Rigorous development of the topology of the real line, theory of metric spaces, and the foundations of calculus. Attention is given to constructing formal proofs. A course of varying content reflecting the needs and interests of students. Time permitting, topics in stochastic processes or statistics are introduced. A course of varying content reflecting the needs and interests of students.
Attention is given to the construction of formal proofs.
Selected topics in ordinary and partial differential equations including Sturm-Liouville problems, Fourier series, Laplace transforms, boundary value problems, and special functions of mathematical physics. A survey of numerical mathematics and continuous algorithms. Topics may include number representation, error analysis, finding roots of equations, interpolation, numerical differentiation and integration, solving systems of linear equations, and numerical methods for differential equations. An advanced analysis course considering topics such as Lebesque measure and integration, Hilbert and Banach spaces, Fourier series, and topology. Topics may include further group theory, field and Galois theory and linear algebra topics such as Jordan normal form.