01:640:357 - Topics in Applied Algebra

Prerequisite: Math 250 Introduction to Linear Algebra and Math 251 Multivariable Calculus.

Course Description: 

This is a course aiming for undergraduate students majoring in math and engineering who are interested in understanding the importance of linear algebra and its application to problems within and outside mathematics.  The basic concepts and results of linear algebra (vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors, orthogonality and diagonalization) will be reviewed. The course will cover the following topics:  least square approximation, discrete Fourier transformation, numerical computations with matrices, graphs and networks, and image compression. Possible additional topics include: finite element method, systems of ordinary differential equations and linear programming. 

The course will involve several MATLAB computer projects. Some prior knowledge of MATLAB is helpful but not necessary. A general familiarity with computers and some basic programming skills are needed. Purchase of MATLAB software is not required, since you can use the MATLAB software in the ARC and other public computer labs at Rutgers. We will also use the public-domain wavelet software package Uvi_Wave (which runs under MATLAB).


Textbook:  For current textbook please refer to our Master Textbook List page

Published version of the textbook available in Spring 2016 from  World Scientific Publishing

Other Resources

Other Recommended Books (not required for course)

A. Jensen and A. la Cour-Harbo, Ripples in Mathematics: The Discrete Wavelet Transform
S. Allen Broughton and Kurt Bryan, Discrete Fourier Analysis and Wavelets
James S. Walker, A Primer on Wavelets and Their Scientific Applications (Second Edition)

Course Materials


  • Midterm 1: Thursday, Feb. 25 (ARC 205)
  • Midterm 2: Thursday, April 14 (ARC 205)
  • Final Exam: Thursday, May 5, 8-11 AM (ARC 205)

MATLAB Assignments

  • Project 1: Digital Signals and Vector Graphics  ( pdf format )
  • Project 2: Convolution and Discrete Fourier Transform  ( pdf format )
  • Project 3: Haar Wavelet Transform  ( pdf format )
  • Project 4: Implementation of Wavelet Transforms ( pdf format )
  • Project 5: Image Analysis by Wavelet Transforms ( pdf format )

For Project 2 you will use the Finite Fourier transform graphic user interface.
Matlab m-file. Here is the link to download this m-file:  fftgui

For Projects 4 and 5 you will use the Uvi_Wave collection of Matlab m-files for wavelet transforms (developed at the University of Vigo, Spain). Here is the link to download these m-files:   Uvi_Wave zip file (unzip the file to use the package)

Using Matlab

Note: You can run Matlab on your own computer (without buying the program) by using the Rutgers X-application server.

  • Click on this apps server link.
  • Log in to the apps server using the connect button at the upper right-hand corner of the screen and your Rutgers NetID.
  • From the Main Menu at the lower left corner of the apps server toolbar, click on Education and then on Matlab
  • From the Main Menu click on Internet and then on Firefox Web Browser to access the Uvi_Wave files from the math 357 course web page.
  • Copy the fftgui.m file and the whole unzipped Uvi_Wave directory into a directory that your create on the X-apps server. Then set the Matlab path to this directory.

Course History

Taught by Prof. R. Goodman 2005-2008 and 2010-2014, Prof. V. Retakh 2009 and 2016, Dr. M. Thibault 2015.

Schedule of Sections

Disclaimer: Posted for informational purposes only

This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.

Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.