Syllabus for Math 398: Abstract Algebra

Course Staff

Brendan Murphy,
Office Hours: 2:00-3:00pm Thursdays

Alex Scheffelin,
Office Hours: 3:30-4:30pm Fridays

Winter Quarter

Our textbook this quarter is Algebra: Chapter 0 by Aluffi.
The Category Theory lecture notes can be found here.

Week Subject Sections from Aluffi Problem Set Lecturer(s)
Winter Break Set Theory and Category Theory Chapter 1 Problem Set Andreas (guest lecturer)
Week 1 The definition of a group and examples Sections 2.1 and 2.2 Problem Set Daniel R.
Week 2 Group homomorphisms and the category of groups Sections 2.3 and 2.4 Problem Set Peter & Yunkyu
Week 3 Subgroups, normality, and quotient groups Sections 2.6 and 2.7 Problem Set Max
Week 4 Cannonical decomposition and Lagrange's theorem, presentations and free groups Sections 2.5 and 2.8 Problem Set Jason
Week 5 Group actions, the conjugation action, and the class formula Sections 2.9 and 4.1 Problem Set Chen
Week 6 The Sylow theorems Section 4.2 Problem Set Omar
Week 7 Composition series and solvability Section 4.3 Problem Set Bashir
Week 8 The symmetric group Section 4.4 Problem Set Zack
Week 9 More products of groups, exact sequences of groups, the extension problem Section 4.5 Problem Set
Week 10 The classification of finite abelian groups Section 4.6

Spring Quarter

Week Subject Sections from Dummit & Foote Problem Set
Week 0 The definition of a ring and examples Sections 7.1 and 7.2 Problem Set
Week 1 Ring homomorphisms, quotient rings, and ideals Section 7.3 and 7.4 Problem Set
Week 2 Euclidean domains, P.I.D.s, and U.F.D.s Sections 8.1, 8.2, and 8.3 Problem Set
Week 3 Polynomial rings Sections 9.1, 9.2, and 9.3 Problem Set
Week 4 More polynomial rings Sections 9.4 and 9.5 Problem Set
Week 5 Field extensions and geometry Sections 13.1, 13.2, and 13.3 Problem Set
Week 6 More field theory Sections 13.4, 13.5, and 13.6 Problem Set
Week 7 The fundamental theorem of Galois theory Sections 14.1 and 14.2 Problem Set
Week 8 Field extensions and geometry Sections 14.4 and 14.5 Problem Set
Week 9 Galois groups of polynomials Section 14.6 Problem Set
Week 10 The Abel-Ruffini theorem Section 14.7