#### Description

The goal of this course is to introduce the students to the modern mathematical techniques which are applied in signal processing and which are used in a variety of areas, ranging from engineering to medicine and finance. Topics include: Applied Linear Algebra, Frame Theory, Dimensionality Reduction and Manifold Learning, Fourier Series, Discrete Fourier Transform, Fast Fourier Transform, Wavelet Bases, Multiresolution Analysis, and Discrete Wavelet Transform, Interpolation and Sampling. Emphasis will be placed upon mathematical foundations of applicable algorithms, as well as on the ability to implement these algorithms. Will use MATLAB.

#### Prerequisites

Minimum grade of C- in MATH141; and 1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and familiarity with MATLAB is required.

Level of Rigor

Standard

Sample Textbooks

MATH416 Lecture Notes by Czaja and Doboszczak

Applications

Signal and Image Processing, Data Science, Economics, Spectroscopy

If you like this course, you might also consider the following courses

MATH420, MATH464, MATH475, STAT426

Additional Notes

An introductory course in Applied Mathematics, highly recommended for all students interested in applications and data science.

#### Topics

Background Material: Numbers and Computer Arithmetic, Vector Spaces and Linear Transformations; Frame Representations; Principal Component Analysis; Graphs; Laplacian Eigenmaps; Fourier Series; Discrete Fourier Transform; Fast Fourier Transform, Trigonometric Transforms; Hartley Transform; Haar Basis; Wavelet Bases; Discrete Haar Transform; Discrete Wavelet Transform; Applications to Communications, Numerical Methods, Detection, and Compression; Interpolation and Sampling.