MAT 9000-001, Spring 2016, CRN 33721; Graduate Math Seminar: Applied Linear Algebra

Instructor: Dr. Timothy Feeman :
Department of Mathematics and Statistics, Villanova University,
800 Lancaster Avenue, Villanova, PA 19085-1699 USA
Office: SAC 373; Phone: (610) 519-4693 ;
email link; Fax: (610) 519-6928

Class meetings schedule: Thursdays, 6:15 pm to 8:45 pm, in Mendel Hall G90.

Spring 2016 Office Hours: My office is room 373 in the St. Augustine Center. I will be available for walk-in office hours on Thursdays before class, from approximately 5:00 pm to 5:45 pm, or by appointment. My office phone and voice mail are at 610-519-4693. You can reach me by email.

CONTENTS: 

Course Description

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 a first course in Linear Algebra (e.g., MAT 3400 at Villanova), 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.

Seminar format: This course will be conducted in a seminar format. To begin with, we will read and study several journal articles on foundational applied linear algebra topics. Following this, each student will select a project topic. Work on the project will include reading several articles pr book chapters on the topic, making three in-class presentations, and writing a substantial report on the topic. The report must be written using LaTeX (see below).

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: A first course in Linear Algebra.

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Text / Reading

There is no required textbook for this course. To begin the seminar, we will focus on reading a variety of journal articles, available for free using Villanova's library subscriptions. 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.

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Software/technical tools

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  

To download LaTeX for a Mac, use the texshop platform: http://texshop.en.softonic.com/mac

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 .

Villanova also has an unlimited site license for individual users of Maple here at Villanova. That means that you can download your own personal copy of Maple onto your own computer. This is a great deal so take advantage of it! To get you started, here is a link to the Maple download page on the UNIT Department web site.

R is an open-source statistical computing environment that is also adept at linear algebra. Download R for free. 

University policy statements on disabilities, learning support, and academic integrity:

·       Office of Disabilities and Learning Support Services:

Students with disabilities who require reasonable academic accommodations should schedule an appointment to discuss specifics with me. It is the policy of Villanova to make reasonable academic accommodations for qualified individuals with disabilities. You must present verification and register with the Learning Support Office by contacting 610-519-5176 or at learning.support.services@villanova.edu  or for physical access or temporary disabling conditions, please contact the Office of Disability Services at 610-519-4095. Registration is required to receive accommodations.

·       Academic integrity statement with link to Academic Integrity Gateway

 Academic integrity is a primary value for any institution of higher education. Cheating on tests, plagiarism, and other forms of academic dishonesty and misconduct are completely unacceptable, especially at Villanova which prides itself on its commitment to the Augustinian values of truth, unity, and love. More information about Villanova's Academic Integrity Policy and Code is available at the Academic Integrity Gateway web site.
timothy.feeman@villanova.edu

last revised: 05-january-2016