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 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.

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.

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.

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

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 differential and integral calculus of functions of several variables.