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

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.

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

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.

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.

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.

This course will begin with an introduction to number theory, covering material on congruences, prime numbers, arithmetic functions, primitive roots, quadratic residues, and quadratic fields. We will then continue our study of number theory by picking special topics which might include some of the following: Finite Fields, Prime Factorization of Ideals, Fermat's Last Theorem, Elliptic curves, Dirichlet's Theorem on Arithmetic Progressions, the Prime Number Theorem, or the Riemann Zeta function.