• 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

  • 2024 Michael Brin Dynamical Systems Prize for Young Mathematicians Awardees

    Math is excited to announce that Francisco Arana-Herrera has been awarded the 5th Michael Brin Dynamical Systems Prize for Young Mathematicians.  The prize was shared between Francisco and Rohil Prasad. Details about eh prize and previous winners can be found at  https://science.psu.edu/math/research/dynsys/dynamical-systems-prize-young-mathematicians Read More

  • UMD Launches Award to Recognize Dual Majors in Computer Science and Mathematics

    Starting Spring 2025, the Grant Family Outstanding Achievement Undergraduate Student Award will recognize graduating seniors excelling in both fields. Link to the article can be read here: https://www.cs.umd.edu/article/2024/11/umd-launches-award-recognize-dual-majors-computer-science-and-mathematics Read More

  • Jonathan Poterjoy and Kayo Ide join new $6.6 million NOAA consortium

    Congratulations to AOSC's Jonathan Poterjoy and Kayo Ide (also of math and IPST) on joining a new NOAA consortium to improve the accuracy of weather forecasts.  Called CADRE, the $6.6 million initiative will focus on data assimilation, which uses observations to improve model predictions of natural systems, like Earth's atmosphere, over time.… Read More

  • Alfio Quarteroni receives the Blaise Pascal Medal in Mathematics

    Congratulations to Alfio Quarteroni for winning the 2024 Blaise Pascal Medal in Mathematics The message from the European Academy of Sciences reads: We are excited to announce that Professor Alfio Quarteroni has been awarded the esteemed 2024 Blaise Pascal Medal in Mathematics for his outstanding contributions to the field, particularly in… 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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