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
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