module outcomes: On completing this module the student should be able to demonstrate fundamental knowledge of the basic structures, data types, methods, classes and objects of an object-based programming language, and their use; to demonstrate the ability to solve unknown problems by designing and implementing object-based programming, debugging, testing and carrying out applications; to demonstrate insight into ethical issues that are related to the wider IT business and to be aware of the risks and dangers that threaten the business.

ITRW212

Module code: ITRW212 Semester 1 Title: Programming II Module outcomes: On completing this module students should have the ability to demonstrate an in-depth knowledge of search, sorting and recursive methods, as well as the use of an object-based programming language and concepts to solve basic problems; to apply in-depth knowledge of other numeric systems, like the binary numeric system, in order to carry out basic computations; to demonstrate skills in solving problems that require file management and exception handling by means of an object-based programming language; to demonstrate the ability to identify, analyse and solve problems by writing a structured, object-based program.

ITRW214

Module code: ITRW214 Semester 1 Title: Decision support systems I Module outcomes: At the end of this module the student ought to have acquired basic knowledge and insight into: decision-making, construction of decision-making systems, formulating simple linear models (break-even analysis, linear programming) and their solution with the aid of spreadsheets;carrying out sensitivity analysis and solving specific problems (transportation and assignment problems and networks). The above techniques will be used in modelling and solving simple operational problems.


ITRW222

Module code: ITRW222 Semester 2 Title: Data Structures and Algorithms Module outcomes: On completing this module successfully, students should be able to demonstrate in-depth knowledge and understanding of data structures (vectors, matrices, switched lists, stacks and queues) and the complexity of algorithms by setting up and manipulating data structures, to use object-orientated methods to create abstract data types for the above mentioned data structures and to solve different data handling problems.

ITRW311

Module code: ITRW311 Semester 1 Title: Databases I Module outcomes: On completing the module, the student should be able to demonstrate well-rounded and systematic knowledge and insight into entity relationship modelling; normalising of database tables and the ability to write and apply SQL and PL/SQL expressions and procedures in designing databases and retrieving information in order to solve unfamiliar concrete and abstract problems in the database environment.

ITRW321

Module code: ITRW321 Semester 2 Title: Databases II Module outcomes: On completing this module, the student should have a well-rounded and systematic knowledge and insight into transaction management; should have the ability to apply control of simultaneous use, distributed database management systems and database administration to the administration of databases in order to solve, as an individual and as a member of a group, unfamiliar concrete and abstract computer problems in the database environment.

STATISTICS AND OPERATIONAL RESEARCH STTN111

Module code: STTN111 Semester 1 Title: Descriptive Statistics Module outcomes: A student who has completed this module should be able to demonstrate the following knowledge: Fundamental knowledge of the most important elementary statistical techniques used every day, such as sampling methods, determining sample size, graphical representation of data, descriptive measures of locality and scattering, least squares line fitting, predictions by means of least squares line fitting, correlation coefficients, time series data and movement components in order to predict future outcomes, practical considerations with regard to questionnaires and sampling sizes; fundamental knowledge of probabilities and probability distributions, the central limit theorem, for large sample sizes the estimation of population parameters by means of point and interval estimation, to demonstrate problem solving skills by solving familiar and unfamiliar problems; to implement the acquired knowledge to problems involving the above-mentioned skills and techniques.


STTN121

Module code: STTN121 Semester 2 Title: Introductory Statistical Inference Module outcomes: A student who has completed this module should be able to demonstrate the following: Fundamental knowledge of probabilities and probability distributions, the central limit theorem, estimation of population parameters by means of point and interval estimation, hypothesis testing for population averages and proportions for one and two samples, one way analysis of variance (ANOVA) and categorical data analysis, contingency tables and basic tests on categorical data; problem solving skills by analyzing familiar and unfamiliar problems, using acquired knowledge to solve simple probability problems, applying the knowledge gained above on data where applicable.

STTK211

Module code: STTK211 Semester 1 Title: Probability Theory Module outcomes: On completing the module, the student should be able to demonstrate knowledge of the following: concepts, such as outcome space, events, probability measures, counting processes, stochastic outcomes of events and the independence of events; important probability theorems, such as the law of total probability and the theorem of Bayes; stochastic variables, distribution functions and mass functions. Special attention will be given to discrete stochastic variables and the following distributions will be discussed in depth: binomial, geometric, negative binomial, hypergeometric and Poisson distributions. The following continuous random variables, together with their distribution functions will be discussed in detail: exponential, gamma and normal distributions. Functions of these variables will also be discussed. Probability structures of two or more stochastic variables will be defined in the same outcome space and functions of joint distributions. The student should be able to demonstrate knowledge of conditional distributions and the ability to apply probability calculations to conditional distributions; to demonstrate knowledge of ordered statistics and the ability to apply it; to demonstrate knowledge of the expectation value of and standard deviation from all the important mass functions and density functions previously discussed; demonstrate knowledge of covariance and correlation of two stochastic variables, together with conditional expectation values and moment generating functions; to demonstrate knowledge of the first and second moment, two of the most important theorems in probability theory, namely the so-called law of large numbers and the central limit theorem.

STTN221

Module code: STTN221 Semester 2 Title: Sampling Theory and Statistical Inference Module outcomes: A student who has completed this module should be able to demonstrate fundamental knowledge of distributions derived from the normal distribution, several sampling methods and their properties, the method of moment estimation and the method of maximum likelihood estimation in order to estimate parameters, the efficiency of an estimator and sufficient statistics; to demonstrate problem solving skills in analysing familiar and unfamiliar problems, in using acquired knowledge to derive properties of distributions derived from the normal distribution, in estimating several parameters when different sampling methods have been applied, in estimating parameters by means of the method of moment estimation and maximum likelihood estimation, in determining whether a estimator is efficient and in finding sufficient statistics for a variety of problems; in applying these concepts to actual data.


STTN311

Module code: STTN311 Semester 1 Title: Statistical Inference Module outcomes: A student who has completed this module should demonstrate the following: fundamental knowledge of statistical concepts, such as complete and sufficient statistics, hypothesis testing, duality of confidence intervals and hypothesis testing, informal measure of fit techniques, methods of summarising data, measures of locality and scattering, comparison of two samplings, comparison of matched samplings, design of experiments, analysis of categorical data and Bayesian inference; should demonstrate the ability to construct complete and sufficient statistics, to use the Neyman-Pearson paradigm to perform hypothesis testing, to apply the relationship between hypothesis testing and confidence intervals in the context of estimation, to draw conclusions by using descriptive statistical methods, to apply methods of summarizing data, to calculate measures of locality and scattering, to implement methods to compare two samplings and matched samplings, to understand different designs of experiment, to analyze categorical data and to use Bayesian inference methods.

STTK321

Module code: STTK321 Semester 2 Title: Linear Models Module outcomes: A student having completed this module should be able to demonstrate an understanding of simple and multiple linear regression; understanding of the reasons for assumptions in the regression model and the derivation of the distributions of test statistics used in the inference that relates to linear regression models; to demonstrate the ability to derive the least squares and maximum acceptability parameters in a linear regression model; the ability to describe the linear regression model in matrix and vector notation; to demonstrate the ability to diagnose any deviation from the assumptions and to apply remedial measures to rectify the deviations. He/she should demonstrate an understanding of the concepts of simultaneous interference as applied in linear regression models; should demonstrate the ability to describe how qualitative and quantitative predictor variables are handled within the frame of linear regression. He/she should demonstrate an understanding of the fundamental concepts of non-linear regression; the ability to describe the process of estimating parameters in non-linear regression models; the ability to describe the following models: logistic regression models and Poisson regression models; an understanding of the way in which these models relate to the general linear model; the ability to perform inferences that are associated with these models; the ability to implement linear regression models using simple calculations and computer software; the ability to diagnose models practically by applying diagnostic steps as discussed in the theory and to apply remedial measures in a practical context; and the ability to implement non-linear regression models using simple calculations and computer software.


STTK322

Module code: STTK322 Semester 2 Title: Statistics Project Module outcomes: A student having completed this module should be able to demonstrate the ability to carry out a successful statistical project, from design to analysis; to identify appropriate models for a given data system and to use SAS or R to implement the appropriate model; to identify the previously learnt theory on basic statistical analysis with the practical nature of the project and to apply the techniques; to compile appropriate documentation for the project; to develop skills in oral presentation to present the project in a professional set-up; to demonstrate the necessary computer skills needed to handle statistical analysis by means of SAS and R, but also to handle a greater variety of problems; to carry out computer-based simulations with the aid of SAS and R.

APPLIED MATHEMATICS TGWN222

Module code: TGWN222 Semester 2 Title: Numerical Analysis Module outcomes: On completing this module the student should be able to do the following: demonstrate fundamental knowledge and insight into the theory of basic numerical methods for general occurring mathematical problems, amongst which are the solving of non-linear equations, determining interpolation polynomials and the numerical determining of definite integrals, demonstrate problem solving skills by solving non-linear equations through iteration techniques, determining the interpolation polynomials of Lagrange and Newton, determining definite integrals by means of the trapezium method, Simpson’s rule, Romberg integration and Gauss quadrature, and the computer application of these techniques, show a fondness for this field of study and demonstrate insight into the relation between reality and abstraction, model and solution; reveal a Christian or alternative perspective on the subject.

