application to graduation

Application to Graduation

• This is a rough guide to the options available to students on the 16 different courses available in the Department of Mathematical Sciences.

• It is not intended to be definitive, and so you should always contact your programme director for advice before selecting your modules.

First Year Modules

MATH101 (Calculus 1)Differentiate and integrate a wide range of functions;

sketch graphs and solve problems involvingoptimisation and mensuration;

understand the notions of sequence and series; and apply a range of tests to determine if a series is convergent.

MATH102 (Calculus 2)Use Taylor series to obtain local approximations to functions;

obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables;

evaluate double integrals using Cartesian and polar co-ordinates

MATH103 (Introduction to Linear Algebra)Manipulate complex numbers and solve simple equations involving them;

solve arbitrary systems of linear equations;understand and use matrix arithmetic, including the computation of matrix

inverses;compute and use determinants;

understand and use vector methods in the geometry of 2 and 3 dimensions;calculate eigenvalues and eigenvectors;

and apply these calculations to the geometry of conics and quadrics.

MATH105 (Numbers and Sets)Use mathematical language and symbols accurately; Understand the nature of a definition, & show that simple definitions are or are not satisfied by given

examples; Use theorems to draw logical conclusions from

given information; Understand the logic of direct proofs & proofs by

contradiction, & construct very simple proofs, including proofs by induction;

Interpret statements involving quantifiers, and negate statements with one or two quantifiers;

Use the language of naive set theory; Understand the integer, rational, real and complex

number systems and the relationship between them.

Computer Science Modules Available:COMP101 (Introduction to Programming in JAVA)

COMP102 (Introduction to Databases)

(GG14 ONLY)COMP103 (Computer Systems)

COMP 108 (Algorithmic Foundations)COMP 109 (Foundations of Computing)

MATH122 (Dynamic Modelling)Solve simple differential equations;

understand some methods of mathematical modelling and, in particular, the need to attach

meaning to mathematical results;develop some differential equations for population

growth, and interpret the results;understand Newton's laws of Mechanics;

do simple problems in projectiles and orbits, some involving polar co-ordinates

Economics & Finance Modules Available:(G1N3, GN11 & GL11 ONLY)

ECON121 (Principles of Microeconomics)ECON123 (Principles of Macroeconomics)

ECON127 (Economic Principles for Business and Markets)ECON130 (Cont Issues in Economic Policy)

ECON159 (European Economic Environment)ACFI 101 (Introduction to Financial Accounting)

ACFI102 (Introduction to Management Accounting)ACFI103 (Introduction to Finance)

MATH162 (Introduction to Statistics)to describe statistical data;

to use the Binomial, Poisson, Exponential and Normal distributions;

to perform simple goodness-of-fit tests;to use the package Minitab to present data, and to

make statistical analysis.

Physics & Environmental Sciences Modules Available:(F344, FGH1, FG31 ONLY)

PHYS102 (The Material Universe)PHYS103 (Wave Phenomena)

PHYS104 (Foundations of Modern Physics)PHYS156 (Practical Skills for Mathematical Physics)

(G1F7 ONLY)ENVS100 (Study Skills and GIS)

ENVS111 (Climate, Atmosphere and Oceans)ENVS158 (Ocean Chemistry and Life)

MATH142 (Numbers, Groups & Codes)Use the division algorithm to construct the greatest

common divisor of a pair of positive integers;Solve linear congruences & find the inverse of an

integer modulo a given integer;Code & decode messages using the public-key

method;Manipulate permutations with confidence;

Decide when a given set is a group under a specified operation & give formal axiomatic proofs;

Understand the concepts of a subgroup, a group action, an orbit & a stabiliser subgroup; use

Lagrange’s theorem;Understand the concept of a group homomorphism

& be able to show that 2 groups are isomorphic;Understand the principles of binary coding & how to construct error-detecting & error-correcting binary

codes.

Psychology & Philosophy Modules Available:(G1X3 ONLY)

PSYC101 (Introduction to Psychology 1)PSYC102 (Introduction to Psychology 2: Development,

Personality & Intelligence)

(GV15 ONLY)PHIL107 (Analysing Philosophical Texts 1)PHIL108 (Analysing Philosophical Texts 2)

PHIL127 (Symbolic Logic 1)

MATH111 (Mathematical IT Skills)Tackle project work, including writing up of reports

detailing their solutions to problems;use computers to create documents containing

formulae, tables, plots and references;use Maple to manipulate mathematical expressions

and to solve simple problems;better understand the mathematical topics covered, through direct experimentation with the computer.

Modern Foreign Languages Modules Available:(GR11 ONLY)

FREN101 (Modern French Language 1)FREN102 (Modern French Language 2)

FREN122 (Introduction to the Short French Narrative)MODL105 (Language Awareness)

(G1R9 ONLY)30 Credits’ worth of Spanish, French or German

Compulsory Modules

Other Mathematical Sciences Modules

Other Subjects’ Modules

MATH248 (Geometry Of Curves)use a computer package to study curves and their evolution in both parametric and algebraic forms.

determine and work with tangents, inflexions, curvature, cusps, nodes, length and other features.

calculate envelopes and evolutes.solve the position and shape of some algebraic curves

including conics.

