Schedule of Lectures
Linear Algebra, Spring 2018
Instructor: Andrew Obus
email: obus [at] virginia.edu
office: Kerchof Hall 208
TTh 12:30-1:45, Clark Hall 102. Please ask questions if anything in lecture is unclear.
Lectures will run the entire 75 minutes.
Please show up on time!
Linear Algebra and its Applications, 5th ed., by David C. Lay.
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 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.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!
Tuesdays 11:00-12:00, Thursdays 2:00-3:00. Kerchof Hall 208 (my
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.
Homework Homework will be assigned on Tuesdays. Each homework assignment will consist of two parts:
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
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.
Final Course Grades
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.
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