MATH 25800
Honors Algebra - Winter 2008




Instructor: Caroline J. Klivans
office: Eckhart 308A
e-mail: cjk (at) math.uchicago.edu
office hours: M, Th 3-4 and by appointment

College Fellow: Tanmay Deshpande Office Hours M F 11:30-1 Problem session T 6-7 Eckhart 308
Lecture: MWF 10:30 - 11:20 Eckhart 203

Course Description: This is the second course in the honors algebra sequence. This sequence covers rings, ideals, fields, vector spaces, linear transformations and matrices, modules, canonical forms of matrices.

Required text:
Abstract Algebra, Dummit and Foote

Homework:
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 Page 231 7,29. Page 247 8,19,26. Page 256 8,13. Read (and convince yourself of) Theorem 8 page 246.
Homework 2 Page 250 34(a)(b). Page 256 25. Page 263 4. Page 267 3,6,7. Read (and convince yourself of) the proof of the general Chinese Remainder Theorem.
Homework 3 Page 278 3,11. Page 282 1,4,8. Page 292 2.
Homework 4 Page 230 3. Page 247 2,17. Page 256 4. Page 267 4. Page 282 3. I consider these good practice problems for the midterm next Friday.
Homework 5 Page 298 5. Page 301 7,8. Page 312 14.
Homework 6 Section 10.2 10. Section 11.1 8,9. Section 11.2 7,8.
Read the remaining exercises from section 11.2 starting just after problem 13. Do not skip this part of the assignment! Take your time and just read through these few pages. It is not difficult but it is important!
Homework 7 Section 10.1 8. Section 10.2 1. Section 11.1 1. Section 11.2 13. Section 11.4 4(b) - in this problem, assume you are working over a field F, and you may use any results stated in the exercises of section 11.2.
Homework 8Section 12.1 7. Section 12.2 1,6. Section 12.3 2.
Practice problems for the final exam
We will have two midterms and a final exam.
Midterm 1: Friday February 8th
Midterm 2: Friday March 7th
Final Exam: Wednesday March 19th 10:30am
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 sally@math.uchicago.edu). Instructors are not permitted to excuse students from the scheduled time of the final exam except in the cases of an Incomplete.