MATH262 (Financial Mathematics II)Modern portfolio theory

Introduction to markets and optionsDiscrete time Finance

Continuous time finance

MATH264 (Statistical Theory & Methods II)

understand basic probability calculus. be familiar with a range of techniques for solving

real life problems of a probabilistic nature.

MATH263 (Statistical Theory & Methods I)

Have a conceptual and practical understanding of a range of commonly applied statistical procedures.

Have also developed some familiarity with the statistical package MINITAB.

MATH261 (Introduction To Methods Of Operational Research)

Appreciate the operational research approach.Be familiar with a range of standard problems.

Be able to formulate simple `real-world' problems using standard models.

Be able to apply standard techniques.Appreciate the importance of sensitivity analysis.

Second Year Modules

MATH228 (Classical Mechanics)the motion of bodies under simple force systems,

including calculations of the orbits of satellites, comets and planetary motions

rigid body motions including geophysical applications such as the precession of the axis of rotation of the earth.

COMP201 COMP202 COMP207


MATH243 (Complex Functions)The central role of complex numbers in mathematics;

All the classical holomorphic functions;Compute Taylor & Laurent series of such functions;

The content & relevance of the various Cauchy formulae and theorems;

The reduction of real definite integrals to contour integrals;

Computing contour integrals.

ECON211 ECON212 ECON221 ECON222

ECON223 ECON224 ECON241

MATH247 (Commutative Algebra)Work confidently with the basic tools of algebra (sets, maps, binary operations and equivalence relations).

Recognise abelian groups, different kinds of rings (integral, Euclidean, principal ideal and unique

factorisation domains) and fields.Find greatest common divisors using the Euclidean

algorithm in Euclidean domains.Apply commutative algebra to solve simple number-

theoretic problems.

(F344, FGH1, FG31 ONLY)PHYS201 PHYS202 PHYS203 PHYS204

(G1F7 ONLY)ENVS202ENVS222ENVS266ENVS260

MATH244 (Linear Algebra And Geometry)

The geometric meaning of linear algebraic ideas,The concept of an abstract vector space & how it is used

in different mathematical situations,apply a change of coordinates to simplify a linear map,manipulate matrix groups (in particular Gln, On & Son),

Bilinear forms from a geometric point of view.

MATH241 (Metric Spaces & Calculus )Be familiar with a range of examples of metric spaces.Have developed their understanding of the notions of

convergence and continuity.Understand the contraction mapping theorem and

appreciate some of its applications.Be familiar with the concept of the derivative of a vector

valued function of several variables as a linear map.Understand the inverse function and implicit function

theorems and appreciate their importance.Have developed their appreciation of the role of proof and

rigour in mathematics.


FREN201FREN202

(G1R9 ONLY)30 Credits’ worth of Spanish, French or German

Mathematical Sciences Modules

MATH201 (Ordinary Differential Equations)

Elementary techniques for the solution of ODE's,Basic properties of ODE, including main features of initial

value problems and boundary value problems, such as existence & uniqueness of solutions;

The solution of linear systems (homogeneous & non-homogeneous)

with constant coefficients matrix of size 2 & 3;A range of applications of ODE.

MATH224 (Introduction To The Methods Of Applied Mathematics)The solution of basic ordinary differential equations,

including systems of first order equations;The concept of Fourier series & their potential application

to the solution of both ordinary & partial differential equations;

Solve simple first order partial differential equations;Solve the basic boundary value problems for 2nd order

linear partial differential equations using the method of separation of variables.

MATH227 (Mathematical Models: Microeconomics & Population

Dynamics)Use techniques from several variable calculus in tackling

problems in microeconomics.Use techniques from elementary differential equations in

tackling problems in population dynamics.Apply mathematical modelling methodology in these

subject areas

MATH225 (Vector Calculus With Applications In Fluid Mechanics)

Work confidently with different coordinate systems.Evaluate line, surface and volume integrals.

Appreciate the need for the operators div, grad & curl together with the associated theorems of Gauss & Stokes.

Recognise the many physical situations that involve the use of vector calculus.

Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and

inviscid fluid flow.

MATH206 (Group Project Module)Work effectively in groups, and delegate common tasks.

Write substantial mathematical documents in an accessible form.

Give coherent verbal presentations of more advanced mathematical topics.

Appreciate how mathematical techniques can be applied in a variety of different contexts.

MATH265 (Measure Theory And Probability )

master the basic results about measures, measurable functions, Lebesgue integrals and their properties;

to understand deeply the rigorous foundations of the probability theory;

to know certain applications of the measure theory to probability and financial mathematics. .

MATH267 (Financial Mathematics I)Time value of money

Annuities Loans and the equation of value

Cash flow models & Investment projects Bonds, Fixed interest security & index-linked security

Term structure of interest rates & Stochastic interest rates models

EDUC500 (Mathematics In Schools)insight into children's mathematical thinking;growing confidence in working with pupils;

an informed view of the role of secondary mathematics teachers and of the environment in which they work;

Experience in the use of computers for word-processing.

