# Math 101. Topics in Algebra

Fall 2008

·         Instructor:         Sergi Elizalde

·         Lectures:           MWF 10:00-11:05 in Kemeny 201

·         (x-hour)             Th 12:00-12:50

·         Office Hours:    M 1:40-3:30, F 11:10-12:00 (and by appt.)

·         Office:               Kemeny 332

·         Email:

·         Phone:               646-8191

Announcements

Here is the current homework assignment.

The midterm exam will be handed out on Friday, Oct. 31, and due on Wednesday, Nov. 5.

The final exam will be handed out on Monday, Nov 24, and due on Wednesday, Dec. 3.

Textbook

Abstract Algebra by Dummit and Foote, 3rd edition. (Available at Wheelock Books.)
Here is their errata page.

Topics

Here is a tentative syllabus for the course.

 Lectures Sections in Text Brief Description Week 1 Chapter 0, 1.1-1.6, 2.1, 2.2, 2.3, 2.4 Groups, examples, homomorphisms, subgroups, cyclic groups Week 2 Chapter 3.1, 3.2, 3.3 Cosets, Lagrange’s theorem, isomorphism theorems, solvable groups Week 3 Chapter 3.4, 4.1, 4.2 Composition series, Jordan-Hölder theorem, Group actions, permutation representations, Cayley’s theorem Week 4 Chapter 4.3, 4.5, 4.6, 5.1 Class equation, conjugacy classes in S_n, Sylow theorems, Direct Products Week 5 Chapter 5.2, 5.4, 5.5 Semidirect Products, finitely-generated abelian groups Week 6 Appendix II, Chapter 6.3, 7.1, 7.2, 7.3 Basic category theory (products, coproducts, functors), free groups, introduction to rings, examples Week 7 7.4, 7.5, 7.6, 15.4 Prime and maximal ideals, localization, Chinese Remainder Theorem Week 8 8.1, 8.2, 8.3, 9.1, 9.2 Euclidean Domains, PIDs, irreducibles and primes in rings, UFDs, polynomial rings Week 9 9.3, 9.4, 9.6, 10.1 Polynomial rings, irreducibility criteria, Noetherian rings, Hilbert’s Basis Theorem, group rings, modules

The course grade will be based on

• homework (30%)
• a take-home midterm exam (30%)
• a take-home final exam (40%)

The homework will consist of a weekly problem set, plus studying some sections of the book. You are encouraged to collaborate on the homework, but the solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.
All homework assignments will be posted here.

No collaboration is permitted on exams.

Students with disabilities: Students with disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested.