- MTH 429H - Honors Real Analysis
Description: Continuation of MTH 327H. Convergence of sequences and series of functions, differentiation and integration in higher dimensional settings. Inverse and implicit function theorems.
- 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: The two primary topics of the course will be Fourier Series and the Fourier Transform. Fourier series are used to express a periodic function in terms of infinite sums of sines and cosines. We will investigate the convergence of Fourier series, which turns out to be a subtle matter. The Fourier transform represents a given function in terms of a continuum of “frequencies”, and has various applications in areas such as Partial Differential Equations, Mathematical Physics, Signal Processing and Medical Imaging. We will develop the theory of the Fourier transform and illustrate its use in the aforementioned areas.
Additional Topics we might cover include (time permitting): Discrete Fourier Transforms, the Fast Fourier Transform (FFT) algorithm, Orthogonal Functions, Abstract Inner Product Spaces, Distributions, and Time-Frequency Analysis.
- 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.
