Transcript Subject GRE / AGRE Maths

A Workshop on
Subject 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 Exam
and 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 calculusbased 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 applicability
This 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/G
RE-Mathematics-REA---The-Best-Test-Prep-forthe-GRE-Test-Preps
• http://sfmathgre.blogspot.com/
http://onlineclasses.nanotechbiz.org/