Math 2406: Abstract Vector Spaces Fall 2007
Lecture Meetings: Skiles 243,
Tuesday and Thursday
Instructor: Professor Silas Alben
Email: alben@math.gatech.edu (the best way to contact me).
Office: Skiles 238, tel. 404-894-3312
Office hours: W., Th.
Course
web site:
http://www.math.gatech.edu/~alben/Math2406Fall2007/index.html
All documents will be posted on this website, until further notice.
TA: no TA.
Course Introduction:
The
goals of this course are two-fold:
1. We
will cover linear algebra at a theoretical and intermediate
undergraduate level. Linear algebra is either the basis for, or a
useful tool
for, many subjects in pure and applied math, and theoretical
engineering and sciences:
differential equations, analysis (functional), abstract algebra,
scientific
computing and numerical analysis, optimization, quantum mechanics are
some
examples.
2. One of the main goals of this course is to let you
see what mathematics is really like. While your previous math courses
mostly concentrated
on formulas and facts, telling you what is true, here we want to find
out why
things are true and how things fit together, and, most importantly, we
want to
prove that things are true. This
requires a new way of thinking, and moreover this new way of
thinking is what underlies all higher mathematics courses. We will
spend a lot
of time proving things, I'll prove things in lecture and you'll prove
things in
homework and exams. I can
recommend some interesting extracurricular reading on the
history/philosophy/sociology of pure mathematics.
Our
technique for learning proofs is therefore “learning by doing:” we
will read, understand, and write proofs of many important results of
linear
algebra. This course provides a transition
between the
calculational introductory mathematics courses and the advanced and
more
theoretical courses.
Intended
Audience. This course is intended for:
(1)
Mathematics and Discrete Mathematics
majors,
(2)
Mathematics minors,
(3)
Students intending to take proof-based
upper-level mathematics courses, such as MATH 4107 (Abstract Algebra
I), MATH
4150 (Introduction to Number Theory), or MATH 4317 (Analysis I).
Prerequisites:
You
must have taken MATH 1502 (Calculus II),
MATH 1512 (Honors Calculus II), MATH 1522 (Linear Algebra for
Calculus), or an
equivalent to one of these.
Course
materials:
There
is only one text for the course: Apostol, Linear Algebra: A
First Course with Applications to Differential Equations, Wiley
’97. Other
material on writing proofs and other topics in linear algebra will be
posted
online occasionally.
Course
topics:
The
course will
mostly follow chapters 1 through 7 of the text.
Homework.
Homework will be posted
mostly weekly (on Thursday), and will be due the following Thursday
by
Homework
Format: Homeworks should be neatly
written on the front side of
the page only, and must be stapled. You are allowed (and
encouraged) to work
together with other students on the homework, as long as you each independently
write up your own solutions. Show your thinking: always
write
clearly the steps that lead to your answer. No credit will be given for
answers
without justification. You are also allowed (and encouraged) to ask me
questions, although you should try to think about the problems before
asking. I
strongly encourage you to work extra problems from the book on your own.
Tests.
There will be two
tests and a final exam. Tentative dates for the tests are
Test 1
Thursday 27 September
Test 2
Thursday 8 November
I try
to discourage make-up tests, so please
let me know of any conflicts immediately.
Final
Exam. The final exam is
scheduled for December 12 (Wednesday)
All
examinations in this course are closed
book. No notes may be used.
Grading.
The tests, homework,
and final examination will be counted with the following weights:
Tests
40%
Homework
30%
Final
Examination 30%
Letter
grades will be based on the overall
average at the end of the term. I have no
predetermined
letter grade cut-offs, but you
may assume they will be at least as favorable as 90, 80, 70, 60. I will
keep
you informed of how you’re doing.
Honor
Code. Please review the
Georgia Tech Honor Code.
Any
evidence of cheating or other violations
of the Georgia Tech Honor Code will be submitted directly to the Dean
of
Students. The institute honor code is available at
http://www.deanofstudents.gatech.edu/Honor
Lateness. Please don’t arrive
late to lecture.
Learning
Disabilities. Any students with learning
disabilities should contact me by email
during the first week of classes.