MAT 5920/8790 Advanced/Applied Linear Algebra; (CRN 22493/24230);
Fall
201
3
; Prof. T.G. Feeman, Dept. of Mathematics & Statistics
Class meeting times:
MWF 9:30 am to 10:20 am in Old Falvey 104.
Prerequisite:
A first course in Linear Algebra, including vector spaces and linear transformations (e.g.,
MAT 3400 or MAT 7660).
This course:
In our first course in Linear Algebra, 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 ran
kings (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 p
ossibly more.
Seminar format:
This course will be conducted primarily in a seminar format. We will read, study, and
discuss a series of journal articles on applied linear algebra topics. In class, we will take turns facilitating
the discussion as we collec
tively seek to understand each article. As part of this process of collective
understanding, we will hash out the details of the arguments and examples presented in the articles
while also creating examples of our own to solidify our knowledge and comprehe
nsion.
Writing:
Each of you will write a
(roughly)
two

page summary review of each article. These reviews will
be in the
format
typically found in the Mathematical Reviews, an online resource for mathematical
researchers. We will familiarize ourselves with
this resource
as part of the course.
Other assignments: Along with
study
ing and writing reviews of
the articles
, other exercises will arise in
the course of our class discussions. For instance, you may be assigned to create an example to illustrate
someth
ing from one of the articles or to look up a result from an
other
article referenced by the article
we are studying.
The readings:
A few of the readings will be chapters from books or lecture notes I have written. I will
give you copies of these in class. T
he bulk of the readings will be articles from mathematical journals
and
will be accessible at no cost
*
through Villanova’s library system
using your Villanova
login.
We will
familiarize ourselves in class with how to find the articles. (* Articles usually will be available through
online databases as pdf files; so there may be some cost to you should you wish to print them out.)
Here
is a preliminary list (not necessar
ily in the order in which we will study them).
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 Kal
man;
The
College
Math
ematics
Journal
,
Vol. 27, No. 1 (Jan.,
1996
), pp. 2

23
.
Using Linear Algebra for Intelligent Information Retrieval, by Michael W. Berry, Susan T.
Dumais, and Gavin W. O’Brien;
SIAM Review
, Vol. 37, No. 4 (Dec., 1995), pp. 573
—
595.
Ma
tri es, Ve tor a es, and n ormation etrieval, by i hael W. Berry, lat o Drma
, and
Elizabeth R. Jessup;
SIAM Review
, Vol. 41, No. 2 (Jun., 1999), pp. 335
—
362.
The Perron

Frobenius Theorem and the Ranking of Football Teams, by James P. Keener;
SIAM
R
eview
, Vol. 35, No. 1 (Mar., 1993), pp. 80
—
93.
Outer Product Expansions and Their Uses in Digital Image Processing, by Harry C. Andrews and
Claude L. Patterson;
The American Mathematical Monthly
, Vol. 82, No. 1 (Jan., 1975), pp. 1

13.
Asset Pricing, Finan
cial Markets, and Linear Algebra, by Marcio Diniz;
The
College
Mathematic
s
Journal
, Vol. 44, No. 1 (Jan., 2013), pp. 2

8.
That’s all or now.
20

August

2013
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