Topics include elements of the theory of matrices and vector spaces.

Topics include elements of the theory of matrices and vector spaces.

Studies some aspects of discrete mathematics. Topics include sets, functions, elementary probability, induction proofs, and recurrence relations.

Studies some aspects of discrete mathematics. Topics include sets, functions, elementary probability, induction proofs, and recurrence relations.

Topics include the real number system, convergence of sequences and series, power series, uniform convergence, compactness and connectedness, continuity, abstract treatment of differential and integral calculus, metric spaces, and point-set topology.

Topics include differentiation and integration of functions of a complex variable, the Cauchy integral formula, residues, conformal mapping, and applications to physical science and number theory.

Abstract algebra is the study of the common principles that govern computations with seemingly disparate objects. One way to begin is by studying rings, which are sets with two operations, typically addition and multiplication. Examples include the integers, the integers modulo n, and polynomials in n variables. Our goal is to study a definition of rings that unifies all of the important examples above and more.

Graph theory gives us both an easy way to pictorially represent many major mathematical results and insights into the deep theories behind them. Graphs seem simple -- they're just collections of dots connected by curves -- but are very rich structures that arise naturally in applications ranging from social networks to electric power grids. We will examine properties such as isomorphism, connectivity, planarity, and coloring using classic examples such as paths, cycles, trees, complete graphs, and polyhedral graphs.

This is an introduction to differential equations for students in the mathematical or other sciences. Topics include first-order equations, second-order linear equations, and qualitative study of dynamical systems

This course develops the ideas of probability simultaneously from experimental and theoretical perspectives. The laboratory provides a range of experiences that enhance and sharpen the theoretical approach and, moreover, allows us to observe regularities in complex phenomena and to conjecture theorems. Topics include: introductory experiments; axiomatic probability; random variables, expectation, and variance; discrete distributions; continuous distributions; stochastic processes; functions of random variables; estimation and hypothesis testing.