## Linear Algebra, Fall 2013
Instructor: Andrew Obus
email: obus [at] virginia.edu
office: Kerchof Hall 208 |

*Linear Algebra and its Applications*, 4th ed., by David C. Lay.

Linear algebra underlies Google's PageRank algorithm, the concept of a best-fit line, and risk models of stock portfolios.

Furthermore, it is only a slight stretch to say that all higher mathematics as it is practiced today (geometry, topology, number theory, analysis, differential equations, etc.) depends fundamentally on linear algebra.

The book contains a plethora of applications of linear algebra. We will cover a few, and I encourage you to read about the other applications that pique your interest! I worked at a hedge fund for a year between college and graduate school doing quantitative analysis, and linear algebra was by far the most useful math class for the job that I had under my belt.

My goal is for you to leave this class not only competent in the skills of linear algebra, but also as a more mature mathematical thinker. If you are interested in taking more mathematics, linear algebra is your ticket into most of the advanced courses.

The main topics we will cover are linear equations, linear transformations, matrices, vector spaces, determinants, eigenvalues, eigenvectors, diagonalization, and applications. These correspond to most of Chapters 1-7 of Lay's book. I also hope to lecture on the Google PageRank algorithm, which is not in the book. I will try to strike a balance between computations, concepts, proofs, and applications. Some short proofs may appear on homeworks and exams.

*Expected Background:*Officially, the prerequisite is
Calculus II. In reality, we will
rarely use calculus; almost everything in this class is accessible with
only a pre-calculus background. On the other hand, this course
will require somewhat more mathematical sophistication than the
calculus courses you have probably taken, and will involve more proofs
and disciplined conceptual thinking. Ideally, you have seen
vectors before and have done some basic operations with them (adding,
subtracting, multiplying by scalars). If not, please let me
know. More generally, if you have any questions concerning your
background, please speak to me as soon as possible.

Mondays 3:30-4:30, Wednesdays 10:00-11:00. Kerchof Hall 208 (my office). If these times do not work for you, please make an appointment with me.

Homework will be due on Wednesdays. It is due in class If you are
going to miss class for whatever reason, you must either submit the
homework to my mailbox in the mailroom of Kerchof Hall before the beginning of
class, or have a friend submit your homework in class.
Late or improperly submitted homework will **never** be accepted.
If you know in advance you will be unable to turn in
homework when it is due, you should plan to turn it in ahead of time. If you have a conflict
with a religious holiday, you must give me advance notice. I will drop your lowest homework score to allow for missed assignments or for assignments that pose
special difficulty.

Homework must be neat, well-organized, and legible. In addition, it must be stapled or paper clipped
(no folding over the top-left corner or anything like that). Please
write in paragraphs, sentences, and English
words (oh my!) when they are called for. Many problems will
require you to write an explanation. The grader should not have
to decipher what you are doing--you should be clear and
unambiguous about your methods on a homework problem.

Homework will be graded and every effort will be made to hand it back promptly. Grades will be posted on UVaCollab.

Schedule of Homework (the homework assignments themselves will be posted on UVaCollab)

Midterms will be in class on Wednesday, October 2nd and Monday, November 11th. If you have a conflict with one of these days, you must let me know now. Another exam on the same day is not considered a conflict.

The final exam is (tentatively) on Wednesday, December 11th, from 2:00PM-5:00PM.

Calculators are not permitted on exams.

20% Homework (not all homeworks are worth the same number of points. See the homework schedule)

20% Each Midterm

40% Final Exam

It is possible for exceptional class participation to be factored into the homework grade.

University of Virginia Undergraduate Math Page

University of Virginia Math Department

If you have (anonymous) comments for me about teaching style or anything related to the course, click here for a feedback form.