Abstract Algebra I, Math 251 

Mondays & Wednesdays, 4:00-5:15 PM, Room S2 108.

Office hours: M-W from 9:05 to 11:35 AM, or by appointment.

IMPORTANT:  If you want to learn your grades so far, and how your scores are compared with the rest of the class please log into Blackboard here.

Syllabus

The textbook can be downloaded for free here. 

Previous qualifying exams in Algebra.  (I guess you should be able to solve these problems, abstract algebra part, before taking this course)


Material covered in class:

08-24: Review of chapter 1.

08-26: Review of chapter 1, continued.

08-31: Review of chapter 2.

09-02: Review of chapter 2, continued.

09-07: Labor Day, no classes.

09-09: Isomorphism theorems. Direct product of groups.

09-14: More on direct product. Semidirect product.

09-16: Examples of semidirect product. main results in Linear Algebra over the integers.

09-21: Proof of the classification theorem of finitely generated Abelian groups.

09-23: More on Abelian groups. Elementary divisors, invariant factors, etc.

09-28: Group actions.

09-30: Stabilizers, the class equation.

10-05: Review.

10-07: Review.

10-12: Exam 1.

10-14: Cauchy's theorem, first Sylow theorem.

10-19: Classification of groups using Sylow theorems.

10-21: More classification, using semidirect products.

10-26: Proof of Sylow II, classification groups of order pq (p and q primes).

10-28: Proof of Sylow III. Introduction to rings and fields.

11-02: Rings, ideals, homomorphisms, kernel of a homomorphism.

11-04: Quotient rings, maximal ideals.

11-09: Prime ideals and more.

11-11: Quotient rings.

11-16: Zero divisors, invertible elements, characteristic, prime fields, irreducible polynomials.

11-18: More on irreducibility of polynomials.
Assignments, Solutions, Handouts, etc. (.pdf files)

HW 1       

HW 1 Solutions       

HW 2                       

HW 3                       

HW 2 Solutions       

HW 4                      

HW 3 Solutions                                   

Exam 1 important info                       

HW 4 Solutions                              

HW 5                                                      

Exam 1 Solutions          

Sylow theorems and classification of groups handout                      

HW 6                                                                                            

HW 5 Solutions                                                                                   

HW 7                                                                                                 

HW 6 Solutions                                                                                       

HW 7 Solutions                                                                                       

HW 8 (and last!)                                                                                      

Exam 2                                                                                                      NEW!!! Final version (Updated 11/18). Misspellings fixed.

HW 8 Solutions                                                                                         NEW!!!  

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