MATHEMATICS WISN111

Module code: WISN111 Semester 1 Title: Introductory Algebra and Analysis I Module outcomes: On completing this module, students should be able to do the following: demonstrate fundamental knowledge of the concept of functions, polynomials in one variable with factor theorem, remainder theorem and synthetic division, rational functions and partial fractions, absolute value function, circle measure and inverse functions, trigonometric and inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, exponential and logarithmic functions, limits, continuity, differentiability and indefinite integrals of all the above mentioned functions, complex numbers; demonstrate problem solving skills by analysing familiar and unfamiliar problems, using the knowledge of techniques to develop powers of first degree polynomials, calculating the limits, derivatives and indefinite integrals of all the above mentioned functions and performing simple operations with complex numbers.


WISN121

Module code: WISN121 Semester 2 Title: Introductory Algebra and Analysis II Module outcomes: On completing this module, students should be able to do the following: demonstrate fundamental knowledge of logic, the system of real numbers, mathematical induction, permutations and combinations and the binomial theorem, De Moivre’s theorem and its applications, L’Hospital’s rule and its applications, the fundamental theorems of differential and integral calculus, the use of derivatives in optimisation and curve sketching, basic concepts of power series and the basic theorems on the converging of series, Taylor series, the basic properties and applications of the definite integral, applications of integration to surfaces, lengths and volumes; demonstrate problem solving skills by analysing familiar and unfamiliar problems, using knowledge of techniques by applying logic to systems of numbers, proving theorems with mathematical induction, determining the number of arrangements and selections from a set, performing operations with complex numbers, judging convergence of power series, calculating Taylor series, determining limits using L’Hospital’s rule, sketching functions, formulating optimisation problems mathematically and using knowledge of derivatives to solve them, by determining definite integrals and calculating surfaces, lengths and volumes.

WISN211

Module code: WISN211 Semester 1 Title: Analysis III Module outcomes: On completing this module, students should be able to do the following: demonstrate a thorough knowledge and insight into al the aspects of the differential calculus of multivariate functions: partial and directional derivatives, the gradient function, optimisation problems, including Lagrange’s method, the theory of multiple integrals to calculate partial derivatives, directional derivatives and gradients, and double and triple integrals; demonstrate problem solving skills by analysing familiar and unfamiliar problems, using knowledge of techniques to solve practical problems modelled with multivariate functions. Students should demonstrate the ability to use the geometric and physical meaning of the above-mentioned concepts to abstract the underlying mathematical structure of applied problems and to interpret the significance of the mathematical solution.

WISN212

Module code: WISN212 Semester 1 Title: Linear Algebra I Module outcomes: On completing this module students should be able to do the following: demonstrate a thorough knowledge and insight into the solvability of systems of linear equations; the basic properties of Euclidic spaces and linear transformations, interdependency of general vector space concepts; demonstrate the ability to determine Eigen values and Eigen vectors; demonstrate problem solving skills by analysing familiar and unfamiliar problems, using knowledge of techniques to solve systems of linear equations in the context of a vector space; to perform matrix operations; to determine bases for subspaces; to calculate Eigen values and Eigen vectors; to execute these matrix calculations and interpret the results.


WISN221

Module code: WISN221 Semester 2 Title: Analysis IV Module outcomes: On completing this module, students should be able to do the following: demonstrate a thorough knowledge and insight into line integrals of scalar valued and vector valued functions of two and three variable functions; the fundamental theorem and Green’s theorem for line integrals and their applications; surface integrals of scalar valued and vector valued functions; the theorem of Stokes and the divergence theorem of Gauss and their applications; the theory of higher order linear differential equations and methods (of undetermined coefficients and the variation of parameters) to solve second order linear differential equations with constant coefficients; sequences and series of real numbers; tests for convergence (integral test, comparison test, limit comparison test) and tests for absolute convergence of series of real numbers (ratio and root tests); demonstrate problem solving skills by analysing familiar and unfamiliar problems; using knowledge of techniques to calculate line integrals of scalar valued and of vector valued functions and use them in solving practical problems (such as the calculation of surfaces and the calculation of word done by forces along curves); by calculating surface integrals of scalar valued and vector valued functions of two and three variables and use them to solve practical problems (such as calculating flow rates through surfaces); by using the Theorem of Stokes to calculate surface integrals by using line integrals along closed curves and vice versa; by using the theorem of Gauss to calculate surface integrals of vector fields over closed surfaces by evaluating triple integrals; by determining the solutions of homogeneous linear differential equations that have constant coefficients and by solving non-homogeneous linear equations using the methods of indeterminate coefficients and the variation of parameters; by using the different (relevant) tests for the convergence of series of real numbers to test for the convergence of these series.

WISN222

Module code: WISN222 Semester 2 Title: Linear Algebra II Module outcomes: On completing this module, students should be able to do the following: demonstrate a thorough knowledge and insight into general vector spaces and bases; inner products; vector norms; linear transformations. The student acquires knowledge and insight into matrix and vector norms and stepwise orthogonal transformations on a matrix; learn to execute LU factorising and to calculate certain systems of differential equations; demonstrate problem-solving skills by analysing familiar and unfamiliar problems; by using knowledge of techniques to determine inner products, vector norms and linear transformations.


WISN311

Module code: WISN311 Semester 1 Title: Real Analysis I Module outcomes: On completing this module, students should be able to do the following: demonstrate a rounded and systematic knowledge and insight into the theory of real numbers; the topology of vector spaces with finite dimensions; compactness and connectedness of sets; continuous and uniform continuous functions; continuous images of compact and connected sets; implicit functions and the implicit function theorem in three dimensions; convergence of sequences and Cauchy sequences; convergence and continuous convergence of sequences of functions; Riemann and abstract integration, sigma algebras and measurable spaces; general measurable and Borel measurable functions; measures on measurable spaces; integral and measurable functions; the monotone convergence theorem; Fatou’s lemma and Lebesgue’s convergence theorem; the relation between Riemann and Lebesgue integrals; the characterisation of Riemann integrable functions in terms of continuity; demonstrate problem solving skills as an individual and as member of a group by analysing familiar and unfamiliar analysis problems, by testing functions for continuity, by solving problems from integration theory and by applying abstract mathematical theorems and concepts in areas such as probability theory.

WISN321

Module code: WISN321 Semester 2 Title: Real Analysis II Module outcomes: On completing this module, students should be able to do the following: demonstrate a rounded and systematic knowledge and insight into the derivative of vector functions and of multivariate functions and applying them to determine differentials; the concept differentiability; the concept directional derivative and its application to solve familiar an unfamiliar problems in the field of real analysis. Students must also have a rounded knowledge of Taylor’s theorem and its applications; the general implicit function theorem; improper integrals and the calculation of integrals, as well as the theorems of Radon-Nikodym and Fubini and how to use them. Students must demonstrate skills to test for convergence by using improper integrals and infinite series; the ability to calculate the maxima and minima of multivariable functions; to apply various theorems from measure and integration theory in areas like probability theory, functional analysis and financial mathematics.

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APPENDIX D: SYLLABI FOR THE Hons. B.Sc. and M.Sc.

PROGRAMMES 2011

LIST OF MODULES BUSINESS MATHEMATICS – FIRST SEMESTER

BWIN611 – Quantitative Risk Analysis I BWIN613 – Financial Engineering I BWIN614 – Investment Theory I BWIN615 – Financial Modelling I BWIN811 – Practical Risk Management SAS RD BWIN812 – Pricing of Derivatives B BWIN813 – Practical Data Mining SAS EM BWIN815 – Industry Integration Project BWIN816 – Modern Portfolio Theory BWIN817 – Retail Credit Risk BWIN818 – Topical research Issues in Risk Analysis BWIN819 – Advanced Business Analytics BWIA612 – Models: Survival Models and Stochastic Processes (A202/CT4) BWIA811/812 – Enterprise-wide Risk Management I (F106/ST9) BWIA813 – Finance and Investments (F105/ST5)

BUSINESS MATHEMATICS – SECOND SEMESTER

BWIN621 – Quantitative Risk Analysis II BWIN622 – Pricing of Derivatives A BWIN623 – Financial Engineering II BWIN625 – Financial Modelling II BWIN826 – Industry Directed Research Project BWIA821 – Enterprise-wide Risk Management II (F106/ST9)

BUSINESS MATHEMATICS – YEAR MODULE

BWIA672 – Actuarial Risk Management (A301/CA1) BWIA673 – Contingencies (A203/CT5)

ECONOMICS – FIRST SEMESTER

ECON617 – Econometrics

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ECONOMICS – SECOND SEMESTER

ECON622 – Fiscal and Monetary Policy ECON623 – Risk Management

COMPUTER SCIENCE AND INFORMATION SYSTEMS – FIRST SEMESTER

ITRI611 – Data Warehousing I ITRI612 – Linear Programming I ITRI613 – Databases I ITRI614 – Information System Engineering ITRI616 – Artificial Intelligence I ITRI618 – Decision Support System I

COMPUTER SCIENCE AND INFORMATION SYSTEMS – SECOND SEMESTER

ITRI621 – Data Warehousing II ITRI622 – Linear Programming II ITRI623 – Databases II ITRI624 – Information Systems Engineering II ITRI626 – Artificial Intelligence II ITRI628 – Decision Support Systems II

STATISTICS AND OPERATIONAL RESEARCH – FIRST SEMESTER

STTN612 – Statistical Data-analysis I: Models (no description) STTN613 – Re-sampling Methods STTN615 – Stochastic Processes I STTN616 – Nonparametric Estimation Methods (no description)

STATISTICS AND OPERATIONAL RESEARCH – SECOND SEMESTER

STTN622 – Statistical Data-analysis II: Time Series Analysis STTN623 – Multivariate Statistics STTN624 – Discrete Data Analysis STTN625 – Stochastic Processes II

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MATHEMATICS – FIRST SEMESTER

WISK613 – Topology of Metric and Normed Spaces WISK614 – Measure and Integration Theory I WISK615 – Differential Equations

MATHEMATICS – SECOND SEMESTER

WISK624 – Measure and Integration Theory II NOTES: In some instances titles of textbooks related to module syllabi are indicated. The purpose thereof is to give prospective students an indication of the type of textbooks that may be used for the module. These are not necessarily the prescribed textbooks. Before the start of the relevant module students should confirm with the lecturer which textbook(s) is (are) prescribed. It is not a foregone conclusion that all modules listed here will be presented every year. Specifically the presentation of optional modules will depend on the number of students interested in taking the course, as well as the availability of lecturers.

