Math 493, Fall 2012. Honors Algebra I

 My office is 4859 East Hall, and my office hours are Thursdays, 1-4pm
and Wednesdays, 1:10-2pm (and also by appointment).
The class meets on Mondays, Wednesdays and Fridays,
2pm-3pm, in room 2866 of East Hall.

The course grader is Joe Varilone.

Syllabus in PDF

Recommended additional reading:
  1. Algebra: a graduate course by I. Martin Isaacs discusses the topics
    we will cover in greater depth, and contains a lot of useful information.
    The presentation of the material is quite nice.
     
  2. Abstract Algebra by David S. Dummit and Richard M. Foote
    contains numerous exercises. If you want to really master the
    subject, it is a good idea to solve as many of them as possible.
     
  3. Abstract Algebra and Topics in Algebra by I.N. Herstein are
    also quite good. The texts mentioned above are all written in
    different styles, and it is worth trying all of them to find the
    one that you enjoy reading the most.


Exams


Review questions for the midterm in PDF
Midterm problems in PDF
Midterm solutions in PDF

The final exam is scheduled for Thursday, December 13, 5-8pm (1360 East Hall).
Homeworks
Homework will be assigned each week on Friday, and will be due the following Friday at the start of class.
The homework assignments are an integral part of the learning experience. No late homework will be accepted.

Homework 1 (due Friday, September 14, at the beginning of class) in PDF
Solutions for Homework 1 in PDF
Homework 2 (due Friday, September 21, at the beginning of class) in PDF
Solutions for Homework 2 in PDF
Homework 3 (due Friday, September 28, at the beginning of class) in PDF
Solutions for Homework 3 in PDF
Homework 4 (due Friday, October 5, at the beginning of class) in PDF
Solutions for Homework 4 in PDF
Homework 5 (due Wednesday, October 17, at the beginning of class) in PDF
Solutions for Homework 5 in PDF
Homework 6 (due Friday, November 2, at the beginning of class) in PDF
Solutions for Homework 6 in PDF
Homework 7 (due Friday, November 9, at the beginning of class) in PDF
Solutions for Homework 7 in PDF
Homework 8 (due Friday, November 16, at the beginning of class) in PDF
Solutions for Homework 8 in PDF
Homework 9 (due Friday, November 30, at the beginning of class) in PDF
Solutions for Homework 9 in PDF
Homework 10 (note the two due dates!) in PDF
Solutions for Homework 10 (first part) in PDF
Approximate course contents (arranged by week)
  1. Introduction to groups; examples (September 5 and 7).
    Suggested reading: Chapter 2 of Artin's book.
     
  2. Cyclic groups; orders of elements; homomorphisms (week of September 10).
    Notes on homomorphisms, isomorphisms and automorphisms in PDF
    Notes on orders of group elements in PDF
     
  3. Subgroups, quotients and isomorphism theorems (week of September 17).
    Notes on subgroups in PDF
     
  4. Group actions and Sylow theorems (week of September 24).
    Notes for the week in PDF
     
  5. Applications of the Sylow theorems (week of October 1).
     
  6. Nilpotent, solvable and simple groups (week of October 8).
    Notes for the week in PDF
     
  7. Symmetric groups (October 17 and 19).
    Proof of simplicity of the alternating group A_n for n=5,6,7,... in PDF
    Notes from Ryan Reich's lecture on 10/19, explaining the same proof
    presented in a different way: PDF
     
  8. Introduction to rings and modules (week of October 22).
     
  9. Quotient rings, Chinese Remainder Theorem, PIDs (week of October 29).
     
  10. Prime factorization in PIDs and applications (week of November 5).
     
  11. Introduction to field theory; finite fields (week of November 12).
    Auxiliary notes on polynomials in PDF
     
  12. More on (finite) fields (November 19 and 21).
     
  13. UFDs and polynomial rings (week of November 26).
    Notes for the week in PDF
    Additional details on Vandermonde determinants in PDF
     
  14. Finitely generated modules over a PID (week of December 3).
    Notes for the week in PDF
     
  15. Review and tying loose ends (December 10).