A Workshop onSubject GRE / AGRE Maths in 9 Classes, II Hours each Day

&Three mock tests for AGRE

By: Satyadhar Joshi

http://onlineclasses.nanotechbiz.org/

Opening Ceremony on Subject Examand Introduction to Subject Exam

• Advantages of Exam for an Admission and financial Aid for MS / PhD• Level of difficulty of the Exam• Time required for preparation to target exam in Nov each year• Resources and books recommended for the exam• Importance For Management and Computer Science Students • Useful in Research and applicability • Solving and discussion on GRE9768, GRE9367, GRE8767, GR0568, 5

Test by ACRO (in all 10 tests to be covered for AGRE)• Many book reviews (Advanced Engineering Mathematics 8th Erwin

Kreyszig, Calculus Tom IN. Apostol Part 1 and 2) & summary of books on AGRE Maths

• Calculus - 50%• Material learned in the usual sequence of elementary calculus courses - differential and

integral calculus of one and of several variables - includes calculus-based applications and connections with coordinate geometry, trigonometry, differential equations, and other branches of mathematics

• Algebra - 25%• Elementary algebra: basic algebraic techniques and manipulations acquired in high school

and used throughout mathematics Linear algebra: matrix algebra, systems of linear equations, vector spaces, linear transformations, characteristic polynomials, and eigenvalues and eigenvectors Abstract algebra and number theory: elementary topics from group theory; theory of rings and modules, field theory, and number theory Additional Topics - 25%

• Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability and integrability, and elementary topology of R and Rn Discrete mathematics: logic, set theory, combinatorics, graph theory, and algorithms Other topics: general topology, geometry, complex variables, probability and statistics, and numerical analysis The above descriptions of topics covered in the test should not be considered exhaustive; it is necessary to understand many other related concepts. Prospective test takers should be aware that questions requiring no more than a good precalculus background may be quite challenging; some of these questions turn out to be among the most difficult questions on the test. In general, the questions are intended not only to test recall of information but also to assess test takers' understanding of fundamental concepts and the ability to apply those concepts in various situations.

About the Extreme Max Session

• This session will be of 5 hours • Pre-Calculus (2 hours)• Calculus 1 (1 hour)• Calculus 2 (1 hour)• Differential equations (1 hour)• Which all accounts to around 50% of the exam • 50% of exam in 5 hours session

Know about the applicabilityThis studies help you in long term

• Application of learning• Mathematical finance• Example: Partial differentiation, probability• Quantitative Marketing• Example:

What is business decision making

• Probability• Statistics • Continuous & discreet functions• Regression• Time series Models• Time-frequency analysis

• Business Statistics: Contemporary Decision Making, 5th Edition by Ken Black, Wiley

Application to quantitative Finance

• Applications in finance: • Binomial asset pricing function, • Brownian motion, • Martingale process , • Stochastic Integrals, • Ito’s and Girsanov’s theorem, • stochastic differential equations, • continuous time financial models, • Hedging strategies, • Black Sholes formulas, Term structure

Plan for Each Day

• Theory of the Chapter and its application in various subjects

• Solved Numerical in the Subject • Test for each chapter of around 20 Question from

the 5 tests released by ETS with detailed solutions

• Formulae book of each chapter to be given• Each topic to end with question of the real exam• Doubt clearing sessions

Pre- Calculus (Day 1)

• Functions • Analytical Geometry• Polynomial Equations • Logarithms• Trigonometry

Business Examples

• Cost is function of time• Many variations may be either of the curves

we study here like earths motion around sun is elliptic, why?

• Degree two equations must be solved • Exponential and logarithmic means that effect

of the problems is dependent as we go along ie. Increasing as a exponential function

Calculus 1 (Day 2)

• Limit • Importance of Convergence • First and Second derivatives• Practical Problems for Rates • Maximum and Minima • Integrals• Series with focus on Taylor Series

Day 2

Calculus 2 (Day 3)

• Vector Calculus and 3D Geometry • Various type of coordinate System• Partial Differentiation and its interpretation • Line Integrals (Also Ab initio)• Double Integrals • Green Theorem

Business Case for class three

Differential Equations (Day 4)

• All types of Linear Differential Equations

Business case for Class 4

Linear Algebra (Day 5, 13th march)

• Matrix, Determinants• Eigen values and vectors • Linear Transformations

Business case for linear algebra

Number Theory & Abstract Algebra (Day 6)

• Divisibility• Group • Euclidean algorithms for greatest common divisor • Congruencies• Binary Structure and Definition of Group• Group Table • Cyclic and Sub Groups • Homomorphism and Isomorphism • Rings and Fields

Business case for class 6

Additional Topics (Day 7)

• Set Theory• Permutations Combinations• Point Set Topology • Complex Variables

Business case for class 7

3 Mock Tests on Maths AGRE (Day 8-9)

• 3 Mock test framed just on the pattern on Subject GRE

• Giving and checking progress on 3 tests provided by ETS

Why mock tests and their use

References

• Crack the GRE Maths exam by Princeton review• http://www.mathematicsgre.com/• http://www.mathcity.org/papers/gre/• Maths Subject Test, Morris Bramson, ACRO 5 test• 4 GRE Maths Subject Test Provided by ETS• http://www.isbnlib.com/preview/0878916377/

GRE-Mathematics-REA---The-Best-Test-Prep-for-the-GRE-Test-Preps

• http://sfmathgre.blogspot.com/http://onlineclasses.nanotechbiz.org/