MATH268 (Operational Research: Probabilistic Models)

be familiar with a range of techniques for solving probabilistic problems arising in OR and Mathematical

Finance.

MATH266 (Numerical Analysis, Solution Of Linear Equations)

apply numerical methods in a number of different contexts;

solve systems of linear & nonlinear algebraic equations to specified precision;

compute eigenvalues & eigenvectors by the power method;

solve boundary value & initial problems to finite precision;

develop quadrature methods for numerical integration.

Computer Science Modules Available:(GG14 & G1R9 ONLY)

Economics & Finance Modules Available:(G1N3, GN11 & GL11 ONLY)

PHIL207PHIL212PHIL215



Philosophy Modules Available:(GV15 ONLY)

Other Subjects’ ModulesPhysics & Environmental Sciences Modules Available:

ENVS332ENVS335ENVS349ENVS366ENVS372

ENVS376ENVS377ENVS389ENVS461

Environmental Sciences Modules Available:(G1F7 ONLY)

MATH349 (Differential Geometry)Using differential calculus to discover geometrical

properties of explicitly given curves & surfaces;the role played by special curves on surfaces & making explicit calculations with these curves;

Acquiring an intuitive ‘feel’ for what is meant by surface shape;

Understanding the difference between extrinsically defined properties and those which depend only on

the surface metric;Understanding the passage from local to global

properties exemplified by the Gauss-Bonnet Theorem.

MATH360 (Applied Stochastic Models )

a grounding in the theory of continuous-time Markov chains and diffusion processes. They should be able to solve corresponding problems arising in

epidemiology, mathematical biology, financial mathematics, etc.

MATH362 (Applied Probability )To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods

of probabilistic model building for ``dynamic" events occurring over time. To familiarise students with an important area of probability modelling.

MATH361 (Theory Of Statistical Inference)

a good understanding of the classical approach to and especially the likelihood methods for statistical

inference. The students should also gain an appreciation of the blossoming area of Bayesian

approach to inference.

MATH351 (Analysis & Number Theory)

Completions & irrationality, diophantine approx’n & its relation to uniform distribution, appreciate that analysis has a complex unity & have a feel for basic computations in analysis. Calculate rational approx’ns to real & p adic numbers & use this in number theoretic situations. Find approx’ns to functions from families of simpler functions. Work with basic tools from analysis, like Fourier series & continuous functions to prove distributional properties of sequences of numbers.

.

Third Year Modules

MATH331 (Mathematical Economics)

Have further extended their appreciation of the role of mathematics in modelling in Economics and the

Social Sciences.Be able to formulate, in game-theoretic terms,

situations of conflict and cooperation.Be able to solve mathematically a variety of standard problems in the theory of games.

To understand the relevance of such solutions in real situations.

COMP304 COMP305 COMP309 COMP310 COMP313

COMP315 COMP317 COMP319 COMP323

MATH342 (Number Theory)understand and solve a wide range of problems

about the integers and rationals, and have a better understanding of the properties of prime numbers.

ECON306 ECON308 ECON311 ECON322 ECON325 ECON326

ECON327 ECON333 ECON335 ECON340 ECON343

ACFI301 ACFI302 ACFI303 ACFI304 ACFI305 ACFI341

MATH344 (Combinatorics)understand the type of problem to which the

methods of Combinatorics apply, and model these problems;

solve counting and arrangement problems;solve general recurrence relations using the

generating function method;appreciate the elementary theory of partitions and its application to the study of symmetric functions.

MATH343 (Group Theory)Understanding of abstract algebraic systems

(groups) by concrete, explicit realisations (permutations, matrices)

The ability to understand and explain classification results to users of group theory.

To have a general understanding of the origins and history of the subject.

MATH334 (Mathematical Physics Projects)

understood an area of advanced theoretical physics had experience in consulting relevant literature

gained experience in using appropriate mathematics

made a critical appraisal of the current understanding of the area

learnt how to construct a written essay and given an oral presentation.

Modern Foreign Languages Modules Available:(G1R9 ONLY)

15 Credits’ worth of Spanish, French or German

Philosophy Modules Available:(GG13 ONLY)

PHIL346



MATH302 (History Of Mathematics)

Acquire a historical perspective on the development of mathematical ideas and their relationship with

contemporary culture, and through the various methods of assessment become more articulate

about their importance and relevance in the educational scene

MATH324 (Cartesian Tensors And Mathematical Models Of Solids

And Viscous Fluids)understand and actively use the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, and apply mathematical methods for analysis of problems involving the flow

of viscous fluid or behaviour of solid elastic materials.

MATH326 (Relativity)understand why space-time forms a non-Euclidean

four-dimensional manifold;be proficient at calculations involving Lorentz

transformations, energy-momentum conservation, and the Christoffel symbols.

understand the arguments leading to Einstein's field equations and how Newton's law of gravity arises as

a limiting case.be able to calculate the trajectories of bodies in a

Schwarzschild space-time.

MATH325 (Quantum Mechanics)solve Schrodinger’s equation for simple systems,

and have some intuitive understanding of the significance of quantum mechanics for both

elementary systems and the behaviour of matter.

