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

An introduction to abstract reasoning in the context of real analysis. Topics will be drawn from the real numbers, mathematical induction, functions, sequences, and continuity. The emphasis is on formal mathematical reasoning and writing through proofs.

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.

Dynamical systems are mathematical models that evolve with time -- for example, the population of a species in an ecosystem or the price of a financial asset. This course will focus on discrete-time models where one iterates a single variable function and follows the evolution of points in its domain. Our aim will be to study the qualitative, long-term behavior of these models by developing mathematical theory and doing simulation. Topics will include periodicity, bifurcations, chaos, fractals, and computation.

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.