Colleg Math in the United States are more less about the math topics outlined below: (Source)
Basics MATH. 1. Introductory Calculus (3 or 4 semester hours). A differential and integral calculus of polynomials and other elementary functions. MATH. 2, 4. Multivcariate Calculus, Limits and Differential Equations (3 or 4 semester hours each). Courses which we describe in two different versions. In the preferred version Math. 2 is a multivariate calculus, while Math. 4 strengthens limits and series and provides an introduction to linear differential equations. A more conventional form is also described in which Math. 2 continues the single variable calculus, while Math. 4 takes up multivariate calculus and a brief introduction to differential equations. MATH. 2P. Introductory Probability. A course of first year level which can follow Math. 1 and may be substituted for Math. 2 when it is appropriate for particular students. MATH. 3. Linear Algebra (3 or 4 semester hours). Linear systems, matrices, vectors, linear transformations, unitary geometry with characteristic values. Applications to geometry.
Advanced level: MATH. 5. Advanced Multivariable Calculus. Primarily vector calculus, Stokes' and Green's theorems and a brief introduction to boundary value problems of partial differential equations. MATH. 6. Algebraic Structures. Groups, rings and fields. MATH 7. Probability and Statistics. Two versions are displayed, one emphasizing statistical inference and one going more deeply into probability. MATH. 8. Numerical Analysis. Numerical methods for integration, differential equations, matrix inversion, estimation of characteristic roots. Oriented towards machine computation. MATH. 9. Geometry. A number of types of courses might do here. We present outlines for a Euclidean geometry for prospective teachers and a differential geometry. MATH. 10. Applied Mathematics. A course to illustrate the principles and basic styles of thought in solving physical or other scientific problems by mathematical methods. Specific content will depend on the persons involved. MATH. 11 or 11-12. Introductory Real Variable Theory. Standard material on the real numbers, continuity, limits, differentiation and integration. The student will learn to make the proofs. MATH. 13. Complex Analysis. Complex numbers, elementary functions, analytic functions, contour integration, Taylor and Laurent Series, conformal mapping, boundary value problems, integral transforms.
Introduction to Computer Science. The computer, algorithms, programming languages, problem solving. Many mathematics departments now offer such a course at first or second year level but for the general mathematics student and for his mathematics teacher CUPM feels that the question of how to begin computation and how to relate it to mathematics is not ready to be resolved by a recommendation.
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