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BUSINESS MATHEMATICS – FIRST SEMESTER BWIN611: QUANTITATIVE RISK ANALYSIS I Author: MF Kruger Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The purpose of this course is to provide students with a thorough understanding of modern financial risk management as practised in financial institutions. Outcome: Knowledge: At the end of this course students should have knowledge and insight into the modelling and management of market risk, credit risk, liquidity risk and operational risk in financial institutions. An integrated value at risk framework will be studied as well as hedging strategies for reducing risk. The important problem of capital allocation in a financial institution will be analysed. The new Basle regulatory requirements for the banking industry will also be analysed. Skills: Students should be able to have the skills necessary to critically evaluate financial risk management problems in financial institutions and provide solutions to these problems. Students will also be able to implement some of the risk models in SAS/IML or MS Excel. Course material:

The Professional Risk Managers’ Handbook, Volume III. BWIN613: FINANCIAL ENGINEERING I Author: MF Kruger Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The purpose of this course is to provide students with a thorough understanding of the concepts involved in the field of Financial Engineering. Outcome: Knowledge: Knowledge and insight into the mathematical modelling of financial instruments, Derive and apply mathematical formulas to price and hedge linear claims such as futures contracts. Understand and formulate equilibrium and no-arbitrage models of the short (interest) rate like the Vasicek and Cox-Ingersoll-Ross models. Derive and apply the Black-Scholes pricing formulas. Derive and apply binomial and risk-neutral Monte Carlo pricing Understand and explain the “Greeks”: delta, theta, vega, rho and gamma. Skills: Use the MS Excel software package (or SAS/IML) to implement the Black-Scholes formulas. Use the MS Excel software package (or SAS/IML) to implement basic numerical procedures to price vanilla options using binomial trees and Monte Carlo simulation. Plan and conduct research according to standard protocol and to employ appropriate processes, procedures and techniques. Operate co-operatively in groups. Communicate effectively, orally and in writing and to make use of appropriate technologies in all communications. Act ethically sound in dealing with issues and people. Course material:

John Hull, Options, Futures and other Derivative Securities, (6th ed.) Prentice Hall. 2005. Selected literature from the field of Financial Engineering. ActEd CT8 Course notes.

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BWIN614: INVESTMENT THEORY I Author: PJ de Jongh Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The aim of the course is to teach the student the basic principles of investment theory. This course together with BWIN613 meet the requirements of AS A205 (IFA CT8). Outcome: The student should be able to: Construct optimal portfolio’s Calculate portfolio inputs Evaluate portfolio’s Construct efficient frontiers Select instruments for inclusion in portfolio’s Knowledge: At the end of the course the student should obtain insight and knowledge about the following concepts: risk and return, risk aversion, utility, the selection of risky assets, the construction of optimal portfolios, single and multi-index models, active and passive management, equilibrium models and the efficient market hypothesis. Skills: In this course the student acquires the skill to assemble optimal portfolios and to select securities in an optimal manner for inclusion in the portfolio. Course material:

BWIN614 Study guide Elton, EJ; Gruber, MJ; Brown, SJ and Goetzmann, WN. Modern Portfolio Theory and

Investment Analysis (6th edition). John Wiley, 2003. Bodie, Z; Kane, A and Marcus,A. Investments. (5th Ed), Irwin/McGraw-Hill, 2002. ActEd CT8 Course notes.

BWIN615: FINANCIAL MODELLING I Author: SE Terblanche Version: 17/09/2010 Contact hours per week: Theory: 1 Practical 1 Purpose: The aim of the course is to teach the student skills that will enable the formulation of mathematical models for general industry problems (e.g. portfolio construction, optimal capital budgeting etc.), as well as to provide the student with a thorough understanding of how to apply numerical methods in solving these mathematical models. Outcomes: Knowledge: Knowledge and insight into numerical methods and techniques for solving problems encountered in the financial industry, as well as have a thorough understanding of the underlying theory that support these methods and techniques. The learners should have the knowledge to apply these methods and techniques as part of a creative problem solving approach, and should have acquired an understanding of the practical issues in developing financial models.

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Skills: Ability to produce computer models, using several important techniques, including use of special functions, iterative methods, approximation, interpolation, simulation and optimisation. The learners should demonstrate an understanding of the pitfalls of numerical computation (e.g. numerical instability) that arise in practical financial applications and should demonstrate skills in applying SAS software to assist in the problem solving approach. Course material:

BWIN615 Study guide P. Brandimarte. Numerical Methods in Finance and Economics (2nd edition). John Wiley,

2006. BWIN811: PRACTICAL RISK MANAGEMENT: SAS RD Author: MF Kruger Version: 17/09/2010 Contact hours per week: Theory: 1 Practical: 2 Purpose: The purpose of this course is to teach the learner to apply the theoretical financial risk management knowledge obtained in other courses in practice using a leading edge technology system. Outcome: The student should be able to: Define basic terms used in risk analysis Identify methods of configuring Risk Dimensions Understand the usage of SAS functions and subroutines. Understand the use of projects within a Risk Dimensions environment Knowledge: At the end of the course the student will have obtained knowledge and insight in the application of financial risk management techniques in a practical context. Skills: After successful completion of the course, the student will be able to create a risk analysis environment, of limited scope, in the SAS Institute’s risk management solution, SAS Risk Dimensions. The student will also be able to do a number of risk analyses. Course material:

SAS Risk Dimensions Technical and User Manuals.

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BWIN812: PRICING OF DERIVATIVES B Author: HP Mashele Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The purpose of this module is to provide students with an understanding of interest rate models in continuous time. Outcome: Knowledge: Understand and explain short rate models such as the Vasicek model, the Ho-Lee model, the Hull-Whites model, etc., and forward rate models such as the Heath-Jarrow-Morton model. Students should also know the difference between the LIBOR and the Swap Market models. Skills: Use the MS Excel software package (or SAS/IML) to implement basic numerical procedures to model an arbitrage-free family of zero-coupon bond price processes (the term-structure). Students should be able to use different short rate models to invert the yield curve. Plan and conduct research according to standard protocol and to employ appropriate processes, procedures and techniques. Operate co-operatively in groups. Communicate effectively, orally and in writing and to make use of appropriate technologies in all communications. Act ethically sound in dealing with issues and people. Course material:

T. Björk, Arbitrage Theory in Continuous Time, 2nd Edition. Oxford University Press, 2004. Selected literature from the field of Financial Engineering.

BWIN813: PRACTICAL DATA MINING: SAS EM Author: DA de Waal Version: 17/09/2010 Contact hours per week: Theory: 1 Practical: 2 Purpose: The aim of the course is to teach the student the basic principles of data mining and to develop the skills to apply the concepts practically on industry problems using a cutting edge technology system. Outcome: At the end of this module the student should be able to explore and analyse data sets with the techniques studied in this module. Furthermore, the student must be able to make future predictions based on the patters occurring in historical data. Knowledge: At the end of the course students will have acquired knowledge and insight about the application of data mining concepts in a practical context. Skills: After successful completion of the course students will be able to independently and by using the Enterprise Miner system of SAS, apply data mining techniques on data sets from the industry. Course material:

SAS Enterprise Miner, Training Material (Course Notes), Technical and User Manuals

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BWIN815: INTEGRATION PROJECT Author: CM Erasmus/ PJ de Jongh Version: 17/09/2010 Contact hours per week: Theory: 1 Practical: 2 Purpose: The primary goal of the course is to teach the student the principles and techniques of project management and to give him/her exposure to the practical implementation thereof in a team context. Outcome: The student will be exposed to a practical problem that will have to be taken through its complete life cycle. This entails the formulation of the user requirement, the planning, scheduling and costing of the project, the determination of a base line, the execution and monitoring of the project, documentation and the presentation of the results. Knowledge and Skills: The course has a few sub goals, such as practical English, problem solving techniques and mental skills. Professional communication and presentations in a team environment will form an integral part of the general procedure. Course material:

BWIN815 Study guide Course notes: Procedure for Conducting BMI Industry Directed Research Projects.

BWIN816: Modern Portfolio Theory Author: T de la Rey Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 2 Purpose: The aim of this course is to teach the student the principles of active investment theory Outcome: Manage a portfolio with a quantitative approach - applying rigorous analysis and a rigorous process to beat the market in investment management. Develop/propose a structured approach for active investment management. This includes constructing as well as analysing a portfolio. Apply investment management methodologies and models to practical problems. Use the BARRA software package to analyse, construct and evaluate portfolios. Knowledge: At the end of this course the student should obtain knowledge and insight about the following concepts: exceptional returns, forecasting exceptional returns, benchmark portfolios, the information ration, value added, the fundamental law of active management, structural risk models, the objective of the active manager, portfolio construction and performance analysis. Practical work will be done with the BARRA system. Skills: In this course the student acquires the skill to do active portfolio management by using the BARRA system. This system is used worldwide for portfolio management. Course material:

Grinold, RC and Kahn, RN, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk. 2nd edition. Irwin/McGraw-Hill, 1999.