MATH323 (Further Methods Of Applied Mathematics )

to use the method of "Variation of Arbitrary Parameters" to find the solutions of some

inhomogeneous ODE’s, solve simple integral extremal problems including cases with constraints;

classify a system of simultaneous 1st-order linear partial differential equations, & to find the Riemann

invariants & general or specific solutions in appropriate cases; classify 2nd-order linear partial differential equations &, in appropriate cases, find

general or specific solutions.

MATH363 (Linear Statistical Models )

General Linear Models: simple linear regression; one-way analysis of variance; estimation and

inference; two and three-way analysis of variance; more complex designs.

Generalized Linear Models: foundations; exponential family of distributions; estimation and

inference; binary response variables; normal response variables; contingency tables and log-

linear models; other applications

MATH367 (Networks In Theory And Practice)

be able to model problems in terms of networks.be able to apply effectively a range of exact and

heuristic optimisation techniques

MATH399 (Mathematical Project Module)

A range of projects are available within each division, as well as a Maths in Society project.

MATH366 (Mathematical Risk Theory )

Decision Theory Applications of Probability Theory to actuarial risk

models (The collective risk model (aggregate loss models)

The individual risk model (group insurance models) Ruin Theory

Claim reserving methods

MATH350 (Analytic Methods In Higher Geometry)

understand the concept of duality in Linear Algebra, be able to work with tensors,

understand the basic concepts of geometry of smooth manifolds,

be able to perform computations with differential forms in local coordinates,

know certain applications of differential forms to topology and Hamiltonian mechanics.

MATH332 (Population Dynamics)Use analytical and graphical methods to investigate population growth and the stability of equilibrium

states for continuous-time and discrete-time models of ecological systems.

Relate the predictions of the mathematical models to experimental results obtained in the field.

Recognise the limitations of mathematical modelling in understanding the mechanics of

complex biological systems..

MATH322 (Chaos And Dynamical Systems)

Understand the possible behaviour of dynamical systems with particular attention to chaotic motion;

be familiar with techniques for extracting fixed points and exploring the behaviour near such fixed

points;understand how fractal sets arise and how to

characterise them.

MATH364 (Medical Statistics)identify the types of problems found in medical

statistics; demonstrate the advantages and disadvantages of different epidemiological study designs; apply appropriate statistical methods to problems arising in epidemiology and interpret

results; explain and apply statistical techniques used in survival analysis; critically evaluate statistical issues in the design & analysis of clinical trials

discuss statistical issues related to systematic review & apply appropriate methods of meta-analysis

apply Bayesian methods to simple medical problems

Economics & Finance Modules Available:(G1N3 & GL11 ONLY)

Computer Science Modules Available:(GG14 ONLY)

PHIL306PHIL309PHIL310PHIL316PHIL317PHIL326

PHIL329PHIL332PHIL340PHIL346PHIL361PHIL362

Philosophy Modules Available:(GG13 & GV15 ONLY)

PHYS363 PHYS370 PHYS374 PHYS375 PHYS377 PHYS378

PHYS381 PHYS382 PHYS387 PHYS388PHYS389 PHYS393

Physics Modules Available:(F344, FGH1, FG31 ONLY)

MATH443 (Curves & Singularities)A confident use of the singularity theory of functions of

one variable, including unfolding theory, in concrete applications. A knowledge of fundamental constructions such as that of an envelope of curves or surfaces, and the dual of a curve or surface. A grounding in the theory of

differentiable manifolds and transversality as geometrical tools. A preparation for further study of singularity theory, including functions of several variables and mappings, and elements of symplectic geometry

MATH449 (Galois Theory)Know why and how a polynomial equation of degree up

to 4 can be solved in radicals.Understand why a solution in radicals is impossible in

general for the degree greater than or equal to 5.Understand when a polynomial can be solved in radicals.Know when a geometric construction can be done by a

ruler and compass.Know what is the Galois group of a polynomial which

permits the above results.

MATH456 (Intro to Knot Theory & Low Dimensional Topology)

tell whether two simple knots in 3-space can be transformed into one another without cutting or tearing;

compute the Jones, Alexander, HOMFLY & Kauffman polynomials in simple cases; represent a link as the

closure of a braid; give e.g.’s of orientable surfaces that bound a given knot in 3-space; determine whether two braids (say given by their diagrams) represent the same element in the braid group; compute the genus & the

Euler characteristic of 2-manifold; compute the genus of a ramified covering of a 2-manifold

MATH455 (Differentiable Functions)technique of reducing functions to local normal forms;

understand the concept of stability of mappings; construct versal deformations of isolated function

singularities.

MATH446 (Lie Groups & Lie Algebras)basic results about Lie groups and Lie algebras and their

relation, classical Lie groups and Lie algebras, basic structure and classification results about Lie groups and

Lie algebras.

Fourth Year Modules

MATH426 (Mathematical Biology)Use techniques from difference equations and ordinary and partial differential equations in tackling problems in

biology.Apply mathematical modelling methodology in this area.

MATH432 (Mathematical Physics Project)

understood an area of advanced theoretical physics had experience in consulting relevant literature

gained expertise in using appropriate mathematicsmade a critical appraisal of the current state of

knowledge of the arealearnt how to construct an essay

gained familiarity with a scientific word-processing package such as TeX

acquired skills of oral presentation.

