Advanced Linear Algebra. Math 5651. Fall 2011
TuTh 2-3:15 pm, Clark 102.
- Instructor: Mikhail Ershov
- Office: Kerchoff 302
- e-mail: ershov at virginia dot edu
- Office hours: 3 hrs TBA and by APPOINTMENT
- Course webpage: http://people.virginia.edu/~mve2x/5651_Fall2011
Text: Linear Algebra, Friedberg, Insel and Spence, fourth edition.
Course outline
This course is aimed at students with some prior exposure to linear algebra.
The goal of the course is to provide a thorough and comprehensive treatment
of the main concepts and theorems of linear algebra. Approximately the first 6 weeks
of the course will be spent on the material discussed in 3351 (elementary linear algebra),
inlcuding vector spaces, bases, linear transformations, solving linear matrix equations and
determinats (Chapters 1-4 of the book). Compared to 3351, these concepts will be investigated
in more depth and the emphasis will be made on theoretical rather than computational aspects.
During weeks 7-12 we will study more advanced topics: diagonalization, Jordan Canonical Form
and bilinear forms (Chapters 5-7 of the book). In the last 2 weeks I plan to discuss
some applications of linear algebra to other areas of mathematics and possibly applications
outside of mathematics.
Prerequisites
There are two main prerequisites for the course:
- A first course in linear algebra at the level of MATH 3351. You should
be comfortable with matrix arithmetic (including computation of determinants) and
solving systems of linear equations using Gaussian elimination. It is also expected
that you are familiar with the notinos of a vector space, linear independence, basis etc.
(formally, all these concepts will be introduced "from scratch", but if you have not
seen any of them before, the course will probably progress too fast for you).
- Substantial prior exposure to proofs. You should be completely comfortable with
the basic proof techniques (induction, contradiction, case exhaustion etc.)
and have experience in both reading (and understanding) proofs and
writing your own proofs. For this reason, it is strongly encouraged that you
take MATH 3310 (Basic Real Analysis) or MATH 3354 (Survey of Algebra) prior to MATH 5651.
There is also some overlap in the material between MATH 3354 and MATH 5651,
so it is recommended that you take MATH 3354 (which is more elementary than MATH 5651)
prior to or concurrently with MATH 5651.
Evaluation
The course grade will be based on homework and three exams.
Homework will count for 30% and exams will count for 70% of your grade. The distribution
of weights between exams will depend on their format (in class, take home or combined),
which has not been determined yet, but will be finalized no later than the end of September.
Exams
The tentative dates of the exams are as follows:
- First midterm exam: Thu, Oct 6th
- Second midterm exam: Thu, Nov 9th
- Third midterm exam: Thu, Dec 6th
According to the current plan, the first and third exams will be take-home,
while the second exam will have both in-class and take-home parts.
Third midterm exam may be replaced by an IN-CLASS final on SAT, Dec 10th, 9-12am.
Make-up policy
- Make-ups or extensions (for take-home exams) will be given only under extreme circumstances (such as
serious illness). Except for emergencies, you must obtain my permission
for a make-up (resp. extension) before the exam (resp. due date).
- If you miss an in-class exam or fail to submit a take-home exam
by the due date without a compelling reason, you will
be assigned the score of 0 on that exam.
- University regulations specifically prohibit early make-ups.
Homework
The homework format is NON-STANDARD, so read this paragrpah carefully.
- Homework will be assigned weekly, except for the midterm weeks.
Each homework will have two parts: the practice part and the quiz part.
The practice part is mandatory to complete, but need not be handed in.
The quiz part must be handed in by the given due date (usually, Thursday, in class),
and your entire homework score will be based on the quiz parts. I will try to
construct homeworks in such a way that a good understanding of problems from the
practice part should be helpful for the quiz part.
- Collaboration policy: Naturally, you may freely discuss
practice problems with each other or with me during office hours.
On the contrary, for the quiz part you MAY NOT discuss problems with other people
or use any resourses (including web) except for the class textbook and your
class notes. You may ask me questions about quiz part problems, but normally
I will only provide very brief hints. The collaboration policy for the take-home
exams is the same as for the quiz parts of homeworks.
- Please STAPLE your homework.
- No late homework will be accepted. However, two lowest
homework scores will be dropped.
Announcements
Major announcements will be made in class and also posted on the course
webpage.
Some other announcements may only be made by e-mail, so check your
e-mail account
regularly.
Add/drop/withdrawal dates:
- Tuesday, September 6 -- Last day to ADD a course, elect the audit
option,
change the grading option (grade or CR/NC), or establish an independent
study
- Wednesday, September 7 -- Last day to DROP a course (deletion
from the transcript)
- Tuesday, October 18 -- Last day to withdraw from a course
(instructor's permission required)
Office hours
During the first week of classes office hours are by appointment only.
The proposed times for regular office hours (starting the second week) are
Tue 4:15-5:45
and Wed 1:15-2:45