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BWIN817: RETAIL CREDIT RISK Author: T de la Rey Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: (Selfstudy) Purpose: The purpose of the module is to teach the learner the basic theory of Retail Credit. This course will focus on Logistic Regression model building and Scorecard building. Outcome: The student should be able to:

Describe the principles and practice of consumer credit risk management Build Scorecards Build Logistic Regression models Apply the data analysis methodology Develop SAS programmes to implement above

Knowledge: After completion of the course, the student would have gained knowledge of and insight into what Retail Credit is. Skills: The student will be able to build Scorecards as well as Logistic Regression models. Course material:

MCNAB, H. & WYNN, A. 2000. Principles and Practice of Consumer Credit Risk Management. Canterbury: Financial World Publishing. 222 p.

SAS Institute Inc. 2000. SAS Institute Course Notes. Predictive Modeling Using Logistic Regression. NC: SAS Institute Inc. 200 p

SIDDIQI, N. 2006. Credit Risk Scorecards: Developing and Implementing Intelligent Credit Scoring. New Jersey: John Wiley & Sons. 196p

BWIN818: TOPICAL RESEARCH ISSUES IN RISK ANALYSIS Author: DCJ de Jongh Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The purpose of this course is to bring the student to the frontier of new research and the analysis of critical issues in the area of financial risk management. Outcome: Knowledge: At the end of this course, students should have knowledge and insight into the most recent research trends and technological breakthroughs in the area of financial risk management. Aspects that will be studied include: market risk, credit risk, liquidity risk, operational risk and model risk. The important problem of the allocation of risk capital for financial institutions will also be studied. The relationship between financial risk and insurance risk will be analysed. Skills: Students should be able to have the skills necessary to critically evaluate cutting edge risk issues and research breakthroughs for possible practical application.

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Course material:

Journal articles from: The Journal of Risk, The Journal of Banking and Finance and The Journal of Financial Economics.

BWIN819: ADVANCED BUSINESS ANALYTICS Author: DA de Waal Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 2 Purpose: The aim of this course is to provide graduates with an analytical tool set that enables them to address business problems. That is, given a business problem, what analytical tool would be the most useful and what data structure is needed to address the problem. Outcome: At the end of the module, the student should be able to think analytically. That is, given a business problem, what opportunities exist for the exploitation of analytics? Furthermore, the student must be able to identify the appropriate analytical techniques, implement the techniques in SAS and assist the business in better decision making. Knowledge: At the end of the course the student will have obtained knowledge and insight in the application of advanced business analytics in a practical context. Skills: After successful completion of the course, the student will be able to apply his/her analytical skills exploiting SAS Institute’s business intelligence and advanced business analytics solutions, Enterprise Guide, Enterprise Miner and Forecast Server to solve real business problems. Course material:

SAS Enterprise Guide, Training Material (Course Notes), Technical and User Manuals SAS Enterprise Miner, Training Material (Course Notes), Technical and User Manuals SAS Forecast Server, Training Material (Course Notes), Technical and User Manuals

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BWIA612: SURVIVAL MODELS AND STOCHASTIC PROCESSES (A202/CT4) Purpose: The aim of the Models (Survival Models and Stochastic Processes) (A202/CT4) module is to provide the student with a grounding in stochastic processes and survival models and their application. Outcome: Knowledge and skills: (a) On completion of the module the student will demonstrate a comprehensive and systematic

knowledge and coherent and critical understanding of: (i) the principles of actuarial modelling. (ii) the general principles of stochastic processes, and their classification into different

types. (iii) the definition and application of a Markov chain. (iv) the definition and application of a Markov process. (v) the concept of survival models. (vi) the estimation procedures for lifetime distributions. (vii) the derivation of maximum likelihood estimators for the transition intensities in models

of transfers between states with piecewise constant transition intensities. (viii) the Binomial model of mortality inclusive of the derivation of a maximum likelihood

estimator for the probability of death and the comparison of the Binomial model with the multiple state models.

(ix) how to estimate transition intensities depending on age, exactly or using the census approximation.

(x) how to test crude estimates for consistency with a standard table or a set of graduated estimates.

(xi) the process of graduation. (b) The student will also as an individual or as a member of a group demonstrate the ability to:

(i) identify, analyse and deal with complex and/or real world problems and issues using evidence-based solutions and theory-driven arguments

(ii) use efficient and effective information retrieval and processing skills (iii) perform a critical analysis, synthesis and independent evaluation of quantitative

and/or qualitative data (iv) understand a range of research methods, techniques and technologies and an ability

to select these appropriately (v) present and communicate academic/professional work effectively, catering for a

range of audiences by using a range of different genres appropriate to the context through integrated assessment of objectives (a) (i) to (xi) in the form of projects.

Course material:

ActEd Course Notes (2011): IFA subject CT4.

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BWIA811/812 AND BWIA821: ENTERPRISE-WIDE RISK MANAGEMENT I and II (F106/ST9) Purpose: The aim of the Enterprise-wide Risk Management I and II (F106/ST9)-modules is to instil in successful students the key principles underlying the implementation and application of ERM within an organisation, including governance and process as well as quantitative methods of risk measurement and modelling. The student should gain the ability to apply the knowledge and understanding of ERM practices to any type of organisation. Outcome: Knowledge and skills: (a) On completion of the module the student will demonstrate a comprehensive and systematic

knowledge and coherent and critical understanding of: (i) the ERM Concept and Framework. (ii) the ERM Process. (iii) Risk Categories and Classification. (iv) Risk Modelling and Aggregation of Risks. (v) Risk Measurement and Assessment. (vi) Risk Management Tools and Techniques. (vii) Economic Capital.

(b) The student will also as an individual or as a member of a group demonstrate the ability to:

(i) identify, analyse and deal with complex and/or real world problems and issues drawing systematically and creatively on the theory, research methods and literature

(ii) use advanced information retrieval and processing skills (iii) perform a critical analysis, synthesis and independent evaluation of quantitative

and/or qualitative data (iv) undertake a study of the literature and current research (v) effectively present and communicate the results to specialist and non-specialist

audiences using the resources of an academic/professional discourse through integrated assessment of objectives (a) (i) to (vii) in the form of projects.

Course material:

ActEd Course Notes (2011): IFA subject ST9.

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BWIA813: FINANCE AND INVESTMENTS (F105/ST5) Purpose: The aim of the Finance and Investment Technical Principles (F105/ST5) module is to instil in successful candidates the ability to apply, in simple situations, the principles of actuarial planning and control to the appraisal of investments, and to the selection and management of investments appropriate to the needs of investors. Outcome: Knowledge and skills: (a) On completion of the module the student will demonstrate a comprehensive and systematic

knowledge and coherent and critical understanding of: (i) State what is meant by a risk-free rate of return, and describe assets that may be

assumed to be risk-free in practical work. (ii) Describe the typical ways in which investment returns are taxed and the effect of the

taxation basis on investor behaviour. (iii) Describe the principal features of financial statements issued by companies

(including pension funds and insurance companies). (iv) Demonstrate knowledge of the influences over the commercial and economic

environment from: (a) central banks (b) main investor classes (c) government policy

(v) Demonstrate a knowledge of the principles of fundamental share analysis. (vi) Discuss the different methods for the valuation of individual investments and

demonstrate an understanding of their appropriateness in different situations. (a) fixed income analytics and valuation (including interest rate swaps and futures) (b) arbitrage pricing and the concept of hedging (c) empirical characteristics of asset prices (d) introduction into fixed income option pricing (e) evaluating a securitisation (including CBOs and MBSs) (f) evaluation of a credit derivative

(vii) Describe methods by which an institution can monitor and control its exposure to the following types of risk: (a) actuarial risk (b) market risk (c) credit risk (d) operational risk (e) relative performance risk and explain in the context of mean-variance portfolio theory what is meant by: (a) opportunity set (b) efficient frontier (c) indifference curves (d) the optimum portfolio.

(viii) Demonstrate a knowledge of the principles underlying the legislative and regulatory framework for investment management and the securities industry.

(ix) Demonstrate a knowledge and understanding of the theory of finance. (x) Demonstrate a knowledge and understanding of the characteristics of specialist

financial instruments: (a) alternative financial instruments available for short-term lending and borrowing (b) corporate debt and credit derivatives (c) swaps and swaptions (d) private debt (e) asset-backed securities (f) securitisation (g) venture capital (h) hedge funds.

(xi) Describe the main types of derivative contracts and define their payoffs.

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(xii) Show how actuarial techniques may be used to develop an appropriate investment strategy: (a) asset pricing models (b) asset / liability modeling (c) asset / liability mismatch reserving (d) credit rating an entity (e) liability hedging (f) cointegration (g) dynamic liability benchmarks.

(xiii) Analyse the performance of an investment and discuss the limitations of such measurement techniques: (a) portfolio risk and return analysis (b) equity price (c) net present value (d) net asset value (e) return on capital.

(xiv) Describe the construction of investment indices and the principal features of major investment indices.

(xv) Analyse the performance of an investment portfolio and discuss the limitations of such portfolio measurement.

(xvi) Demonstrate a knowledge and understanding of the principal techniques in portfolio management including risk control techniques.





audiences using the resources of an academic/professional discourse through integrated assessment of objectives (a) (i) to (xvi) in the form of project(s).

