• Archana Receives the Donna B. Hamilton Award

    Archana Khurana has been selected to receive the Donna B. Hamilton Award for Excellence in Undergraduate Teaching in a General Education Course.  Awards are based solely on student nominations and are solicited from across campus.  From the many nominations received, the selection committee was very impressed by the student experience… Read More

  • Yanir Receives a Do Good Campus Fund Grant

    Yanir’s proposal on “Incorporating outreach into the curriculum via experiential learning” is one of the only 27 projects out of 140 submissions that were funded by the UMD Do Good Campus Fund. Read More

  • Congrats to 3 CMNS Students Named Goldwater Scholars

    Congratulations to UMD’s 3 Goldwater Scholars this year, all from CMNS: Junior physics and mathematics double-degree student Yash Anand Sophomore atmospheric and oceanic science and physics double-degree student Malcolm Maas Junior biological sciences and mathematics double-degree student Jerry Shen Over the last 15 years, UMD’s nominations yielded 49 scholarships—No. 2… Read More

  • Maria Cameron Receives the 2024 MURI Award

    Congratulations to Maria Cameron for her MURI award. MURI are multidisciplinary university research initiative grants that are awarded by the department of defense. Cameron’s grant is sponsored by the office of naval research. Her team includes Balakumar Balachandran (ME) and Miao Yu (ME). This is a project on “disorder-influenced collective… Read More

  • A $27.2M Gift to the Math Department by the Brin Family

    The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students. The official university’s press… 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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