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

Topics include algebraic structures: groups, rings (including some elementary number theory), fields, and vector spaces.

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.

A selection of projects with a goal of discovery of properties and patterns in mathematical structures. The choice of projects varies from year to year and is drawn from algebra, analysis, discrete mathematics, geometry, applied mathematics, and statistics.

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 elements of the theory of matrices and vector spaces.

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

Topics include differential and integral calculus of functions of several variables.

Topics include differential and integral calculus of functions of several variables.