Topics include real vector spaces, subspaces, linear dependence, span, matrix algebra, determinants, basis, dimension, inner product spaces, linear transformations, eigenvalues, eigenvectors, and proofs. Ordinary differential equations and first-order linear systems of differential equations; explicit solutions; qualitative analysis of solution behavior; linear structure, existence, and uniqueness of solutions. Partial differential equations.

Ordinary differential equations and first order linear systems of differential equations; methods of explicit solution; qualitative methods for the behavior of solutions; theoretical results for the linear structure, existence, and uniqueness of solutions.

Real vector spaces, subspaces, linear dependence and span, matrix algebra and determinants, basis and dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, proofs of basic results.

Set theory, logic, proof techniques, mathematical induction, relations and functions, recursion, combinatorics, elementary number theory, trees and graphs, analysis of algorithms. Emphasis on topics of relevance to mathematics and computer science majors.

Advanced calculus course focusing on vectors, curves and surfaces in 3-dimensional space, differentiation and integration of multivariate functions, line and surface integrals, and, in particular, the theorems of Green, Stokes, and Gauss.

A second course in single-variable calculus. Applications of integration, techniques of integration, numerical integration, indeterminate forms, improper integrals, parametrized curves, polar coordinates, infinite sequences and series, and power series.

First course in a three-semester calculus sequence, this course covers differential calculus through the study of limits, continuity, differentiation, applications of differentiation, and an introduction to integration.

Math 100B is the second course in a two-semester sequence in applied calculus. Techniques of integration, periodic functions, Taylor polynomials, multi-variable calculus, and differential equations, with applications to business, economics, and science.

MATH 100A is the first course in a two-semester sequence in applied calculus. Lines, algebraic functions, exponential functions, logarithmic functions, limits, derivatives, and integrals, with applications.

Trigonometric functions and their graphs; trigonometric identities and equations; inverse trigonometric functions; solving triangles; complex numbers.