I just need a QR. I don't need math in my major:
If there is any chance you will need calculus eventually (for example, if you might major in Economics or take the Political Economy track in Politics) then take a course from the calculus sequence (MAT103/MAT104/MAT201) while you still remember the math you learned in high school. Note: for some programs MAT102 is acceptable, but not for others.) Students majoring in humanities or a non-quantitative social science should consider MAT189 or MAT190, a very popular choice that requires only a little knowledge of algebra from high school. Alternatively, students who don't need calculus should search the QR offerings of other departments. COS has at least one very popular choice.
I will likely major in physics, but maybe math:
MAT203/MAT204 is an intermediate sequence of multivariable calculus and linear algebra courses, more theoretical than 201/202 but more concretely computational than 218/217. Recommended for future physics majors or for anyone seriously interested in applied mathematics (rather than 201/202).
I want to be a math major:
Most future math majors take the honors sequence MAT215/217/218 which covers calculus and linear algebra more thoroughly and more theoretically. Note: many future physics majors, especially those interested in theoretical physics, take these courses. Students curious about life beyond calculus may opt to start with MAT214, an introduction to rigorous proofs and formal mathematical argument in a more algebraic setting. All these courses require very strong interest in and aptitude for independent mathematical thinking.
Brief course descriptions and links:
MAT101/102: two semester sequence equivalent to MAT103. Differential calculus with extensive review of precalculus. Introduction to integration. 101 is offered in only in the Fall, 102 only in the Spring. 101 does not fufill the QR requirement.
MAT103: First semester of the standard 3-semester calculus sequence. Topics include limits, continuity, derivatives and their applications, introduction to the definite integral. Offered only in the Fall semester.
MAT104: Second semester of the 3-semester calculus sequence. Topics include techniques and applications of integration, convergence of infinite series and improper integrals, Taylor's theorem, introduction to differential equations and complex numbers.
MAT189 : An introduction to mathematical thinking through interactive explorations in elementary number theory. No prerequisites beyond high school algebra. To be offered in Spring 2012. Course web page under construction but available.
MAT190 :(The Magic of Numbers) Explores some of the intriguing and beautiful mathematics that underlie the arts, technology, and everyday life. Needs only some knowledge of high school algebra. Spring only. Last offered Spring 2010. Course web page not yet available.
MAT200: One semester of multivariable mathematics for finance certificate or for math-track economics majors. Covers selected topics from linear algebra and multivariable calculus in order to give minimal preparation for upper division quantitative courses in economics. (Not sufficient preparation for 300-level math courses).
MAT201: A continuation of 103/104, the third semester in the calculus sequence gives a thorough introduction to multivariable calculus. Topics include limits, continuity and differentiability in several variables, extrema, Lagrange multipliers, Taylor's theorem, multiple integrals, integration on curves and surfaces, Green's theorem, Stokes' theorem, divergence theorem.
MAT202: Linear Algebra, mostly in real n-space. Companion course to 201. Main topics are matrices, linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvalues, eigenvectors and their applications to quadratic forms and dynamical systems.
MAT203: Advanced multivariable calculus. More theoretical version than 201, but less theoretical than 218. A course for those with a strong mathematical background. Recommended for physics majors. Fall Only.
MAT204: Advanced Linear Algebra. Companion course to 203. Spring Only.
MAT214: Rigorous, proof-based intro to classical number theory. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions and quadratic reciprocity. Fall Only.
MAT215:Introduction to analysis. Topics include the rigorous &epsilon - &delta treatment of limits, convergence, and uniform convergence of sequences and series. Continuity, uniform continuity, and differentiability of functions. The Heine-Borel theorem, the Riemann integral, conditions for integrability of functions and term by term differentiation and integration of series of functions, Taylor’s theorem.
MAT217: Rigorous course in linear algebra. Topics include vector spaces, linear transformations, inner product spaces, determinants, eigenvalues, the Cayley-Hamilton theorem, Jordan form, linear systems of differential equations, the spectral theorem for normal transformations, bilinear and quadratic forms.
MAT218: Rigorous course in multivariable analysis. Continuation of 215/217 (or 203/204, with instructor's permission). Topics include metric spaces, completeness, compactness, total derivatives, partial derivatives, inverse function theorem, implicit function theorem, Riemann integrals in several variables, Fubini's theorem, change of variables theorem, and the theorems of Green, Gauss, and Stokes.