Student Projects in Linear Algebra

Instructor: David Arnold

Adobe Acrobat Reader

You will need Adobe Acrobat Reader to read the files on this site. You can down load the necessary software from the Adobe Site by selecting the AAR link. AAR is free software and has no timelimit on its ownership.

The Scientific Notebook

You will need to use the Scientific Notebook to read the earlier files on this site. However, most of these files have duplicates that can be read in the Acrobat Reader.

Fall 1997

The following students teams have selected their project topics.

Anonymous--- Principal Components Analyis in Remote Image Sensing
Darren Tully and Pat Chavez --- Fractal Music

Todd Douglas and Dustin Helliwell --- Hill Ciphers

Aaron Ambrosini and Thomas Thomaides --- NFL Quarterback Rating System
Mery Apple and Karen Glinden --- Forest Management --- Sustainable Harvesting

Tammie Huff and Chris Ogden --- The Singular Value Decomposition in Image Compression

Jim Fahey and Mike Asher --- Spotted Owl Population

Lori Williford and Randy Cessna --- Fourier Series and the FFT

Anonymous--- Mapping Using Distance Between Cities
Gabe Petersen --- Arnold's Cat Map

Scientific Notebook Version
Adobe Acrobat Version
The file, catbox.exe, is a self-extracting zip file containing a Matlab program that performs the Arnold's cat map transformation. Unzip this file in a directory on your Matlab path.

Peggy Morton and Arne Petersen --- Image Compression with the Haar Wavelet Transform

Woody Burley and Neva Holloday --- Fractals

Scientific Notebook Version
Adobe Acrobat Version
The files, frac.m and enter1.m, can make fractal images to user specification. After downloading these files into a directory on the Matlab path, type help frac or help enter1 to display help on how to use these programs.

Jennifer Terwilliger --- Analysis of Seismic Data

Kevin Yokoyama and I are compiling a list of articles and links on this page that might find potential use as student projects in linear algebra.

The College Mathematics Journal is produced by the Mathematical Association of America and contains article accessible by community college students. You can find this journal at the Humboldt State University Library in the periodical stacks. Each of the following is an article on linear algebra selected from The College Mathematics Journal.

On Transformations and Matrices, Marc Swadener, 4:3, 1973, 44-51, 4.4
Binomial Matrices, Jay E. Strum, 8:5, 1977, 260-266
Mathematics in Archaeology, Gareth Williams, 13:1, 1982, 56-58, C
Visual Thinking about Rotations and Reflections, Tom Brieske, 15:5, 1984, 406-410, 4.4
Harvesting a Grizzly Bear Population, Michael Caulfield and John Kent and Daniel McCaffrey, 17:1, 1986, 34-46, 4.6, 9.10
Why Should We Pivot in Gaussian Elimination?, Edward Rozema, 19:1, 1988, 63-72, 4.6
Rotations in Space and Orthogonal Matrices, David P. Kraines, 22:3, 1991, 245-247, C, 4.3, 4.4, 4.5
Number Theory and Linear Algebra: Exact Solutions of Integer Systems, George Mackiw, 23:1, 1992, 52-58, 9.3
Gems of Exposition in Elementary Linear Algebra, David Carlson and Charles R. Johnson and David Lay and A. Duane Porter, 23:4, 1992, 299-303, 1.2, 4.5, 4.7
A Random Ladder Game: Permutations, Eigenvalues, and Convergence of Markov Chains, Lester H. Lange and James W. Miller, 23:5, 1992, 373-385, 4.5, 9.10
Graphs, Matrices, and Subspaces, Gilbert Strang, 24:1, 1993, 20-28, 3.1, 4.3
Linear Algebra and Affine Planar Transformations, Gerald J. Porter, 24:1, 1993, 47-51, 0.4, 4.4
Iterative Methods in Introductory Linear Algebra, Donald R. LaTorre, 24:1, 1993, 79-88, 4.5, 9.6
How Does the NFL Rate the Passing Ability of Quarterbacks?, Roger W. Johnson, 24:5, 1993, 451-453, C
The Surveyor's Area Formula, Bart Braden, 17:4, 1986, 326-337, 5.2.6, 5.2.8
Cramer's Rule via Selective Annihilation, Dan Kalman, 18:2, 1987, 136-137, C, 4.3
Convex Coordinates, Probabilities, and the Superposition of States, J.N.Boyd and P.N.Raychowdhury, 18:3, 1987, 186-194, 9.7
Determinantal Loci, Marvin Marcus, 23:1, 1992, 44-47, C
Roots of Cubics via Determinants, Robert Y. Suen, 25:2, 1994, 115-117, 0.7
Vectors Point Toward Pisa, Richard A. Dean, 2:2, 1971, 28-39, 6.3
Arithmetic Matrices and the Amazing Nine-Card Monte, Dean Clark and Dilip K. Datta, 24:1, 1993, 52-56
A Geometric Interpretation of the Columns of the (Pseudo)Inverse of A, Melvin J. Maron and Ghansham M. Manwani, 24:1, 1993, 73-75, C
The Matrix of a Rotation, Roger C. Alperin, 20:3, 1989, 230, C, 8.3
The Linear Transformation Associated with a Graph: Student Research Project, Irl C. Bivens, 24:1, 1993, 76-78, 3.1, 9.1
Constructing a Map from a Table of Intercity Distances, Richard J. Pulskamp,
Systems of Linear Differential Equations by Laplace Transform, H. Guggenheimer, 23:3, 1992, 196-202, 6.2
Approaches to the Formula for the nth Fibonacci Number, Russell Jay Hendel, 25:2, 1994, 139-142, C, 0.2, 5.4.2, 9.3, 9.5
Connecting the Dots Parametrically: An Alternative to Cubic Splines, Wilbur J. Hildebrand, 21:3, 1990, 208-215, 5.6.1, 9.6
Some Applications of Elementary Linear Algebra in Combinatorics, Richard A. Brualdi and Jennifer J. Q. Massey, 24:1, 1993, 10-19, 3.2

Fall 1998

The following students teams have selected their project topics.