Course material:


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BUSINESS MATHEMATICS – SECOND SEMESTER BWIN621: QUANTITATIVE RISK ANALYSIS II Author: DCJ de Jongh Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: This course is an extension of the material presented in Quantitative Risk Analysis I. The purpose of this course is to provide students with a thorough understanding of more advanced mathematical models in the field of Financial Risk Management. Outcome: Knowledge: At the end of this course, students should have knowledge and insight into advanced mathematical modelling of market risk, credit risk, liquidity risk and operational risk in financial institutions. Skills: Students should be able to critically evaluate advanced mathematical models in financial risk management. Students will also be able to implement some of the risk models in a practical environment. Course material:

Market Models. Carol Alexander. John Wiley and Sons, 2001. Advanced Credit Risk Analysis. Didier Cossin and Hugues Pirotte. John Wiley and Sons,

2001. Modelling, measuring and hedging operational risk. Marcelo G. Cruz. John Wiley and

Sons,2002. Selected journal articles.

BWIN622: PRICING OF DERIVATIVES A Author: HP Mashele Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The purpose of this module is to provide students with an understanding of both the discrete time and the continuous time mathematics involved in the field of Financial Derivatives. Outcome: Knowledge: Understand and explain single-period and multi-period discrete time financial market models. Formulate and apply Fundamental Theorem of Financial Mathematics, the Feynman-Kac Stochastic Representation Formula, the Martingale Representation Theorem, the Girsanov Theorem, and the Ito Formula. Understand and formulate stochastic processes such as Wiener processes. Skills: Use the MS Excel software package (or SAS/IML) to implement basic numerical procedures to price exotic options and derive hedging strategies using binomial trees and Monte Carlo simulation. Apply Ito calculus at an introductory level. Formulate and apply continuous time arbitrage theorems in a variety of situations. Interpret and apply Girsanov’s theorem in the pricing of derivatives. Derive continuous time hedging strategies. Solve simple stochastic differential equations analytically. Solve more complex stochastic differential equations using numerical methods. Plan and conduct research according to standard protocol and to employ appropriate processes, procedures and techniques. Operate co-operatively in groups. Communicate effectively, orally and in writing and to make use of appropriate technologies in all communications. Act ethically sound in dealing with issues and people.

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Course material:

T. Björk, Arbitrage Theory in Continuous Time, 2nd Edition. Oxford University Press, 2004. Selected literature from the field of Financial Engineering.

BWIN623: FINANCIAL ENGINEERING II Author: MF Kruger Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: This course is an extension of the content presented to the student in BWIN613: Financial Engineering I. The purpose of this course is to provide students with a thorough understanding of further concepts involved in the field of Financial Engineering, and will have a stronger focus on interest rate derivatives. Outcome: Knowledge: Understand and explain the relationship between a volatility smile and the risk-neutral probability measure used in binomial pricing of options. Understand and formulate the short (interest) rate lattice models like the Black-Derman-Toy, Ho-Lee and Hul-White models. Derive and apply mathematical formulas to price interest rate derivatives by using previous knowledge in other disciplines like statistics, computer science and economics in an integrative way. Understand and explain numerical methods like Least Squares Monte Carlo and Finite Differences for pricing exotic options found in insurance. Skills: Use the MS Excel software package (or SAS/IML and SAS/ETS) to implement basic numerical procedures to price more general (including path-dependent) options using binomial trees, finite difference methods and Monte Carlo simulation. Use the MS Excel software package (or SAS/IML and SAS/ETS) to implement basic numerical procedures to estimate and forecast volatilities and correlations. Use the MS Excel software package (or SAS/IML and SAS/ETS) to implement basic numerical procedures to calculate Value-at-Risk (VaR) using Monte Carlo simulation. Plan and conduct research according to standard protocol and to employ appropriate processes, procedures and techniques. Operate co-operatively in groups. Communicate effectively, orally and in writing and to make use of appropriate technologies in all communications. Act ethically sound in dealing with issues and people. Course material:

John Hull, Options, Futures and other Derivative Securities, (7th ed.) Prentice Hall, 2005. Selected literature from the field of Financial Engineering.

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BWIN625: FINANCIAL MODELLING II Author: SE Terblanche Version: 17/09/2010 Contact hours per week: Theory: 1 Practical 1 Purpose: This course is an extension of the contents presented to the student in BWIN615. The purpose of this course is to equip the student with the necessary skills to make use of numerical methods in solving problems encountered in the financial industry. Outcome: Knowledge: Knowledge and insight into applying numerical methods and techniques to specific applications in quantitative finance. Emphasis is placed on advanced portfolio optimisation problems and pricing problems. Skills: Ability to apply numerical and simulation techniques for portfolio construction under a range of different risk measures, and to do pricing of different exotic option classes. The learners should demonstrate skills in applying SAS software to assist in doing a practical project that will integrate their knowledge obtained from different subjects. Course material:

BWIN625 Study guide P. Brandimarte. Numerical Methods in Finance and Economics (2nd edition). John Wiley,

2006. BWIN826: INDUSTRY DIRECTED RESEARCH PROJECT Author: CM Erasmus / PJ de Jongh Version: 17/09/2010 Contact hours per week: Theory: 1 Practical: 24 Purpose: The purpose of the course is to expose the learner in a controlled and structured way to the dynamics and politics involved in implementing projects in industry. Outcome: The student should be able to solve those problems encountered in his/her field of study in a structured way. Knowledge and Skills: This course occupies the last semester of the M.Sc. programme and is similar to the Business Integration Project (BWIN815), apart from the fact that the student now has to formulate and solve the problem on his own. In the process he/she will still receive academic support from his/her study leader at the Centre, but a greater degree of independence will be expected from the student. The student team will be expected to conduct the project in accordance to the guidelines specified in the procedure that has been developed to manage such projects. The study is concluded with the formal documentation of the problem, together with the solution as a report (paper), which will also be considered for inclusion in the BMI Centre's publication series. Course material:

Course notes: Procedure for Conducting BMI Industry Practice Projects

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BWIA811/812 AND BWIA821: ENTERPRISE-WIDE RISK MANAGEMENT I and II (F106/ST9) Purpose: The aim of the Enterprise-wide Risk Management I and II (F106/ST9)-modules is to instil in successful students the key principles underlying the implementation and application of ERM within an organisation, including governance and process as well as quantitative methods of risk measurement and modelling. The student should gain the ability to apply the knowledge and understanding of ERM practices to any type of organisation. Outcome: Knowledge and skills: (a) On completion of the module the student will demonstrate a comprehensive and systematic

knowledge and coherent and critical understanding of: (i) the ERM Concept and Framework.

(ii) the ERM Process. (iii) Risk Categories and Classification. (iv) Risk Modelling and Aggregation of Risks. (v) Risk Measurement and Assessment. (vi) Risk Management Tools and Techniques. (vii) Economic Capital.





audiences using the resources of an academic/professional discourse through integrated assessment of objectives (a) (i) to (vii) in the form of projects.

Course material:


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BUSINESS MATHEMATICS – YEAR MODULE BWIA672: ACTUARIAL RISK MANAGEMENT (A301/CA1) Purpose: The aim of the Actuarial Risk Management (A301/CA1) module is that upon successful completion that a student should understand strategic concepts in the management of the business activities of financial institutions and programmes, including the processes for management of the various types of risk faced, and be able to analyse the issues and formulate, justify and present plausible and appropriate solutions to business problems. Outcome: Knowledge and skills: (a) On completion of the module the student will demonstrate a comprehensive and systematic

knowledge and coherent and critical understanding of: (i) how to do a professional job. (ii) stakeholders and their needs. (iii) he general environment (risk environment, regulatory environment, external

environment, investment environment and capital requirements). (iv) specification of the problem (contract design, project planning and project

management). (v) data. (vi) risk management. (vii) producing the solution (modelling, assumption setting, expenses, developing the cost

and price, investment management, provisioning and the relationship between assets and liabilities).

(viii) living with the solution (maintaining profitability, determining the expected results, reporting actual results, asset management, capital management, surplus management, insolvency and closure and options and guarantees).

(ix) monitoring the actual experience. (x) the principal terms used in financial services and risk management.






range of audiences by using a range of different genres appropriate to the context through integrated assessment of objectives (a) (i) to (x) in the form of projects.

Course material:

ActEd Course Notes (2011): IFA subject CA1.

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BWIA673: CONTINGENCIES (A203/CT5) Purpose: The aim of the Contingencies (A203/CT5) module is to provide a grounding in the mathematical techniques which can be used to model and value cashflows dependent on death, survival, or other uncertain risks. Outcome: Knowledge and skills: (a) On completion of the module the student will demonstrate a comprehensive and systematic

knowledge and coherent and critical understanding of: (i) simple assurance and annuity contracts, and the developing of formulae for the

means and variances of the present values of the payments under these contracts, assuming constant deterministic interest.

(ii) practical methods of evaluating expected values and variances of the simple contracts defined in objective (i).

(iii) using ultimate or select mortality to calculate net premiums and net premium reserves of simple insurance contracts.

(iv) the calculation, using ultimate or select mortality, of net premiums and net premium reserves for increasing and decreasing benefits and annuities.

(v) the calculation of gross premiums and reserves of assurance and annuity contracts. (vi) straightforward functions involving two lives. (vii) methods which can be used to model cashflows contingent upon competing risks. (viii) the technique of discounted emerging costs, for use in pricing, reserving, and

assessing profitability. (ix) the principal forms of heterogeneity within a population and the ways in which

selection can occur. (b) The student will also as an individual or as a member of a group demonstrate the ability to:





range of audiences by using a range of different genres appropriate to the context through integrated assessment of objectives (a) (i) to (ix) in the form of projects.

Course material:

ActEd Course Notes (2011): IFA subject CT5.

