Graduate algebra I

Math 6130

Graduate algebra I
MWF 9am
ECST 1B21

Book

Dummit and Foote, Abstract Algebra.

Instructor

Nat Thiem

Math 309
303.492.7628
thiemn AT the university's state DOT edu

Office hours

M 10-12; F 12-13; or by appointment

Tentative schedule

• 08.27–08.31; group axioms and examples
    m. introduction (preliminaries)
    w. 1.1, 1.3
    f. 1.2

• 09.05–09.07; group homomorphisms and actions; homework 1 due
    w. 1.6
    f. 1.4, 1.7

• 09.10–09.14; subgroups through actions; homework 2 due
    m. 2.2, 2.4
    w. 2.2
    f. 2.5, 3.2

• 09.17–09.21; quotient groups and isomorphism theorems; homework 3 due
    m. 3.1
    w. 3.2, 4.1
    f. 3.3

• 09.24–09.28; simple groups and composition series; homework 4 due
    m. 3.4
    w. 3.5
    f. 4.2

• 10.01–10.05; conjugacy classes and automorphisms; homework 5 due; midterm 1
    m. 4.3
    w. 4.4
    f. midterm 1

• 10.08–10.12; Sylow Theory and simplicity of alternating groups;
    m. 4.5
    w. 4.5
    f. 4.6

• 10.15–10.19; Products of groups and series; homework 6 due
    m. 5.1, 5.4
    w. 5.5
    f. 6.1

• 10.22–10.26; Nilpotent groups and finite abelian groups; homework 7 due
    m. 6.1
    w. 6.1
    f. 5.2

• 10.29–11.02; free groups and presentations; homework 8 due
    m. 6.2
    w. 6.3
    f. 7.1

• 11.05–11.09; rings and ideals; homework 9 due
    m. 7.1, 7.2
    w. 7.3
    f. 7.4

• 11.12–11.16; ring of fractions, chinese remainder theorem and PIDs; homework 10 due; midterm 2
    m. 7.5
    w. 7.6, exam handed out
    f. exam collected, 8.2

• 11.26–11.30; euclidean domains and unique factorization domains
    m. 8.1, 8.2
    w. 8.3
    f. 9.1, 9.2

• 12.03–12.07; polynomial rings; homework 11 due
    m. 9.3
    w. 9.4
    f.

• 12.10–12.12; conclusion; homework 12 due
    m. 9.5
    w.
  

• Final; December 19, 13:30 - 16:00.