Math 81. Abstract Algebra

Winter 2009

         Instructor:         Sergi Elizalde

         Lectures:           MWF 8:45-9:50 in Haldeman 028

         (x-hour)  Th 9:00-9:50

         Office Hours:    M 11:00-12:30, W 9:50-11:00 (and by appt.)

         Office:               Kemeny 332


         Phone:               646-8191


Here is the latest homework assignment.

The final exam will be distributed on Wednesday, March 4, and due on Monday, March 9.


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


Here is a tentative syllabus for the course. For a more up-to-date list of covered material, check the homework page.


Sections in Text

Brief Description

Week 1

Chapters 7-9, 13.1

Review: rings, prime and maximal ideas, quotient rings. Prime fields, finite extensions.

Week 2


Algebraic extensions

Week 3

13.3, 13.4

Compass and straightedge constructions, splitting fields, algebraic closures

Week 4

13.5, 13.6

Cyclotomic polynomials, separable and inseparable extensions

Week 5


Fixed fields and automorphism groups

Week 6


Fundamental Theorem of Galois Theory

Week 7

14.2, 14.3

Finite fields

Week 8

14.4, 14.5

Composite and simple extensions, cyclotomic and abelian extensions

Week 9

14.6, 14.7

Galois groups of polynomials


Homework, exams, and grading

The course grade will be based on

The homework will consist of weekly problem sets, which will be collected in class on their due date. No late homework will be accepted.
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.
Write neatly, use full sentences, and justify all the steps. Give references for theorems that you use from the text and from class.
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.