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　　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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