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 1/28/21)
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 ).
- Read When is one thing equal to some other thing? by B. Mazur
- Read about the role of algebra in applied mathematics

Week 2

Text Readings: Jacobson II: 3.10
Week 2 Problem set 2 (Due 2/4/21)
Week 2 expository reading:
- Read Notes on exterior algebras and the Cauchy-Binet formula which are relevant to problem set 2
- Read Notes on when the tensor product of two elements equals 0 and do the exercise at the end.
- Read Minimal amount of definitions for Category Theory

Week 3

Text Readings: Jacobson II: 3.2, 3.5
Week 3 Problem set 3 (Due 2/11/21)
Week 3 expository reading:
- Read Notes on the expression of determinants of square matrices in terms of products of determinants of submatrices
- Read Notes on the set of $k$-dimensional subspaces of an $m$-dimensional vector space

Week 4

Text Readings: Jacobson II: 4.1-4.4
Week 4 Problem set 4 (Due 2/18/21)
Week 4 expository reading:
- Read this centennial celebration article about group representations
- Read notes on the structure of semisimple rings .

Week 5

Text Readings: Jacobson II: 4.5, 5.1, 5.2
Week 5 Problem set 5 (Due 2/25/21)
Week 5 expository reading:
- Read the second part of the centennial celebration article about group representations
- Read notes showing all left Artinian rings are left Noetherian

Week 6

Text Readings: Jacobson II: 5.1, 5.2, 5.3, 5.5, 5.6
Week 6 Problem set 6 (Due 3/4/21)

Week 7

Text Readings: Field extensions, Galois extensions: Jacobson I: 4.1,4.5
Week 7 Problem set 7 (Due 3/11/21)

Week 8

Text Readings: Galois Extensions, Gauss Lemma: Jacobson I: 2.16, 4.5
Week 8 Problem set 8 (Due 3/25/21)

Week 9

Text Readings: Separable polynomials and Galois Theory: Jacobson I: 4.4,4.5
Week 9 Problem set 9 (Due 4/1/21)

Week 10

Text Readings: Galois Theory and Theory of Fields: Jacobson I: 4.5,4.6
Week 10 Problem set 10 (Due 4/8/21)
Week 10 expository reading:
- Read Galois for 21st-Century Readers

Week 11

Text Readings: Solvable groups, Solvability by Radicals, Galois groups of polynomials: Jacobson I: 4.6,4.7,4.8-4.11,4.16
Week 11 Problem set 11 (Due 4/15/21)

Week 12

Text Readings: Applications of finite fields; Central Simple Algebras: Jacobson I:4.16, Jacobson II:4.6, 4.7
Week 12 Problem set 12 (Due 4/22/21)

Week 13

Text Readings: More on Central Simple Algebras: Jacobson I:4.16, Jacobson II:4.6, 4.7

HOMEWORK submissions

Homework will be accepted for grading until 5:00 PM, May 8. It can be submitted in Canvas.

Final problem set. Version 2' (4/30/21 10:00 AM)

There will be a final problem set in place of an in-class final. It should be turned in as a Canvas assignment.