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ECONOMICS – FIRST SEMESTER ECON617: ECONOMETRICS Author: JJA Pearson Version: 17/09/2010 Contact hours per week : Theory: 2 Practical: 16 Purpose: The purpose of this course is to integrate economic, financial, statistical and computer theory in an econometric application of practical economic phenomena. Outcome: Knowledge: Having completed this course the learner should have acquired basic knowledge and insight into: market efficiency, predictability of asset returns, event- study analysis, Arch-Garch models, volatility, co-integration and error correction models. Skills: The learner should be able to apply the theoretical concepts to model and understand practical economical phenomena. Course material:

Elton & Gruber, Modern Portfolio Theory and Investment analysis (5th Ed), Wiley, 1995. Campbell, Lo & MacKindlay, The Econometrics of Financial Markets, Princeton University

Press, 1997. Hull, Options Futures and other Derivatives, Prentice Hall, 2000 Walter Enders, Applied Econometrics Time Series, Wiley, 1995.

ECONOMICS – SECOND SEMESTER ECON622: FISCAL AND MONETARY POLICY Author: W Krugell Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: This module is about the economic questions that policymakers and economic researchers are facing in South Africa today. The aim of the course is to equip students with knowledge about the latest issues. In 2007 the focus is specifically on government’s Accelerated and Shared Growth Initiative (ASGI-SA) and the question is asked whether fiscal and monetary policy, infrastructure investment and competition policy can ensure a better life for all. Outcome: At the end of this module the student should be able to: Discuss the ASGI-SA strategy. Analyze and evaluate the different components of the strategy, for example fiscal policy or

infrastructure investment, with specific reference to the latest empirical studies. Write well-reasoned essays as to how the policy challenges should be approached, with a

balance of theoretical models and empirical evidence. Make a presentation about one of the policy issues covered in this module.

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Knowledge: The student should have knowledge of the latest research looking into, for example, the drivers of growth in South Africa, the way forward with inflation targeting policies, the infrastructure investment needs and concentration and lack of competition in the South African economy. Skills: The students have to sharpen both their writing and presentation skills. The essays require extensive reading of literature in order to present structured arguments, using theoretical models and empirical evidence. Course material:

The prescribed material consists of articles from academic journals and working papers from web sites such as the Trade and Industrial Promotion Secretariat (TIPS) and the Economic Research Southern Africa (ERSA) network.

ECON623: RISK MANAGEMENT Author: P Styger Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 1.5 Purpose: The very important role of banks as financial intermediaries in the economy, together with the different risks with which banks are presently confronted, are already known from the undergraduate work. This course plans to teach how a bank should be managed in the changing environment in order to maintain the necessary balance between risk-taking and profitability. Strategic risk management will be the focus. Outcome: The course will therefore extend the theoretical knowledge base, although the practical aspects and application will be emphasised strongly to enable the student to apply this directly in his/her current or future work situation. The specific course objectives are: To teach the student how different risks are managed by the ALCO in a bank. to indicate the important role and influence of BASEL II, the Banks Act and Bank Supervision; and to provide the student with first-hand practical experience of Bank Asset and Liability Management in a typical South African bank with the aid of case studies and the ALMAN computer package for Assets and Liabilities Management as well as interest rates forecasting. Knowledge: On completion of this subject the candidate: will have an in-depth knowledge of the characteristics of the various financial risks faced by banks, and the prescriptions of Basel II on how to measure and manage these risks. Skills: On completion of this subject the candidate will be able to: Make a meaningful contribution, as a member of a bank or related institution’s risk management team, towards the management of the risks and the compliance to Basel II. Course material:

J. Bessis, Risk Management in Banking (2nd ed.), London, 2001 W. Koch, Bank Management (4th Int. Ed), Harcourt Brace, NY, 2000.

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COMPUTER SCIENCE AND INFORMATION SYSTEMS – FIRST SEMESTER ITRI611: DATA WAREHOUSING I Author: M Huisman Version: 17/09/2010 Contact hours per week: Theory: 1 Practical: 2 Purpose: The purpose of the module is to teach the learner basic Data Warehouse concepts. This course focuses on the design of a data warehouse. The students internalise the theoretical principles by means of a practical course on the implementation of a data warehouse. Outcome: Knowledge: After completion of the course, the student would have gained knowledge and insight regarding the application of Data Warehouse design principles in a practical context. Skills: After successful completion of the course the student will be amble to independently and through the use of the Warehouse Administrator module of SAS implement Data Warehouse principles from industry. Course material:

The Data Warehouse Lifecycle Toolkit – Kimball, Reeves, Ross & Thorntwaite. 1998. ISBN 0-471-25547-5. Wiley.

SAS Warehouse Builder, Training Material (Course Notes), Technical and User Manuals. ITRI612: LINEAR PROGRAMMING I Author: G Hattingh Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to equip the learner with a basic insight of the theory and application of linear programming. Outcome: After successfully completing this module you should: have obtained advanced knowledge on modelling and linear programming; have mastered the subject language so that you can easily communicate with colleagues; go about in a problem-solving way; demonstrate a passion for the field of study and demonstrate comprehension for the solution of optimising problems within the larger relation of Mathematical Programming. Knowledge: Having completed this course the learner should have acquired basic knowledge and insight into: The formulation of problems as linear programming problems, basic results on linear algebra and convex analysis in conjunction with a geometrically-based study of polyhedral sets, details of the simplex method, obtaining feasible solutions, degeneration, duality and sensitivity analysis.

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Skills: At the end of the course the learner will be able to demonstrate that he/she can apply the theoretical knowledge acquired, in solving problems in the discipline and its application areas. In particular, the student will be able to formulate simple industrial problems as linear programming problems, and solve them using the simplex method. The student will have the ability to analyse the simplex method, degeneration and infeasibility of problems using algebraic and geometric arguments. Course material:

The textbook that is prescribed is Linear Programming and Network Flows by Bazaraa, Jarvis en Sherali (3de edition).

Other textbooks for additional reading and examples: Sets, Matrices and Linear Programming, by Childress (elementary book to help build your

intuition) Linear Programming, by Chvatal V.

ITRI613: DATABASES I Author: T Steyn Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 2 Purpose: The objective of the course is to equip the learner with thorough background knowledge of the theory and application of databases. Outcome: Knowledge: Having completed this course the learner will have acquired basic knowledge and insight into the following aspects regarding databases: purpose and architecture, the relation model, handling big data files, different types of indexes and their operation, external sorting procedures, relational algebra as a query medium, SQL and other query methodologies and security measures. Skills: At the end of the course the learner will be able to demonstrate that he/she can apply the theoretical knowledge acquired, in solving problems in the discipline and its application areas. Specific skills acquired with respect to Oracle, will prepare and allow the student to sit for certain of the certification examinations of the Oracle Academic Initiative. Course material:

R. Ramakrishnan, Database Management Systems (2nd Ed), McGraw-Hill, 1999 ITRI614/624: INFORMATION SYSTEM ENGINEERING Author: M Huisman Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to equip the learner with basic knowledge of different systems development methodologies.

D25

Outcome: Knowledge: The development of a suitable information system is a difficult and expensive process. In this course, alternative methodologies for the development of information systems will be considered, among others the object-orientated approach, CASE aids, prototyping, spiral model and the incrementing model. Significant attention will be paid to the object-oriented approach. Specific emphasis will be placed on the development of re-usable systems and the quality of the system. The automation of the process will be discussed by using a CASE tool. A project is done in a group context. Skills: Students will be able to critically evaluate systems development methodologies and recommend an appropriate method for a specific project. Students will be able to apply systems development methodologies to major projects (both structured and object oriented methodologies). Course material:

Information Technology Project Management - Kathy Schwalbe. Information Systems Development: Methodologies, Techniques and Tools - David Avison and

Guy Fitzgerald. ITRI616/626: ARTIFICIAL INTELLIGENCE Author: T du Toit Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to familiarise the learner with the building of intelligent agents. This is accomplished by using modern techniques in artificial intelligence. It is further demonstrated how different agent designs can be used to solve a wide range of problems. Outcome: At the end of this module the student should be able to:

Define Artificial Intelligence and critically evaluate a definition Describe the principles of knowledge-based agents Solve problems by making use of various informed and uninformed search methods Define Propositional Logic and Predicate Logic (both syntax and semantics) and draw

inferences in Propositional Logic and Predicate Logic Discuss and use various neural network models and architectures in order to solve practical

problems Knowledge: The techniques that were studies in previous courses, such as search methods and predicate logic, are placed within the framework of intelligent agents. New techniques such as neural networks are studied and emphasis is put on the practical use of these techniques. An integrated and coherent view of the field, built on the idea of an intelligent agent, is provided.

D26

Skills: The learner is required to be able to design and build simple intelligent agents and to master new techniques that can be used to analyse and build current and future intelligent agents. Course material:

Stuart Russell & Peter Norvig, Artificial Intelligence - A Modern Approach, Prentice Hall, 1995. M.T. Hagen, H.B. Demuth & M. Beale, Neural Network Design, PWS Publishing Company,

1996. ITRI618/628: DECISION SUPPORT SYSTEMS I/II Author: H Kruger Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to equip the learner with further knowledge of mathematical modelling, with the emphasis on stochastic models. Outcome: Knowledge: Having completed this course the learner will have acquired basic knowledge and insight into: stochastic/mathematical models, optimisation of models, sensitivity analysis, decision theory, inventory models, queuing models, forecasting models and stochastic modelling in project management. Skills: At the end of the course the learner will be able to demonstrate that he/she can apply the theoretical knowledge acquired in solving problems in the discipline and its application areas, in particular the ability to formulate, solve and interpret the constructed models. He/she will also be able to demonstrate the ability to manage and apply the modelling approach to problem solving. Course material:

H. Bierman(Jnr), C.P. Bonini & W.H. Hausman, Quantitative Analysis for Business Decisions, Irwin, 1991

S.M. Lee & J.P. Shim, Micro Management Science(2nd Ed), Allen and Bacon, 1990 M. Klein & L.B. Methlie, Expert Systems A Decision Support Approach, Addison-Wesley,

1990. COMPUTER SCIENCE AND INFORMATION SYSTEMS – SECOND SEMESTER ITRI621: DATA WAREHOUSING II Author: R Goede Version: 17/09/2010 Contact hours per week: Theory: 1 Practical: 2 Purpose: The purpose of the course is to enable the learner to implement basic Data Warehouse principles. A project forms the main element of this course and students must implement all the phases of a data warehouse project from the theoretical foundation.

