## Linear Algebra, Spring 2018
Instructor: Andrew Obus
email: obus [at] virginia.edu
office: Kerchof Hall 208 |

*Linear Algebra and its Applications*, 5th ed., by David C. Lay.

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 will 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.

Tuesdays 11:00-12:00, Thursdays 2:00-3:00. Kerchof Hall 208 (my
office).
If these times do not work for you, please make an appointment with
me. I am also teaching Math 3315 this semester. For the
Tuesday office hour, students in both classes will have equal
priority. For the Thursday office hour, students in Math 3351
will have priority.

1) Online Homework: This will be assigned using the MyLab Math package from Pearson included with your textbook. I will send the class an email with instructions for setting this up. The online homework will tend to consist of relatively straightforward problems, and you have as many chances as you need to get the problems correct! This will be due by 12:00 noon on Tuesdays.

2) Written Homework: Written homework is due in class on Tuesdays, or in my mailbox at the front of Kerchof Hall by the beginning of class if you cannot make it to class for any reason. The written homework may include some more difficult problems than the online homework.

Late 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. I will drop your lowest online and your lowest written homework score to allow for missed assignments or for assignments that pose special difficulty.

Homework should 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. Some 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. It is very important that you truly understand the homework solutions you hand in. In previous classes I have taught, the students who were the most unpleasantly surprised with their exam grades have been the ones who have "phoned in" their homework (keep in mind that the exams count much more than the homework!). In particular, you should always work the online homework problems until you have them correct!

If you work together on homework, you must write the names of your collaborators on the front.

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

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

Midterms will be in class on Tuesday, February 20th and Tuesday, April 3rd.
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 Friday, May 4th, from 2:00PM-5:00PM.

Calculators are not permitted on exams.

7% Online Homework

13% Written Homework

20% Each Midterm

40% Final Exam

It is possible for exceptional class participation to be factored into your grade in borderline cases.

University of Virginia Undergraduate Math Page

University of Virginia Math Department