Mathematics 552 Information

Abstract Algebra II

Description

Week 1

Text Readings: Jacobson I:7.1-7.2, Jacobson II: 1.1-1.3 , 3.1, 3.7-3.9
Week 1 Problem set 1 (Due 2/5/13)
Week 1 expository reading:
- Read What is Algebra? from Algebra I by A. I. Kostrikin and I. R. Shafarevitch (Encyclopaedia of Mathematical Sciences Volume 11, Springer-Verlag ).

Week 2

Text Readings: Jacobson 3.10
Week 2 Problem set 2 (Due 2/5/13)
Week 2 expository reading:
- Read When is one thing equal to some other thing? by B. Mazur
- Read Notes on exterior algebras and the Cauchy-Binet formula which supplement the lecture of 1/31 and are relevant to problem set 2

Week 3

Text Readings: Jacobson II: 3.2, 3.5
Week 3 Problem set 3 (Due 2/12/13)
Week 3 expository reading:
- Read sections 1-3 of this article by Baez and Dolan which discusses categorification
- Read Notes on the expression of determinants of square matrices in terms of products of determinants of submatrices which supplement the lecture of 2/5.
- Read Notes on the set of $k$-dimensional subspaces of an $m$-dimensional vector space which supplement the lecture of 2/5.

Week 4

Text Readings: Jacobson II: 5.1
Week 4 Problem set 4 (Due 2/26/13 - Note change from 2/19/13)
Week 4 expository reading:
- Read this centennial celebration article about group representations
- Read Notes on when the tensor product of two elements equals 0 and do the exercise at the end.

Week 5

Text Readings: Jacobson II: 4.5, 5.1, 5.2
Week 5 Problem set 5 (Due 2/26/13)
Week 5 expository reading:
- Read the second part of the centennial celebration article about group representations

Week 6

Text Readings: Jacobson II: 4.6, 4.7 , 5.3
Week 6 Problem set 6 (Due 3/12/13 - Note change from 3/5/13)

Week 7

Text Readings: Wrapup of semisimple algebras: Jacobson II: 4.5-4.7 , 5.1-5.3
Week 7 Problem set 7 (Due 3/12/13)
Oral Midterm exams will be the week of 3/25-3/29. The possible times are listed here . After you have chosen an open time slot, email me your choice. I will update the available times as students are scheduled on a first come first served basis.

Week 8

Text Readings: Field extensions, splitting fields, separable polynomials: Jacobson I: 4.1,4.3,4.4
Week 8 Problem set 8 (Due 3/26/13)

Week 9

Text Readings: Separable polynomials and Galois Theory: Jacobson I: 4.4,4.5
Week 9 Problem set 9 (Due 4/9/13 (changed from 4/2/13))

Week 10

Text Readings: Galois Theory and Theory of Fields: Jacobson I: 4.5
Week 10 Problem set 10 (Due 4/9/13. Note slight correction made 4/9/13)
Week 10 expository reading:
- Read Galois for 21st-Century Readers

Week 11

Text Readings: Solvable Groups: Jacobson I: 4.6
Week 11 Problem set 11 (Due 4/16/13 )

Week 12

Text Readings: Solvability by radicals : Jacobson I: 4.7
Week 12 Problem set 12 (Due 4/30/13)

Week 13

Text Readings: Galois groups of polynomials : Jacobson I: 4.8,4.9,4.16
Week 13 Problem set 13 (Due 4/30/13)

Week 14

Text Readings: Applications of Galois Theory to Classical Problems : Jacobson I: 4.2
Week 14: No homework for week 14, the last week of class. There will be a take home final problem in lieu of a final exam.
Week 14 expository reading:
- Read Discriminants and Resultants concerning the computation of discriminants.

HOMEWORK submissions

Homework will be accepted for grading until 5:00 PM, May 13. A scan or pdf file of any homework that you wished to have graded should be emailed to me before that cutoff time.

Final problem set. Note version 5 correcting yet another error in 5bc posted 8:10 PM 5/11/13. And version 6 straightening out a confusion between a division algebra and its opposite in problem 4 posted 4:15 PM 5/12/13.

There will be a final problem set in place of an in-class final. The problem set will appear here by 10:00 PM 5/6 and will be due at or before 10:00 PM on 5/13. You may use any books or references that you wish, but do not talk to people other than me about the problems. The submission of the completed final problem set will be by email to me. If you have a pdf copy send that, otherwise scan your submission and email that to me. I will not be around to receive physical copies. Check back periodically to see if any updates to the problem set are posted. Each posted version has a version and date at the top. New versions will only be needed if misprints or errors are found.