# GRE Mathematics Syllabus

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GRE MATHEMATICS SUBJECT TEST SYLLABUS (AS PUBLISHED BY ETS)

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

NOTE:

• The above content descriptions may assist students in preparing for the test. The percents given are estimates; actual percents will vary somewhat from one edition of the test to another

• The above descriptions of topics covered in the test should not be considered exhaustive; it is necessary to understand many other related concepts

### About GRE Mathematics Subject Test Preparation (by ETS)

GRE Mathematics Subject Test questions are designed to measure skills and knowledge gained over a long period of time. Although you might increase your scores to some extent through preparation a few weeks or months before you take the test, last minute cramming is unlikely to be of further helpful.

• A general review of your college courses is probably the best preparation for the test. However, the test covers a broad range of subject matter, and no one is expected to be familiar with the content of every question.

• Use Practice Books to become familiar with the types of questions in the GRE Mathematics Test, paying special attention to the directions. If you thoroughly understand the directions before you take the test, you will have more time during the test to focus on the questions themselves.