MATH442 (Representation Theory of Finite Groups )

use representation theory as a tool to understand finite groups;

calculate character tables of a variety groups.

Physics Modules Available:(F344, FGH1, ONLY)

PHYS480PHYS489PHYS490PHYS491PHYS493PHYS497PHYS499

MATH441 (Higher Arithmetic )apply analytic techniques to arithmetic functions

understand basic analytic properties of the Riemann zeta function

understand Dirichlet characters and L-seriesunderstand the connection between Ingham's theorem

and the Prime Number Theorem

MATH431 (Introduction To Modern Particle Theory)

The Feynman diagram pictorial representation of particle interactions.

The role of symmetries & conservation laws in distinguishing the strong, weak & electromagnetic

interactions.Spectrum & interactions of elementary particles & their

embedding into Grand Unified Theories (GUTs).The flavour structure of the standard particle model &

generation of mass through symmetry breaking.Phenomenological aspects of GUTs.


FREN301FREN302

PLUS OTHER FRENCH MODULES



MATH410 (Manifolds, Homology & Morse Theory)

give examples of manifolds, particularly in low dimensions;

compute homology groups, Euler characteristics and degrees of maps in simple cases;

determine whether an explicitly given function is Morse & to identify its critical points & their indices;

use the Morse complex to compute Euler characteristics and, in simple cases, homology.

MATH423 (Introduction To String Theory)

The properties of the classical string.The basic structure of modern particle physics and how it

may arise from string theory.The basic properties of first quantized string and the

implications for space-time dimensions.String toroidal compactifications and T-duality.

MATH425 (Quantum Field Theory)be able to compute simple Feynman diagrams,

understand the basic principles of regularisation and renormalisation

be able to calculate elementary scattering cross-sections.

MATH424 (Analytical & Computational Methods For Applied

Mathematics)obtain solutions to certain important PDEs using a variety

of analytical techniques and should be familiar with important properties of the solution.

apply a range of standard numerical methods for solution of PDEs and should have an understanding of relevant

practical issues

MATH421 (Linear Differential Operators in Mathematical Physics)

understand and actively use the basic concepts of mathematical physics, such as the concept of generalised

functions, Sobolev spaces, weak solutions, and apply powerful mathematical methods to problems of electro-

magnetism, elasticity, heat conduction and propagation of waves

MATH490 (Project For M.Math)(30 Credits)

Gained a greater understanding of the chosen mathematical topic. Gained an appreciation of the

historical context. learned how to abstract mathematical concepts and explain them.

had experience in consulting related relevant literature. Learned how to construct a written project report. Had

experience in making an oral presentation. Gained familiarity with the standard scientific word-processing

packages LaTeX or TeX

MATH444 (Elliptic Curves)The ability to describe and to work with the group

structure on a given elliptic curve. Understanding and application of the Abel-Jacobi theorem. To estimate the

number of points on an elliptic curve over a finite field. To use the reduction map to investigate torsion points on a curve over Q. To apply descent to obtain so-called Weak Mordell-Weil Theorem. Use heights of points on elliptic curves to investigate the group of rational points on an

elliptic curve. Understanding and application of Mordell-Weil theorem. Encode and decode using public keys.

MATH427 (Waves. Mathematical Modelling)

Students will learn essential modelling techniques in problems of wave propagation. They will also

understand that mathematical models of the same type can be successfully used to describe different physical

phenomena. Students will also study background mathematical theory in models of acoustics, gas

dynamics, and water waves

MATH420 (Advanced Mathematical Physics Project)

understood an area of current research in theoretical physics

had experience in locating and consulting relevant research material, particularly through use of journals

and the Internet learnt & deployed appropriate mathematical techniques

learnt how to produce a dissertation acquired and practised skills of oral presentation

MATH499 (Project For M.Math)(15 Credits)

Gained a greater understanding of the chosen mathematical topic. Gained an appreciation of the

historical context. learned how to abstract mathematical concepts and explain them.

had experience in consulting related relevant literature. Learned how to construct a written project report. Had

experience in making an oral presentation. Gained familiarity with the standard scientific word-processing

packages LaTeX or TeX

G100: BSc MathematicsFrom Application to Graduation

Application Successful!

Graduation!

Year 1Compulsory Modules

MATH101 Calculus 1

MATH102 Calculus 2

MATH103 Introduction to Linear Algebra

MATH105 Numbers and Sets

MATH122 Dynamic Modelling

MATH142 Numbers, Groups and Codes

MATH162 Introduction to Statistics

And One ofMATH111 Mathematical IT Skills

COMP101 Introduction to Programming in JAVA


MATH201 Ordinary Differential Equations

MATH243 Complex Functions

MATH244 Linear Algebra and Geometry

At least one fromMATH241 Metric Spaces and Calculus

MATH247 Commutative Algebra

MATH248 Geometry of Curves

And at least one from

MATH224 Introduction to the Methods of Applied mathematics

MATH225 Vector Calculus with Applications in Fluid Mechanics

MATH227 Mathematical Models: Microeconomics and Population Dynamics

MATH228 Classical Mechanics

MATH266 Numerical Analysis, Solution of Linear Equations

And a further 3 modules from the above list or

MATH206 Group Project

MATH261 Introduction to Methods of Operational Research

MATH262 Financial Mathematics 2

MATH263 Statistical Theory and Methods 1


MATH265 Measure Theory and Probability

MATH267 Financial mathematics 1

MATH268 Operational Research: Probabilistic Models

EDUC500 Mathematics in Schools

Or modules in computer science, physics, geophysics, or geology.

