GRE stands for Graduate Record Exam.

Many graduate math programs require or recommend taking the GRE Math Subject Exam for admission to their department. There is also a GRE General Exam that may be required, which is different, and less important (it is similar to the SAT test).

Here is some old descriptive info from 2012: The Math Subject exam is 2 hours and 50 minutes long, and it consists of approximately 66 multiple-choice questions drawn from courses commonly offered at the undergraduate level.

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 equuations, 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.

Additional Topics – 25%: 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.

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GRE general test info (verbal and quant), including free study material.

http://www.ets.org/gre/revised_general/prepare/

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GRE subject exam info: you might search for:

gre_0809_math_practice_book.pdf

GRE subject exam sample (former students have recommended this study guide):

http://www.randomhouse.com/princetonreview/catalog/display.pperl?isbn=9780375429729

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. There was a discussion entry there about finding past GRE math subject exam questions to practice on: http://math.stackexchange.com/questions/5892/gre-past-papers