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# Mathematics Subject GRE

If you are in college or university, Mathematics Subject GRE Test is important. It is used by American Universities to select candidates for Ph.D. programs.

Cheenta Advanced College Mathematics Program covers all the topics tested in Math Subject GRE. Additionally, we have general application assistance tools (for selecting universities, writing Statement of Purposes, seeking Recommendation Letters).

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## What is Math Subject GRE?

Mathematics subject GRE is a 170 minute - 66 question - 990 points examination, that tests a student's proficiency in college level mathematics. The test is offered several times (3 to 4 times) every year and costs about USD 200 (including test price, score sending price, books etc.). For registration, test dates and availability of test center, refer to ets.org.

In this article, we discuss test-taking strategies, available resources and preparation methods.

Bottom Line: 170 minutes; 66 multiple choice problems;

Scoring: +1 for every correct answer; -1/4 for every incorrect answer (raw score is scaled later)

## Syllabus

### 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 group theory, rings and modules, field theory, and elementary number theory.

Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability, and integrability, and elementary topology of R and $R^n$. Discrete math logic, set theory, combinatorics, graph theory, and algorithms. General topology, geometry, complex variables, probability and statistics, and numerical analysis.

## Books

The following book-list is useful for a test-focused preparation. (For advanced conceptual clarity and general theoretical development, these titles are NOT ideal.)

• James Stewart's Calculus; Early Transcendental
• Single Variable Calculus
• Multi-Variable Calculus
• Differential Equation
• 50% of the questions are calculus oriented
• Kai Lai Chung's Elementary of Probability Theory with Stochastic Processes
• Probability Theory
• Princeton Review's Mathematics Subject GRE
• Graph Theory
• Mathematical Logic and SET Theory
• Kumaresan's Topology of Metric Spaces
• Topology
• Freitag and Busam, Complex Analysis
• Complex Analysis
• Gallian's Contemporary Abstract Algebra
• Groups, Rings, Fields
• Gilbert Strang's Introduction to Linear Algebra
• Linear Algebra
• Introduction to Real Analysis by Robert G. Bartle, Donald R. Sherbert
• Real Analysis
• Test of Mathematics at 10+2 Level
• Number Theory, Combinatorics, arithmetic

## Before the Test

• A 3-month to 1-year preparation time is sufficient for the test (if you have the basics in place).
• If the fundamental ideas from each of these (most of these) topics are unknown, then one should prepare for at least one to two years.
• Every 15 days of preparation should be followed by one model test. It is the time management, that is most critical of all aspects of the test.
• In Calculus, it is extremely important to be able to relate graphs with first and second derivatives.
• In differential equation and probability, expect easy questions. However, you need to 'know' the basic information (solutions to different types of differential equations etc.)
• Do not worry about topology or complex analysis if you do not know them already (there will be only three questions from these two topics combined)
• Set a realistic goal. 55 to 60 problems can lead to very good scores and percentiles.

## During the Test

• Rapidly work on 30 to 40 easy problems and do not wait and try the difficult ones. This should be done within the first hour.
• Guessing is potentially harmful. Avoid it unless you have eliminated at least three choices in an educated manner.
• Carry pencils, sharpeners, and erasers to the hall.

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