### Linear Algebra, Spring 2015

Instructor: Andrew Obus
email: obus [at] virginia.edu
office: Kerchof Hall 208
phone: 434-424-4930
website: http://people.virginia.edu/~aso9t/math3351s15.html

### MW 2:00-3:15, Monroe Hall 111.  Please ask questions if anything in lecture is unclear. Lectures will run the entire 75 minutes. Please show up on time!

Schedule of Lectures

### Textbook

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

### Content

Linear Algebra is, essentially, the study of linear equations.  No doubt you have seen such equations in high school.  You probably even solved some systems of 2 or 3 simultaneous linear equations (in 2 or 3 variables).  Linear algebra takes a deeper look at such systems and examines questions such as:  How do we know when a system of m linear equations in n variables has a solution?  How many solutions can there be?  How do we find them efficiently?  If there is no solution, then how close can we get to one?  These questions may seem somewhat narrow at first glance.  But they are in fact fundamental to physics, computer science, and statistics.  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 great variety 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.

If you fall too far behind in this course, it will be very difficult to catch up.  Please see me promptly if things stop making sense!

### Office Hours

Mondays 12:45-1:45, Wednesdays 12:00-1:00. Kerchof Hall 208 (my office). If these times do not work for you, please make an  appointment with me.

### Homework

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 not 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.

You are encouraged to work together on homework!  But you must write up your own solutions.  I have found that it is helpful if I think about the problems myself first, and then discuss the more difficult questions with others.

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)

### Exams

Midterms will be in class on Wednesday, February 18th and Wednesday, April 1st.  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.  If you have two other exams on the same day, talk to me.

The final exam is on Wednesday, April 30th, from 2:00PM-5:00PM.

Calculators are not permitted on exams.

### Final Course Grades

20% Homework
20% Each Midterm
40% Final Exam

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

### Honor

The University of Virginia Honor Code applies in this class.  You will be asked to sign a statement before each exam acknowledging that you understand this.

### Some Useful Links

University of Virginia Undergraduate Math Page

University of Virginia Math Department