- MTH 828 - Real Analysis I (graduate-level)
Description: Lebesgue measure on real line, general measure theory. Convergence theorems, Lusin's theorem, Egorov's theorem, Lp-spaces, Fubini's theorem. Functions of bounded variation, absolutely continuous functions, Lebesgue differentiation theorem.
- MTH 419H - Honors Algebra II
Description: Algebraic field extensions, Galois theory. Classification of finite fields. Fundamental Theorem of Algebra.
- MTH 496 - Capstone in Mathematics: Fourier Analysis with Applications
Description: Fourier series and their convergence. Orthonormal systems and completeness. Discrete and Fast Fourier Transforms. The Fourier Transform, Inverse Fourier Transform, and Abstract Inner Product Spaces. Elementary Theory of Distributions. Applications to Ordinary and Partial Differential Equations, Physics, Signal Processing, and Sturm-Liouville Theory.
- MTH 347H - Honors Ordinary Differential Equations
Description: Separable and exact equations, linear equations and variation of parameters, higher order linear equations, Laplace Transforms, first-order linear systems, classification of singularities, nonlinear systems, partial differential equations and Fourier Series, existence and uniqueness theorems. Emphasis on theory.
- STT 441 - Probability and Statistics I: Probability
Description: Probability, conditional probability and independence. Random variables. Discrete, continuous, univariate, and multivariate distributions. Expectation and its properties, moment generating functions. Law of large numbers, central limit theorem.
- MTH 461 - Metric and Topological Spaces
Description: Set theory, metric spaces, topological spaces, maps, product and quotient topologies. Connected and compact spaces, separation axioms, pointwise and uniform convergence.
