LINEAR ALGEBRA AND VECTOR GEOMETRY MATH 2700.002

VENUE: WH#316 (WOOTEN HALL) TR 1830-1950

INSTRUCTOR: TUSHAR DAS email - tushardas@my.unt.edu

OFFICE+HOURS: GAB#480 MW 1700-1900

 

The best Project Papers/Presentations from the class - Congratulations!

 

Gabrien Clark - Computer Graphics; paper and presentation.

Miranda Coulter - Solving Fibonacci; paper and presentation.

Lucas Davidson - Input-Output and Inter-Industry Models; paper and presentation.

Vincent Leith - Rijndael Block Cipher; paper and presentation.

Kelan Lu - Least Squares; paper and presentation.

Joseph Magagnoli - Least Squares and North Carolina Crime; paper and presentation.

Randy Whitehead - Game Theory and Rationality; paper and presentation.

Eric Wiedner - Cryptography; paper and presentation.

Brian Worthington - Hill Ciphers; paper and presentation.

 

HOMEWORK ASSIGNED

 

A few papers/books from where you might find a Project Idea that interests you :-

1.      A geometric approach to determinants by John Hannah, Monthly May 1996

2.      Music: a Mathematical Offering by Dave Benson

3.      Beyond the third dimension: Geometry, computer graphics and higher dimensions by Tom Banchoff

4.      Flatland by Edwin A. Abbott, also available in html via Banchoffs Geometry Center page.

NOTE - please do not borrow the books from the library that are recommended on this list, since others may want to use them as well. A good idea might be to work on the book at the library, make notes, copies etc. and then return the book to the drop-box so that it can be re-shelved.

 

Some sites where you can see some examples of Linear Algebra Projects:

1.      Student Projects in Linear algebra - David Arnold

2.      Applications of Linear Algebra - Ali A. Dad-del at UC Davis

3.      More Applications of Linear Algebra by Joseph Khoury at Uni. Ottowa

4.      Some modules on Linear Algebra - from the Connected Curriculum Project at Duke University

 

Some Applications from the book by Anton on Linear Algebra (see files beginning with <linear proj>)

Note that you should consider each of these sections as a project. Doing the Exercises and the Technology Exercises would count as fair amount of work towards the project. You may use these examples to estimate how much work you should put in towards your project.

 

1.      CRYPTOGRAPHY prerequisites - Matrices, Gaussian elimination, Matrix operations, Linear independence, Linear transformations

2.      EQUILIBRIUM TEMPERATURE DISTRIBUTIONS prerequisites - Linear systems, Matrices, Intuitive understanding of Limits

 

You can access the College Mathematics Journal via the UNT Library site or directly through JSTOR or Pro Quest - note that you will have to have on-campus access for the latter; or if using a personal computer you would have to go through the UNT Library site and then use your EUID and password to get access.

A nice list of articles in the College Mathematics Journal (by Douglas Arnold and Kevin Yokoyama)

  • 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

 

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