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