- Spring 2008
||Caroline J. Klivans
||office: Eckhart 308A
e-mail: cjk (at) math.uchicago.edu
office hours: M, Th 3-4 and by appointment
|| Tanmay Deshpande|
|Office Hours T 4:30-6:00 F 3:00-4:00|
|Problem session T 6-7 Eckhart 308
||MWF 10:30 - 11:20 Eckhart 203
Course Description: This is the third course in the honors
algebra sequence. We will start by covering field extensions and
Galois theory. Further topics will be determined by the interests of the class.
Abstract Algebra, Dummit and Foote
There will be weekly homework assignments. You are encouraged to
work together but all students must independently write up their
solutions. All homeworks
are due at the beginning of class unless otherwise noted.
Homework 1 due Wednesday April 9th. Section 13.1 5. Section 13.2 12, 13, 14.
Homework 2 due Wednesday April 16th. Section 13.4 3. Section
13.5 7. Prove the uniqueness (up to isomorphism) of the algebraic
closure. Construct an example of a splitting field of degree n! for a
polynomial of degree of n.
Homework 3 due Wednesday April 23rd. Section 14.1 2, 3, 7 Section 14.2 3, 8
Homework 4 due Wednesday April 30th. Section 14.6 Read subsections: Polynomials of degree 2, polynomials of degree 3. Section 14.2 11, 15. Section 14.6 4, 12, 22.
Homework 5 due Wednesday May 14th. Hmwk5
If not otherwise specified, assume you are working over a field of characteristic 0. Also, in the last problem, Z >= 0 should be Z^n >= 0.
Homework 6 due Wednesday May 21st. From your textbook: Page 332 16 (you may use #1),19,34, Page 686 8.
MISTAKE in the text: page 332, Exercise 16, line 3
reads: (LT (g1 ), . . . , LT (gm), LT (S (gi , gj )) is strictly larger than the ideal (LT (g1 ), . . . , LT (gm)).
Conclude that the algorithm . . .
should be: (LT (g1 ), . . . , LT (gm), LT (r)) is strictly larger than the ideal (LT (g1 ), . . . , LT (gm)), where
S (gi , gj )
Homework 7 Since I mistakenly did not get the homework up on Wednesday, your homework is now to study for the midterm! Have a good weekend.
Practice problems for the final exam
It is the policy of the Department of Mathematics that the following
rules apply to final exams in all
undergraduate mathematics courses:
1. The final exam must occur at the time and place designated on the
College Final Exam Schedule. In
particular, no final examinations may be given during the tenth week of
the quarter, except in the case
of graduating seniors.
2. Any student who wishes to depart from the scheduled final exam time
for the course must receive
permission from Paul Sally (office is Ry 250, phone is 2-7388, email is
are not permitted to excuse students from the scheduled time of the
final exam except in the
cases of an Incomplete.