Year 38 modules from

MATH302 History of Mathematics

MATH322 Chaos and Dynamical Systems

MATH323 Further Methods of Applied Mathematics

MATH324 Cartesian Tensors & Mathematical Models of Solids and Viscous Fluids

MATH325 Quantum Mechanics

MATH326 Relativity

MATH331 Mathematical Economics

MATH332 Population Dynamics

MATH334 Mathematical Physics Projects

MATH342 Number Theory

MATH343 Group Theory

MATH344 Combinatorics

MATH349 Differential Geometry

MATH350 Analytic Methods in Higher Geometry

MATH351 Analysis and Number Theory

MATH360 Applied Stochastic Models

MATH361 Theory of Statistical Inference

MATH362 Applied Probability

MATH363 Linear Statistical Models

MATH364 Medical Statistics

MATH366 Mathematical Risk Theory

MATH367 Networks in Theory and Practice

MATH399 Project Module

In exceptional cases, up to 2 MMath modules may be taken, subject to

approval. See G101 board for details

General MathsApplied Maths / Theoretical PhysicsPure MathsStatistics / ORProject ModulesOther Subjects

G1X3: BSc Mathematics With EducationFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2


One ofMATH105 Numbers and Sets

PSYC101 Introduction to Psychology 1

One ofMATH111 Mathematical IT Skills


And Three of MATH142 Numbers, Groups and Codes



PYSC102 Introduction to Psychology 2

If any of MATH122, MATH142 OR MATH162 are not taken in the first year, they must be taken in the second year.





At least two fromMATH241 Metric Spaces and Calculus




And at least two fromMATH206 Group Project













And one more module from the above lists or in computer science, physics,

geophysics, or geology subject to approval



MATH399 Project Module (Maths in Society)

And six modules fromMATH322 Chaos and Dynamical Systems




MATH326 Relativity

















approval. See G101 board for details of MMath modules


G110: BSc Pure MathematicsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2





MATH111 Mathematical IT Skills


Either MATH111 or MATH122 may be replaced by suitable non-mathematical

sciences modules. Please talk to programme director for further details.

If MATH111 is not taken in Year 1, it must be taken in Year 2





At least one modules from MATH241 Metric Spaces and Calculus



And 4 modules from those above or















In exceptional cases, up to 2 non mathematical sciences modules may be

taken, subject to approval.

Year 3At least 4 modules from







MATH399 Project Module (Pure Mathematics)

And 4 modules from those above orMATH302 History of Mathematics





MATH326 Relativity











In exceptional cases, 1 non mathematical sciences module or up to 2 MMath modules may be taken, subject to approval. See G101 board for details. No more than 2 project modules may be

taken


G1F7: BSc Mathematics with Ocean and Climate StudiesFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2




ENVS100 Study Skills and GIS

ENVS111 Climate, Atmosphere and Oceans

ENVS158 Ocean Chemistry and Life






ENVS202 Key Skills for Ocean Scientists

ENVS222 Statistics for Environmental Scientists

ENVS266 Estuaries – Their Geochemistry and Life

And one of ENVS260 Water and Air




ENVS332 Ocean Dynamics

ENVS335 Ocean Carbon Cycle

ENVS349 Sea Practical

ENVS366 Marine Sciences – Special Topics

ENVS377 Ocean Sciences Research Project

And 2 modules from MATH322 Chaos and Dynamical Systems


ENVS372 Fluvial Environments

ENVS376 Coastal Environments: Spatial and Temporal Change

ENVS389 Climate Change – A Critical Review

ENVS461 Evolution, Oceans and Climate


GG13: BSc Mathematics and StatisticsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2







And One of MATH142 Numbers, Groups and Codes

COMP102 Introduction to Databases





At least one from





And at least three fromMATH142 Numbers, Groups and Codes






MATH241 Metric Spaces and Calculus








Up to two additional modules, usually from the list above




At least one module fromMATH360 Applied Stochastic Models





Five more modules from the list above or the list below






MATH326 Relativity










PHIL346 Philosophy of Mathematics




GG14: BSc Mathematics & Computer ScienceFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2




One ofCOMP103 Computer Systems

COMP109 Foundations of Computing




COMP202 Complexity of Algorithms


At least two fromCOMP201 COMP213

COMP207 COMP219

And at least one fromCOMP104 COMP218

And at least two from



MATH227 Mathematical Models: Microeconomics & Population Dynamics
















A total of 8 modules from the above must be taken.

Year 3Compulsory Module

COMP317 Semantics of Programming Languages

Two modules fromCOMP304 COMP305


One module fromCOMP310 COMP313 COM315

At least three modules fromMATH302 History of Mathematics





MATH326 Relativity


















A total of 8 modules from the above must be taken.


