Special topics in advanced mathematics selected largely by student interest and faculty agreement. May be repeated for credit.
Real Analysis II (Metric spaces and Lebesgue’s measure theory)
This course serves as a sequel to MATH 310 Real Analysis. The first part of this course will cover the main topics surrounding the topology, theory, and applications of metric spaces and their morphisms. In particular we will study certain function spaces that arise as normed vector spaces. Completeness, separability, compactness, and connectedness are some of the themes that will appear throughout the course. Fundamental results in Analysis such as the Heine-Borel Theorem, the Baire Category Theorem, the Bernstein Approximation Theorem, the Stone-Weierstrass Theorem, and the Arzela-Ascoli Theorem will be proved and applied. The second part of this class will be devoted to developing the Lebesgue measure on the real line and the Lebesgue integral along with powerful convergence theorems. Time permitting we will study some Fourier series.
Prerequisite: MATH 310 or permission of instructor.
Advanced Differential Equations
The course will consist of advanced topics in differential equations not usually seen in either ordinary differential equations or partial differential equations, such as: delay differential equations and stochastic differential equations. Boundary value problems, numerical methods, and infinite series solutions.
Prerequisite: MATH 340 or MATH 342 or permission of instructor.
Knot Theory
How knots are described mathematically, how one can distinguish different knots, create new knots, classify knots. Topics include: Reidemeister moves, links, knot colorings, alternating knots, braids, knots and graphs, knot invariants, mirror images, unknotting, number crossing, number applications to biology and chemistry.
Prerequisite: MATH 210, MATH 212, or MATH 214 or permission of instructor