Instructor:
Dr. Timothy Feeman :
Department of Mathematics and Statistics, Villanova
University,
800 Lancaster Avenue, Villanova, PA 19085-1699 USA
Office: SAC373; Phone: (610)519-4693 ;
e-mail:
click for email link Fax:
(610)519-6928
Final presentation schedule: (word document) April 30: 10:00 11:15 am; May 5: 11:30 am - 2:00 pm; in White Hall 115.
Class meetings schedule: T,Th 10:00 am to 11:15 am in White Hall 115.
From its humble beginnings solving systems of linear equations, Linear
Algebra has grown into a diverse and widely applied branch of mathematics
intimately tied to many of today's technological achievements. One key to
this growth is the realization that matrices not only provide a convenient way
to store coefficients of a system of equations but can be used to represent
linear transformations. In other words, Linear Algebra can be used to analyze
any physical process that can be approximated by a linear model.
In our first course in Linear Algebra (e.g., MAT
3400), we learn a lot about vector spaces and linear transformations, but we
have scarce little time to learn about the many applications of these concepts
that exist in the real world. This course will attempt to begin to address this
shortcoming. Among the applications we will consider are: Markov processes,
algorithms for creating ratings and rankings (e.g., of pages on the World Wide
Web or of sports teams), least squares approximation, matrix methods in digital
image processing, the singular value decomposition, QR factorization, latent
semantic indexing (for search engine text retrieval), and possibly more.
As part of your continued development as mathematicians and scientists, this course will also emphasize learning to read, write, and think independently about mathematical problems and ideas.
Prerequisite course: MAT 3400, Linear Algebra (or equivalent course).
The required text for the course is Numerical Linear Algebra, by Trefethen and Bau; published by SIAM; ISBN13: 9780898713619. Our course will start with studying the first two chapters (eleven sections) from this classic text. I selected this particular text because (a) it is an excellent book, with important topics we need at the right level of mathematical sophistication, and (b) it is comparatively inexpensive. You are free of course to use other linear algebra books as additional references.
After that, we will focus on reading a variety of journal articles, available for free using Villanova's library subscriptions. The first two articles we will study are (click on title for pdf file of article):
·
The Fundamental Theorem
of Linear Algebra, by Gilbert Strang; The
American Mathematical Monthly, Vol. 100, No. 9 (Nov., 1993), pp. 848--855.
·
A Singularly Valuable
Decomposition: The SVD of a Matrix, by Dan Kalman;
The College Mathematics Journal, Vol.
27, No. 1 (Jan., 1996), pp. 2--23.
LaTeX download information: You will use the technical typesetting program known as LaTeX for your project presentations and reports. LaTeX is the "industry standard" in mathematics for producing publication-quality work. Most mathematics journals and many mathematical books are produced using LaTeX. To use LaTeX, you will need both the program itself and an editing environment program in which to create your documents. A short introduction to how to install the free MikTeX - Texnic Center combination along with a short introduction to LaTeX is here: http://maths.anu.edu.au/~huerta/latexforbeginners.html
Some online resources for learning and working with LaTeX are available at the following sites. http://en.wikibooks.org/wiki/LaTeX ; ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf ; http://latex.silmaril.ie/veryshortguide/ ; http://www.tug.org/twg/mactex/tutorials/ltxprimer-1.0.pdf .
last revised: 20-january-2015