Mathematics
110
Fall, 2002
Course Control Number
54987
Office: 510 642 0648
Fax: 510 642 8204
email:
ribet@math.berkeley.edu
Office hours
Lectures:
3
LeConte
Hall,
TuTh 2:10-3:30
Optional discussion sections: Monday, 3:10-4
in 247 Cory Hall
and Thursday, 11:10-12
in 285 Cory.
This course doubled
in size because of its large waiting list.
As a result,
graduate student instructor
Tom Coates
will be working with this class in a number of ways.
His
Web page for Math 110
contains
information for our course.
Tom will conduct the two weekly discussion sections, hold
office hours, and assist with quiz and exam
grading.
Prerequisites
Math 54 required, Math 53 and experience with
proofs highly recommended. If you have never taken an upper-division
math course before and expect to have trouble with proofs,
you should consider taking Math 74 as a bridge to the upper division.
Syllabus
The catalog proposes that we cover:
Matrices, vector spaces, linear transformations, inner
products, determinants.
Eigenvectors. QF (sic.) factorization. Quadratic forms and Rayleigh's
principle. Jordan canonical form, applications. Linear functionals.
This
intimidating list
gives you some idea of what will go on,
but we
won't cover every topic!
I will follow the book as closely as possible.
Linear
Algebra, third edition, by
A
fourth
edition has just been announced, but I am told that the bookstore
received the older edition.
See the authors'
list
of errata
for corrections that are tailored to your copy of the book.
Recommended Reading:
There are quite a few good
linear algebra books in circulation; see the
textbook
lists for some examples.
Whenever you feel stuck when reading our
text,
feel free to consult alternative treatments.
Reading several discussions
of one topic is often illuminating.
One excellent book is
Linear Algebra Done Right
by
Sheldon Axler.
Quizzes
Short written quizzes will be given in class
roughly every 10 days. The quizzes are intended to test
your understanding of fundamental points that emerge during
the lectures.
You might have found the
Moffitt
Library Exam Files
useful in preparing for exams.
Grading
Your course grade was based on a composite numerical grade
that Tom and I computed
as a linear combination of your homework,
quiz, and examination scores. The intention was to make the
various course components count as follows:
Homework 10%, quizzes 20%, midterms 15% each, final 40%.
Because there were 200 homework points, 50
final points, and so on, the composite grade
was
computed as the sum of the homework grade divided by 20, 4/5 of
the final exam grade, 3/8 of the sum of the two MT exam grades and
2/3 of the quiz grade.
A student who received perfect scores on all components would have
received a composite grade of 100. The actual composite grades
obtained by the 61 students who sat for the final exam ranged from
14.64 to 97.68. After examining the composite grades and looking at
representative final exam papers, I awarded 61 grades as follows:
15 As, 20Bs, 13Cs, 12Ds and 1F. Those students who took the course on
a P/NP basis had their letter grades converted into either P or NP.
I awarded Fs to those students who were signed up for the course but
did not take the final exam. I believe that all of them left the course
early on in the semester and had forgotten to drop the class.
For problems that request proofs (``show that...''),
write your answers in complete
English sentences. For computational questions, write supporting
sentences that explain what you are doing and what is going on.
- Assignment due September 3:
- § 1.1:
1ac, 2d, 3c, 4, 7
- § 1.2:
1 (all parts),
7, 9, 11, 17, 18, 19, 21
- § 1.3:
1 (parts b, c, d, e), 2h, 8 (all parts), 9, 10, 11
- Assignment due September 10:
- § 1.4:
1, 2af, 3af, 4d, 8, 11
- § 1.5:
1, 3, 5, 7, 10
- § 1.6:
1, 4, 5, 8, 11, 12, 14
- Assignment due September 17:
- § 1.6:
21, 22, 23, 24
- § 2.1:
1, 2, 4, 5, 6, 9(a-e), 10, 12, 13, 14, 16
- Assignment due September 24:
- § 2.1:
17, 18, 19, 22, 24, 26, 27, 28, 29
- § 2.2:
1, 2 (a,c,e,f), 4, 5 (all parts)
- § 2.3:
3, 8
- Assignment due October 8:
- § 2.3:
9, 10, 11, 12, 15
- § 2.4:
1 (all parts), 2, 5, 12, 14
- § 2.5:
1 (all parts), 2 (a, c)
- Assignment due October 15:
- § 2.5:
5, 6, 8, 9
- § 2.6:
1 (all parts), 2 (all parts), 3 (both parts), 4, 5, 8
- § 3.1:
1 (all parts), 2
- Assignment due October 22:
- § 3.1:
3, 5, 7, 9
- § 3.2:
1 (all parts), 2 (e, f, g), 4a, 5 (g, h), 6 (a, c, e), 7, 11, 14
- Assignment due October 29:
- § 3.3:
1 (all parts), 2 (d, e, f), 3 (d, e, f), 6, 7 (a, c, e), 8, 10
- § 3.4:
1 (all parts), 2d, 3, 5, 6
- § 4.1:
1 (all parts), 3b, 4c
- Assignment due November 12:
- § 4.2:
1 (all parts), 3, 11, 23, 28
- § 4.3:
1 (all parts), 5, 9, 10, 11, 12, 14, 19, 20, 22
- § 4.4:
1 (all parts)
- Assignment due November 19:
- § 5.1:
1 (all parts), 2 (a and b), 3 (a and b), 4, 14, 16, 17
- § 5.2:
1 (all parts except h and i), 2 (a and b), 3 (a and b), 7, 8, 13
- § 5.4:
1 (all parts)
- Assignment due November 26:
- § 5.4:
2 (ace), 4, 5, 6a, 9a, 10a, 13-14, 16, 20
- § 6.1:
1 (all parts), 3, 4, 5, 8
- Assignment due December 5:
- § 6.2:
1 (all parts), 2c, 4, 6, 7, 9, 10
- § 6.3:
2b, 3 (a,b), 6, 7, 9, 10, 11, 12, 16
- § 6.4:
1 (all parts), 3, 5, 6, 7, 8