GV15: BA Philosophy & MathematicsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2


PHIL107 Analysing Philosophical Texts 1

PHIL108 Analysing Philosophical Texts 2

PHIL127 Symbolic Logic 1

One of MATH142 Numbers, Groups and Codes


And one additional Philosophy Module


PHIL207 Symbolic Logic 2

Four Modules from




















And a further 3 modules from PHIL212 PHIL215

PHIL219 PHIL227

PHIL228 PHIL236

PHIL237 PHIL239


PHIL346 Philosophy of Mathematics

Four modules fromMATH302 History of Mathematics





MATH326 Relativity


















And a further 3 modules fromPHIL306 PHIL309 PHIL310

PHIL316 PHIL317 PHIL326

PHIL329 PHIL332 PHIL340

PHIL361 PHIL362


GL11: BA Economics and Mathematics From Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2



One ofMATH105 Numbers and Sets


AndECON159 European Economic Environment



AndECON130 Cont Issues in Economic Policy



At least two from

ECON222 ECON224

ECON211 ECON241

Three fromMATH201 Ordinary Differential Equations




















Up to two additional modules, usually from the list above

Year 3Two modules from



At least one module fromECON306 ECON308 ECON326

ECON340 ECON343

4 more modules from the list belowMATH302 History of Mathematics





MATH326 Relativity






















Graduation!


MATH101 Calculus 1

MATH102 Calculus 2




ACFI101 Introduction to Financial Accounting

ACFI102 Introduction to Management Accounting

ECON127 Economic Principles for Business and Markets




And a further 2 modules fromMATH243 Complex Functions







MATH227 Mathematical Models: Microeconomics & Population Dynamics










Plus four modules fromACFI201 ACFI204 ACFI205 MKIB227

ULMS251 ECON254 MKIB256 ACFI260

ACFI206 ECON212 ECON221 ECON223

ECON233 EBUS209 ACFI202 ACFI203

ECON241 MKIB230 MKIB255 MKIB261

ULMS202 MKIB225 ECON211 ECON222

ECON234 ACFI207 ECON224 ULMS266

ULMS252 ULMS268

Year 3At least 1 module from




2-3 modules to give a total of 4 fromMATH342 Number Theory










MATH326 Relativity










Plus four modules fromACFI304 ACFI320 ECON325 ACFI305MKIB356 ECON311 ACFI301 ECON333ECON335 ECON354 MIKB362 MKIB337ULMS370 MKIB372 ECON322 ECON327ACFI303 ACFI341 ULMS353 MKIB359ACFI302 MKIB338 MKIB363 ECON326

ECON306 ULMS352 ULMS366 ECON308ACFI310

GN11: BSc Mathematics & Business StudiesFrom Application to Graduation


G1N3: BSc Mathematics with FinanceFrom Application to Graduation


Graduation!


MATH201 Ordinary Differential Equations*





ACFI204 Financial Management

2-3 modules to give a total of 8 fromMATH111 Mathematical IT Skills*




MATH224 Introduction to the Methods of Applied mathematics*




ECON241 Securities Markets

*these modules are not available to students coming from XJTLU



ACFI304 Business Finance

ECON311 Methods of Economic Investigation 1: Time Series Econometrics

ACFI341 Finance and Markets

At least two modules fromMATH322 Chaos and Dynamical Systems










And up to two fromACFI301 Theory and Practice of Auditing

ACFI305 Taxation Policy and Practice

ECON308 Financial Economics

ACFI302 Financial Statements Analysis

ACFI303 Advanced Management Accounting


MATH101 Calculus 1

MATH102 Calculus 2



ACFI101 Introduction to Financial Accounting

ACFI103 Introduction to Finance

ECON121 Principles of Microeconomics

ECON123 Principles of Macroeconomics


FG31: BSc Physics and MathematicsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2



PHYS102 The Material Universe

PHYS156 Practical Skills for Mathematical Physics

PHYS103 Wave Phenomena

PHYS104 Foundations of Modern Physics






PHYS201 Electromagnetism

PHYS202 Condensed Matter Physics

PHYS203 Quantum and Atomic Physics

PHYS204 Nuclear and Particle Physics

Year 3One of


PHYS361 Quantum Mechanics & Atomic Physics

EitherPHYS379 Physics Project

Or both ofPHYS378 Advanced Practical Physics


2-4 modules to give a total of 4 maths modules from




MATH326 Relativity

Additional Physics modules to make up to 60 credits

PHYS241 Communicating Science

PHYS246 Accelerators and Radioisotopes in Medicine

PHYS251 Introduction To Stellar Astrophysics


PHYS370 Advanced Electromagnetism

PHYS374 Relativity and Cosmology

PHYS375 Nuclear Physics

PHYS377 Introduction to Particle Physics

PHYS381 Surface Physics

PHYS382 Physics of Life

PHYS387 Materials Physics

PHYS388 Physics of Energy Sources

PHYS389 Semiconductor Applications

PHYS393 Statistical and Low Temperature Physics


FGH1: MMath Mathematical PhysicsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2


















