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

Abstract algebra is the study of the common principles that govern computations with seemingly disparate objects. One way to begin is by studying groups, which are sets with a single operation under which each non-identity element is invertible. Examples include the integers with addition, invertible matrices of size n, permutations of a fixed set, and the symmetries of an object. Our goal is to study a definition of groups that unifies all of the important examples above and more.

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.

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.

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.