• Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More

  • Announcing the Winners of the Frontiers of Science Awards

    Congratulations to our colleagues who won the 2025 Frontiers of Science Award: - Dan Cristofaro-Gardiner, for his join paper with Humbler and Seyfaddini: “Proof of the simplicity conjecture”, Annals of Mathematics 2024. - Dima Dolgopyat & Adam Kanigowski, for their joint paper with Federico Rodriguez Hertz: “Exponential mixing implies Bernoulli”, Annals of Mathematics… Read More

  • 2024 Putnam Results

    We are very excited to report that our MAryland Putnam team ranked 7th among 477 institutions that participated in the 2024 Putnam math competition. Our team members this year were Daniel Yuan, Isaac Mammel, and Clarence Lam. Daniel Yuan ranked 26th among 3,988 participants. Clarence Lam and Isaac Mammel were recognized for… Read More

  • From Math Olympiads to Diplomacy: Meet Visiting Math Professor Qendrim Gashi

    Maryland Global, published a great interview with our visiting professor (and diplomat), Qendrim Gashi. The interview is available at https://marylandglobal.umd.edu/about/news/math-olympiads-diplomacy-meet-visiting-math-professor-qendrim-gashi Read More

  • Eugenia Brin, Longtime Supporter of Science and Performing Arts at UMD, Dies

    Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 Read More
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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.

 

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