Ken Cabeen and Peter Gent --- Applications of the DCT

Jody Hourigan and Lynn McIndoo --- The Singular Value Decomposition in Image Compression

Sky McKinley and Megan Levine --- Cubic Spline Interpolation

Scientific Notebook Version
Adobe Acrobat Version
M-files associated with project: c_spline.m (updated 2/22/99)
You can view a Power Point slide show of our presentation here.

Matt Tanner and Joel Aguirre --- Image Compression with the Haar Wavelet Transform

Scientific Notebook Version
Adobe Acrobat Version
M-files associated with project.

Paul Chesler --- Digital Audio Synthesis Using Matlab

Scientific Notebook Version
Adobe Acrobat Version
M-files associated with project.

Kristian Cozyris and Craig Anderson --- The Fourier Series and the Discrete Fourier Transform

Scientific Notebook Version
Adobe Acrobat Version
M-files associated with project.

Fall 2000

The following students teams have selected their project topics.

Jeremy Miller and Ken Menkveld --- Quatrainment

Mike Oremus and Ottopaskal Rice -- Image Compression

Adobe Acrobat screen version of their paper.

Matthew Lincoln and Adrienne Carter -- Fourier Series and the Discrete Fourier Expansion

Adobe Acrobat screen version of their paper.

Shavez Kaleem and Al Abrahamsen

Cubic Bezier Curves

Fall 2001

The following students teams have selected their project topics.

Leland O'Driscoll and Rhyan Pink --- Iterative Relocation of Earthquake Hypocenters

Jesse and Tim Trutna --- JPEG Image Compression

LiHong Huang--- The Haar Wavelet Transformation and Image Compression

Power Point Presentation
Adobe Acrobat Paper

Lee has provided his code for compression, project1.m. He also includes a sample image, bird.gif, to use with his code.

Shinichi Tokoro --- Cryptography

Robin R. Rumple and William Pence --- The Mathematics of GPS Through Linear Algebra

Adam Abrahamsen and David Richards --- The Singular Value Decomposition and Image Compression

Doug Saucedo and Jonathan Gent --- Projecting into Fourier

Emilia Brinkhaus --- Lights Out

Greg Brown and Liya Zhu --- Information Retrieval using Vector Spaces

Adobe Acrobat Presentation
Adobe Acrobat Paper

Greg and Liya have provided a Matlab demonstration of information retrieval, retrieval_test.zip

Iris Jensen --- Input-Ouput Analysis using the Leontief Open-Production Model

Fall 2002

The following student teams have selected their projects.

Mike Land and Tara Puzin --- Warps and Morphs

Adobe Acrobat Presentation
Adobe Acrobat Paper
Mike and Tara also have a number of Matlab M-files that they used on their project. These can be downloaded here.

Greg Ames -- Image Compression Using Haar Wavelet Transform

David Frank --- Circulant Matrices and Polynomials

Liz Arnold and Tiffany Blaszak --- Merlin's Magic Squares

Steve Richards and Azuree Lovely --- Matrices, Vector Spaces, and Information Retrieval

Mike Bruce and Emily Shernock --- Stage Based Population Projection Matrices and Their Biological Applications

Tim Honn and Seth Stone ---

Fall 2005

Ken Huffman -- Interpolating Data with the DFT
- Slides
- Paper
Jacob Prystowsky and Levi Gill --- Calculating Web Page Authority Using the PageRank Algorithm
- Slides
- Paper
Chris Moody and Boden Hegdahl --- Differentiation Matrices
Brian Meyer and Garrett Jackson --- The N-Site Problem (GPS)
- Slides
- Paper
Mike Liu and Elika Ketabchi --- Edge Detection Using Linear Spatial Filtering
- Slides
- Paper
Nina Manuel and Bethany Adams --- The SVD and Image Compression
- Slides
- Paper
Ben Ohanen and Matt Wisan --- JPEG Image Compression
- Paper
Peter Spiegel and Tim Meyers --- Warps and Morphs
Kyle Shaw --- Arnold's Cat Map
- Slides
- Paper

Fall 2006

Damien Adams and Halsey Patterson --- Haar Wavelet Transformation: Compression and Reconstruction>/li>
- Slides
- Paper
Ben Allen --- Finite Element Model for Earthquakes

Andrea Brown and Katie Moe --- Fractal Tilings
Ken Gibson and Travis Chlossey --- Linear Algebra and Azulejos

Ian Cooper and Craig Lorenc --- Image Compression Using Singular Value Decompositon

Alison Pool and Lydia Silva --- Modeling Prey and Predator Populations