MATH326 Relativity

And one of MATH325 Quantum Mechanics

PHYS361 Quantum Mechanics and Atomic Physics

And one ofPHYS488 Modelling Physical Phenomena

(Project)MATH432 Mathematical Physics Essay

Additional modules from the below list to make up 30 credits at Level 3










PHYS378 Advanced Practical Physics







Additional modules from the Year 4 list to make up 30 credits at Level M



MATH420 Advanced Mathematical Physics Project

PHYS480 Advanced Quantum Physics

Additional modules from the below list to make up 30 credits at Level M

MATH421 Linear Differential Operators

MATH423 Introduction to String Theory

MATH425 Quantum Field Theory

MATH433 Asymptotic Methods for PDEs

MATH426 Mathematical Biology

MATH427 Waves, Mathematical Modelling

MATH431 Intro to Modern Particle Physics

PHYS489 Advanced Particle Physics

PHYS490 Condensed Matter Theory

PHYS491 Advanced Nuclear Physics

PHYS493 Research Skills

PHYS497 Magnetic Structure and Function

PHYS499 Nanoscale Physics and Technology

Additional modules from the Year 3 list to make up 45 credits at Level 3For FGH1 you should emphasise

Mathematics Modules in Years 3 and 4

F344: MPhys Theoretical PhysicsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2

















MATH326 Relativity

And one of MATH325 Quantum Mechanics

PHYS361 Quantum Mechanics and Atomic Physics

And one ofPHYS488 Modelling Physical Phenomena

(Project)MATH432 Mathematical Physics Essay

Additional modules from the below list to make up 45 credits at Level 3











PHYS378 Advanced Practical Physics







Additional modules from the Year 4 list to make up 30 credits at Level M


MATH420 Advanced Mathematical Physics Project

PHYS480 Advanced Quantum Physics

Additional modules from the below list to make up 30 credits at Level M

MATH421 Linear Differential Operators



MATH433 Asymptotic Methods for PDEs


MATH427 Waves, Mathematical Modelling

MATH431 Intro to Modern Particle Theory

PHYS489 Advanced Particle Physics

PHYS490 Condensed Matter Theory

PHYS491 Advanced Nuclear Physics

PHYS493 Research Skills

PHYS497 Magnetic Structure and Function

PHYS499 Nanoscale Physics and Technology

Additional modules from the Year 3 list to make up 45 credits at Level 3

For F344 you should emphasise Physics Modules in Years 3 and 4


G101: MMath MathematicsFrom Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2












At least one fromMATH241 Metric Spaces and Calculus



And at least one from



MATH227Mathematical Models:

Microeconomics and Population Dynamics



And a further 3 modules from the above list or










Or modules in computer science, physics, geophysics, or geology.







MATH326 Relativity
















Plus 3 modules from the Year 4 List, excluding MATH490.


MATH410 Manifolds, Homology & Morse Theory

MATH421 Linear Differential Operators in Mathematical Physics


MATH424 Analytical & Computational Methods for Applied Mathematics



MATH427 Waves. Mathematical Modelling

MATH431 Introduction to Modern Particle Theory

MATH432 Mathematical Physics Project

MATH441 Higher Arithmetic

MATH442 Representation Theory of Finite Groups

MATH443 Curves and Singularities

MATH444 Elliptic Curves

MATH446 Groups and Lie Algebras

MATH449 Galois Theory

MATH455 Differentiable Functions

MATH456 Introduction to Knot Theory and Low Dimensional Topology

MATH499 Project Module for MMath*

MATH490 Project Modulefor MMath (Counts as 2 modules)*

Plus 3 modules from the Year 3 list.*These two modules cannot both be

taken in Year 4


G1R9: BSc Mathematical Sciences with a European Language From Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2




And Two of MATH122 Dynamic Modelling




Plus 30 credit’s worth in your chosen language



And one ofMATH201 Ordinary Differential Equations


And at least one ofMATH244 Linear Algebra and Geometry





And at least one ofMATH206 Group Project




Microeconomics and Population Dynamics



And 2 modules from the above list or






Or modules in computer science.Plus 30 credit’s worth in your chosen

language.

Year 2AYear Spent Abroad

Year 3At least 6 modules from






MATH326 Relativity

















Plus at least 15 credit’s worth in your chosen language.


approval. See G101 board for details.


GR11: BA French and Mathematics From Application to Graduation


Graduation!


MATH101 Calculus 1

MATH102 Calculus 2


FREN101 Modern French Language 1

MODL105 Language Awareness

FREN102 Modern French Language 1

FREN122 Introduction to the Short French Narrative

And one ofMATH122 Dynamic Modelling



FREN201 FREN202

At least one ofMATH201 Ordinary Differential Equations


And 2 modules from the above list orMATH206 Group Project




Microeconomics & Population Dynamics














Plus 2 additional Year 2 French modules.

Year 2AYear Spent Abroad


FREN301 FREN302

4 modules fromMATH302 History of Mathematics





MATH326 Relativity

















Plus 2 additional Year 3 French modules.


approval. See G101 board for details.


application to graduation

Documents

simple proofs

use taylor series

javacomp102 introduction

financemath162 introduction

comp101 introduction

simple equations

simple goodness

simple definitions