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Outcome: Knowledge: After completion of the course, the student would have gained knowledge and insight regarding the practical difficulties and integration problems encountered in the implementation of Data Warehouse concepts in a practical context. Skills: After successful completion of the course the student will be able to independently integrate various packages like Java, Oracle and SAS to overcome typical implementation problems. Course material:

The Data Warehouse Lifecycle Toolkit – Kimball, Reeves, Ross & Thorntwaite. 1998. ISBN 0-471-25547-5. Wiley.

SAS Warehouse Builder, Training Material (Course Notes), Technical and User Manuals. ITRI622: LINEAR PROGRAMMING II Author: G Hattingh Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: To equip students with the necessary knowledge and skills to formulate and solve integer programs (IP), binary integer programs (BIP), mixed integer programs (MIP), stochastic programs (SP) and network flow proplems (NF). Outcome: Knowledge: On completion of this module the learner should be able to: Understand the formulation of IP, BIP, MIP, SP, and NF problems; Know the theory related solution techniques for solving IP, BIP, MIP, SP, and NF problems; Skills: On completion of this module the learner should demonstrate that the knowledge and insight acquired can be applied to the formulation and solution of linear programs: Formulate IP, BIP, MIP, SP, and NF from problem narratives; Solve IP, BIP, MIP, SP, and NF problems by means of relevant solution techniques; Make use of commercial software packages such as CPLEX and SAS to solve linear programs. Course material:

Bazaaraa, Jariv & Sherali, Linear Programming and Network Flows, 2nd edition from Wiley. ITRI623: DATABASES II Author: E Taylor / T Steyn Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 2 Purpose: The objective of the course is to equip the learner with thorough knowledge of more advanced aspects of the theory and application of databases.

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Outcome: Knowledge: Having completed this course the learner will have acquired basic knowledge and insight into: methods to evaluate relational operators, ER and relation models, basic design principles, integral restrictions and dependencies; relational schemes and axioms in dependencies, algorithms for design problems, delineations between ER diagrams and relational schemes, scheme transformations, examples of data bases (based on the Oracle system) during design, and database administration methodologies and techniques. Skills: At the end of the course the learner will be able to demonstrate that he/she can apply the theoretical knowledge acquired, in solving problems in the discipline and its application areas. Specific skills acquired with respect to Oracle, will prepare and allow the student to sit for certain of the certification examinations of the Oracle Academic Initiative. Course material:

R. Ramakrishnan, Database Management Systems (2nd Ed), McGraw-Hill, 1999 ITRI614/624: INFORMATION SYSTEM ENGINEERING Author: M Huisman Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to equip the learner with basic knowledge of different systems development methodologies. Outcome: Knowledge: The development of a suitable information system is a difficult and expensive process. In this course, alternative methodologies for the development of information systems will be considered, among others the object-orientated approach, CASE aids, prototyping, spiral model and the incrementing model. Significant attention will be paid to the object-oriented approach. Specific emphasis will be placed on the development of re-usable systems and the quality of the system. The automation of the process will be discussed by using a CASE tool. A project is done in a group context. Skills: Students will be able to critically evaluate systems development methodologies and recommend an appropriate method for a specific project. Students will be able to apply systems development methodologies to major projects (both structured and object oriented methodologies). Course material:

Information Technology Project Management - Kathy Schwalbe. Information Systems Development: Methodologies, Techniques and Tools - David Avison and

Guy Fitzgerald.

D29

ITRI616/626: ARTIFICIAL INTELLIGENCE Author: T du Toit Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to familiarise the learner with the building of intelligent agents. This is accomplished by using modern techniques in artificial intelligence. It is further demonstrated how different agent designs can be used to solve a wide range of problems. Outcome: At the end of this module the student should be able to:

Define Artificial Intelligence and critically evaluate a definition Describe the principles of knowledge-based agents Solve problems by making use of various informed and uninformed search methods Define Propositional Logic and Predicate Logic (both syntax and semantics) and draw

inferences in Propositional Logic and Predicate Logic Discuss and use various neural network models and architectures in order to solve practical

problems Knowledge: The techniques that were studies in previous courses, such as search methods and predicate logic, are placed within the framework of intelligent agents. New techniques such as neural networks are studied and emphasis is put on the practical use of these techniques. An integrated and coherent view of the field, built on the idea of an intelligent agent, is provided. Skills: The learner is required to be able to design and build simple intelligent agents and to master new techniques that can be used to analyse and build current and future intelligent agents. Course material:

Stuart Russell & Peter Norvig, Artificial Intelligence - A Modern Approach, Prentice Hall, 1995. M.T. Hagen, H.B. Demuth & M. Beale, Neural Network Design, PWS Publishing Company,

1996. ITRI618/628: DECISION SUPPORT SYSTEMS I/II Author: H Kruger Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The objective of the course is to equip the learner with further knowledge of mathematical modelling, with the emphasis on stochastic models. Outcome: Knowledge: Having completed this course the learner will have acquired basic knowledge and insight into: stochastic/mathematical models, optimisation of models, sensitivity analysis, decision theory, inventory models, queuing models, forecasting models and stochastic modelling in project management.

D30

Skills: At the end of the course the learner will be able to demonstrate that he/she can apply the theoretical knowledge acquired in solving problems in the discipline and its application areas, in particular the ability to formulate, solve and interpret the constructed models. He/she will also be able to demonstrate the ability to manage and apply the modelling approach to problem solving. Course material:

H. Bierman(Jnr), C.P. Bonini & W.H. Hausman, Quantitative Analysis for Business Decisions, Irwin, 1991

S.M. Lee & J.P. Shim, Micro Management Science(2nd Ed), Allen and Bacon, 1990 M. Klein & L.B. Methlie, Expert Systems A Decision Support Approach, Addison-Wesley,

1990. STATISTICS AND OPERATIONAL RESEARCH – FIRST SEMESTER STTN612: STATISTICAL DATA ANALYSIS I: MODELS There is no detailed description available at this time. Detailed information will be provided in 2011 to those students taking the module in 2011. STTN613: RESAMPLING METHODS Author: J Swanepoel/L Santana Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 1 Purpose: The purpose of the course is to acquaint the learner with the basic concepts of resampling methods. Outcome: Knowledge: New computer-intensive bootstrap inference methods and techniques will be learned and applied where classical methods are not applicable. Students learn to derive bootstrap estimators by using standard errors of estimators, to compute bootstrap confidence intervals, to do hypothesis testing and other inference by using bootstrap methods for regression time series models. The programming language Fortran will be studied to do Monte Carlo simulation studies. Skills: Having completed the course, the student will be able to identify which problems and inference tasks can be solved by applying the bootstrap method, will be able to use the Fortran programming environment, including the IMSL libraries, to perform statistical inference for certain problems which were previously not possible. Course material:

B. Efron en R.J. Tibshirani, An introduction to the bootstrap, Chapman & Hall, 1993.

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STTN615 STOCHASTIC PROCESSES I Author: J Swanepoel Version: 17/09/2010 Contact hours per week: Theory : 2 Purpose: The purpose of this course is to introduce the learner to the basic concepts of stochastic processes. Outcomes: Knowledge: This course provides the student with the opportunity to master the fundamentals of stochastic processes. After introductory sessions on probability theory and the basic concepts of stochastic processes, discrete time Markov chains are discussed. Attention is given to transition probabilities, the Chapman-Kolmogorov equations, classification of states, limiting behaviour, branching processes, modeling and simulation of Markov chains, and applications to financial models. The study of continuous time Markov processes includes the Poisson process, the Forward and Backwards Kolmogorov equations, basic applications, non-homogeneous Markov processes, and the modeling and simulation of Markov processes. Skills: Having completed the course, the learner will be able to identify stochastic processes and carry out the appropriate probability calculations. Course material:

Lecturer’s notes. STTN616: NONPARAMETRIC ESTIMATION METHODS There is no detailed description available at this time. Detailed information will be provided in 2011 to those students taking the module in 2011. STATISTICS AND OPERATIONAL RESEARCH – SECOND SEMESTER STTK622: STATISTICAL DATA ANALYSIS II: TIME SERIES ANALYSIS Author: FC van Graan Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 1 Purpose: The purpose of the course is to acquaint the learner with the basic concepts of time series analysis. Outcome: Knowledge: This course offers the student the opportunity to study stationary, non stationary as well as seasonal time series models, to identify specific models in practice and to apply inference techniques such as computing parameters and making forecasts. The manner in which S-PLUS handles time series will be learned and applied. Skills: Having completed the course the student will be able to use time series data in practical situations, to identify the presence of time dependent relations, to compute relevant parameters and to do forecasting by using a software package such as S-PLUS or other applicable packages.

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Course material:

W.W.S. Wei, Time Series Analysis, Addison-Wesley, 1990 STTK623: MULTIVARIATE STATISTICS Author: FC Van Graan Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 1 Purpose: The purpose of the course is to acquaint the learner with the concepts of multivariate statistics Outcome: Knowledge: The course supplies the student with a general theoretical background as well as practical abilities to gain knowledge on selected topics in multivariate statistics, such as inference of multivariate mean vectors, multivariate linear models, principal components, factor analysis, canonical correlation analysis, discriminant analysis, classification and cluster analysis. The application of programming packages such as S-PLUS, SAS and STATISTICA in the above-mentioned cases will be studied. Skills: Having completed the course, the student will be able to apply inference models on practical situations of selected topics in multivariate statistics, such as: the comparison of multivariate mean vectors, prediction and model fitting of multivariate linear models, determining principal components of complex populations, performing canonical correlation analysis, to differentiate and classify observations of different populations and to apply cluster analysis. Program packages such as S-PLUS, SAS and STATISTICA are used. Course material:

Johnson & Wichern, Applied multivariate Statistical Analysis, (5th Ed.) Prentice-Hall, 2002. STTK624: DISCRETE DATA ANALYSIS Author: CJ Swanepoel Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 1 Purpose: The purpose of the course is to acquaint the learner with the basic concepts of statistical inference on categorical data Outcome: Knowledge: The purpose of this course is to provide the learner with the ability to do inference by using categorical data constructively. Asymptotic methods, the 0- and o-notations, convergence of stochastic sequences, convergence of movements and the -method for determining asymptotic distributions form part of the course, as well as model differentiation, model fitting, determining parameters for log-linear models, logistic and logit models. The use of SAS and S-PLUS to do computations will also be studied. Skills: Having completed the course, the learner will be able to perform categorical data (discrete data), inference using log-linear models, logistic and logit models, apply model fitting criteria to do model selection, do parameter estimation and make practical interpretations.

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Course material:

Bishop, Feinburg en Holland, Discrete Multivariate Analysis, MIT Press, 1975. Agresti, Alan , Categorical Data Analysis, John Wiley & Sons

STTK625: STOCHASTIC PROCESSES II Author: J Swanepoel Version: 17/09/2010 Contact hours per week: Theory: 2 Purpose: The purpose of the course is to provide the student with knowledge pertaining to specific continuous time stochastic processes which are applicable in financial economics. The most important of these is Brownian motion. Stochastic Calculus, based on the Ito integral, is discussed so that stochastic differential equations can be used to model stochastic processes. Outcomes: Knowledge: At the end of this course, the student will have gathered knowledge on specific continuous time stochastic processes such as Brownian motion, the Ornstein-Uhlenbeck process, geometric Brownian motion, and Levy processes. The learner’s knowledge of Stochastic Calculus, based upon the Ito integral, will be developed and the student will be adept at using stochastic differential equations. Skills: The learner will be able to apply the gained knowledge in order to identify continuous time stochastic processes, to demonstrate their applications, and to make use of basic Stochastic Calculus. Course Material:

Lecturer’s Notes. MATHEMATICS – FIRST SEMESTER WISK613: TOPOLOGY OF METRIC AND NORMED SPACES Author: Prof Jan Fourie Version: 17/09/2010 Contact hours per week: Theory: 2 Practical: 2 Purpose: The purpose of this course is to introduce the student to the theory and applications of Topology. Outcome: Knowledge: At the end of this course, the student will have obtained basic knowledge of and acquired insight into the topological properties of metric and normed spaces. The student will know and understand the concepts of convergence of sequences, completeness of spaces, continuity of functions and compactness of sets in the context of metric and normed spaces.

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Skills: At the end of the course, the student will be able to test the metric properties of metric spaces and to verify the topological properties of metric and normed spaces, such as closedness and compactness of sets and the completeness of some important metric and normed spaces. The student will be able to apply the acquired knowledge and skills and will be able to demonstrate that he/she can characterize finite dimensional normed spaces as those normed spaces for which the closed unit ball is compact. Applying his/her knowledge of bases in finite dimensional spaces, the student will be able to prove that such spaces are complete and that all the norms on a given finite dimensional space are equivalent. The student will be able to define bounded linear operators (and their norms) on normed linear spaces and to describe continuity of linear operators on normed spaces in terms of convergent sequences. He/she will be able to prove that some important operators on normed spaces are bounded and will also be able to compute the norms of such operators. The student will be able to characterize bounded linear functionals on certain classical normed spaces; he/she will be able to show that finite dimensional normed spaces are isomorphic to their dual spaces and in particular that they are reflexive. Course material:

Kreyszig, Erwin. 1989. Introductory Functional Analysis with Applications WISK614: MEASURE AND INTEGRATION THEORY I Author: JJ Grobler Version: 17/09/2010 Contact hours per week : Theory : 2 Practical: 2 Purpose: It is the purpose of this course to equip the learner with the basic knowledge and skills of real analysis and measure and integration theory. Outcome: After the completion of this module, the learner should have all the knowledge and skills as required in N.2.5 of the Calendar of the Faculty of Natural Sciences. In particular the learner will have acquired the following knowledge and skills: Knowledge: The learner knows the Carathéodory extension theory of measures defined on algebras of subsets. The learner can prove the existence of Stieltjes-Lebesque measures and is acquainted with the potential applicability of these measures. The learner is acquainted with the theory of absolutely continuous functions and the differentiation of Lebesgue measurable functions. Skills: The learner is skilled in applying the techniques used for the solution of problems in the theory; the learner is skilled in presenting the theory through seminars; the learner is able to do the necessary research in preparation for a seminar lecture.

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Course material:

Reële Analise en Maat- en Integrasieteorie, JJ Grobler, Derde Uitgawe, Potchefstroom (2005)

Mathematical Analysis, TM Apostol, Second Edition, Addison- Wesley, Reading, Massachusetts

Analysis 1 and 2 W Walter, Dritten Auflage, Springer-Lehrbuch, Springer-Verlag, Berlin, Heidelberg, New York

Probalility and Measure Theory, RB Ash and CA Doleans-Dade, Second Edition, Harcourt-Academic Press San Diegeo, San Francisco, New York, Boston, London, Toronto, Sydney, Tokyo

Measure Theory PR Halmos, D van Nostrand, Princeton, New Jersey Integration AC Zaanen, North-Holland, Amsterdam

WISK615: DIFFERENTIAL EQUATIONS I Author: DB Janse van Rensburg Version: 17/09/2010 Contact hours per week: Theory : 2 Practical : 2 Purpose: The purpose of this course is to introduce the student to the theory and application of differential equations. Outcome: Knowledge: At the end of this course the student will have basic knowledge and insight in the use of differential equations in modeling of physical and financial phenomena. Also the student will have knowledge of the basic existence and uniqueness theorems; the analytical and numerical solving and quantitative description of solutions of the following types of differential equations: initial value problems and systems of initial value problems, linear differential equations of second and higher order and boundary value problems. Skills: The student obtains in the module the skill to model real life phenomena with the use of ordinary differential equations. The student can apply the existence and uniqueness theorems of solutions to initial value problems and can solve first order ordinary differential equations, linear differential equations and systems thereof using several techniques. The student can give a qualitative description of systems of nonlinear differential equations. Furthermore the student can solve boundary value problems analytically and in obtaining this skill also learn how to use power series and Sturm-Liouville theory. Finally the student has the skill to solve initial value problems numerically with Runge-Kutta methods, and boundary value problems with finite difference methods, as well as the implementation of these methods on a computer. Course material:

Differential Equations and boundary value problems by Edwards & Penney Numerical Analysis by Kincaid en Cheney

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MATHEMATICS – SECOND SEMESTER WISK624: MEASURE AND INTEGRATION THEORY II Author: JJ Grobler Version: 17/09/2010 Contact hours per week : Theory: 2 Practical: 2 Purpose: The purpose of this course is to introduce the learner to more advanced topics in the theory of measure and integration and to equip the learner with the necessary tools to understand and apply modern analytic theories. Outcome: After the completion of this module, you should have the knowledge and skills specified in the Calendar of the Faculty of Natural Sciences. In particular your will have acquired the following knowledge and skills: Knowledge: You should know the theory of function spaces and be conversant with the different modes of convergence of a sequence of functions. Your should know the elementary properties of Lp spaces and know the Theorem of Egoroff. You should be acquainted with the notion of uniform integrability of sets of functions. The theory of the Daniell integral should be known including the Daniell representation theorem. You should be conversant with the different criteria of weak convergence of measures defined on metric spaces. You should know how to define a measure as the limit of a projective system of measures and be able to show that it exists (Theorem of Kolmogorov). As an application you should be able to show that there exists a stochastic process with the properties of Brownian motion. Skills: You should be skilled the techniques used for the solution of problems in the theory, you should be skilled in presenting the theory through seminars; you should be able to do the necessary research in preparation for a seminar lecture and to solve the problems set as exercises in the course. Course material:

Reële Analise en Maat- en Integrasieteorie, JJ Grobler, Derde Uitgawe, Potchefstroom (2005)

Mathematical Analysis, TM Apostol, Second Edition, Addison- Wesley, Reading, Massachusetts

Analysis 1 and 2 W Walter, Dritten Auflage, Springer-Lehrbuch, Springer-Verlag, Berlin, Heidelberg, New York

Probalility and Measure Theory, RB Ash and CA Doleans-Dade, Second Edition, Harcourt-Academic Press San Diegeo, San Francisco, New York, Boston, London, Toronto, Sydney, Tokyo

Measure Theory PR Halmos, D van Nostrand, Princeton, New Jersey Integration AC Zaanen, North-Holland, Amsterdam

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