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GRE Mathematics Subject Test Prep

The essence of mathematics is its freedom. -- Georg Cantor

According to ETS, the test consists of:
  • Calculus -- 50%
    • Material learned in the usual sequence of elementary calculus courses -- differential and integral calculus of one and 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

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