## MATH 25900 Honors Algebra - Spring 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 T 4:30-6:00 F 3:00-4:00 Problem session T 6-7 Eckhart 308 Lecture: 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.

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 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
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 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.