## Advanced Calculus and Linear Algebra I, Spring 2018
Instructor: Andrew Obus
email: obus [at]
virginia [dot] edu
office: Kerchof Hall 208 |

The primary purpose of these sessions is to review/flesh out material from the previous week, as well as to correct any pervasive misconceptions arising from the homework. Attendance at discussion sessions will be extremely useful, and is in any case mandatory.

I will also be running a problem session most weeks (see "Office Hours" below).

Alternative References:

Linear Algebra: "Linear Algebra and Its Applications" by David C. Lay.

Differential Equations: "Differential Equations: Techniques, Theory, and Applications" by MacCluer, Bourdon, and Kriete.

Tu 11:00-12:00, W 5:00-6:00, Th 2:00-3:00. The Tuesday and
Thursday office hours are
standard "drop-in" office hours held in Kerchof 208 (my office).
At the Thursday office hour, priority will be given to students from
the Math 3351 class I teach this semester.

The Wednesday office hour will sometimes be a standard drop-in office
hour in Kerchof 208 (with priority for Math 3315), and it will sometimes be a problem session
where
we can work problems that you or I select (room TBA). Toward the
end of the semester, it will be used for student presentations.
The Wednesday sessions
are optional until students start presenting (early April), at which point they will become mandatory.
See the section on papers/presentations below. If you have a
conflict between 5:00 and 6:30 on Wednesdays, please let me know immediately. Generally we will end by 6, but on presentation days we may go later in order to have time for three presentations.

If these times do not work for you, please make an appointment with me.

I will let you know each week whether there is a problem session or
a regular office hour that Wednesday. On Wednesday January 17th
(the first week of class), it will be a regular office hour.

We will study linear algebra for the first half of the course. In addition to its applications to multivariable calculus that we have seen in Math 2315, linear algebra is 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.

In particular, linear algebra is fundamental to the study of differential equations, which will be the subject of the second half of the course. Differential equations are used to model how systems evolve through time and space. This can be interpreted quite generally (particle motion, fluid mechanics, population dynamics, national economies,...). We will study various types of differential equations and various methods of solving them, but we will try to keep things as conceptual and related to linear algebra as possible. We will conclude with a brief study of Fourier Series, and their applications to the heat and wave equations.

In terms of the book, we will cover most of Chapter 3 and Chapters 10-14 (although I expect that you have already seen most of the material in Chapter 10 and the first half of Chapter 14 in your BC Calculus course or equivalent). I will also be emailing out some (handwritten) lecture notes from Andrei Rapinchuk that we will use as a resource. We will go somewhat deeper into linear algebra --- especially its applications --- than the book does.

*Expected Background:* Math 2315, or Math 2310 and some knowledge of linear algebra.

Homework will be posted on Collab on Thursdays. Each homework
assignment, in addition to a reading assignment, will consist of two
parts:

1) A comprehension quiz that is due in my mailbox in Kerchof by 8:00pm on Mondays.
This will consist of straightforward problems meant to check your basic
understanding of the material. If you find the comprehension
quizzes difficult/confusing, that is a sign that you should be coming
to office hours/problem sessions/making an appointment with me to
discuss!

2) The regular assignment that will be due Thursdays
by 5:00pm in Aron's mailbox in Kerchof (you can also hand it to me in
class if you wish). Some of these problems are meant to be
difficult --- don't be alarmed if you find them so!

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 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.

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.

There will be a take-home midterm in lieu of a homework assignment due on March 1st at 5:00pm.

The final exam will also be a take-home exam. It will be due on Thursday, May 3rd (the day the final exam for our class is scheduled) at 6:00pm.

For both exams, you may use your textbook, course notes, and old homework assignments, but no other sources (including people and internet)! In particular, you may not work with classmates.

You will be responsible for writing a short (5-8 pages) basic
expository paper on a topic in mathematics of your choice (I will give
a long list of possible topics, or you can pick your own, subject to my
approval). This is meant to give you an early introduction to
mathematical writing. I will give further guidelines for the
paper in an email, but note that it is not
expected that your papers display great originality.
Rather, the paper is meant so that you get some practice with the
patterns of mathematical exposition while learning about a new topic
(this is the "book report" of academic papers). Papers must be typed.
If you can pull this off in Microsoft Equation Editor, more power to
you, but I recommend typesetting your paper in LaTeX (this is what
virtually all mathematicians, and many physicists, economists, and
computer scientists use to typeset their papers). There is a bit
of a startup cost to learning LaTeX, but the dividends it pays in
beauty and clarity are well worth it. Aron's first Monday session
will be a basic LaTeX introduction. I will also post some LaTeX
help documents on Collab.

In addition to your paper, you will give a 20 minute presentation on
your topic (plus 5-10 minutes for Q&A) in one of the Wednesday
evening sessions toward the end of the semester. You may use
slides if you wish (LaTeX integrates very well with slides using the
program "Beamer"), or you may use the chalkboard.

Your choice of paper topic as well as partner (if you have one) must be presented to me by February 1st. Presentations will take place during the Wednesday sessions on 4/10, 4/17, 4/24, and possibly 4/3, depending on how many groups there are. Final papers will be due along with the last homework assignment on April 26th. Do not leave your writing until the last week --- mathematical writing always takes longer than you think it will!

HW#1: 1/25

HW #2, Paper topic: 2/1

HW #3: 2/8

HW #4: 2/15

HW #5: 2/22

Take-Home Midterm: 3/1

HW #6: 3/15

HW #7: 3/22

HW #8: 3/29

HW #9: 4/5

HW #10: 4/12

HW #11: 4/19

HW #12, Final Paper: 4/26

Take-Home Final: 5/3

10% Comprehension quizzes

20% Homework

10% Paper

5% Presentation

20% Midterm

35% Final Exam

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.

University of Virginia Undergraduate Math Page

University of Virginia Math Department

Comments

If you have (anonymous) comments for me about teaching style or anything related to the course, you can make them on the Collab page for the course.