MAT205: Abstract Algebra II

Ma, Jia-Jun — Xiamen University Malaysia

Part I: Advanced Group Theory (Weeks 1–6)

WeekLectures
1 L01: Review of Basicslive PDF
HW
L02: Group Actions Reviewlive PDF HW
2 L03: Cauchy & Sylow Theoremslive PDF
HW
L04: Applications of Sylowlive PDF HW
3 L05: Free Abelian Groups & the Subgroup Theoremlive PDF HW
L06: Classification of F.G. Abelian Groups & Applicationslive PDF HW
4 L07: Free Groupslive PDF
L08: Subnormal Series, Solvable & Nilpotent Groupslive PDF
5 L09: Finite Simple Groups Through Three Exampleslive PDF
L10: Rings, Polynomial Rings, and Polynomial Functionslive PDF
6 L11: Review of Part I Quiz 1
L12: Reserve / Q&A coming

Week 7: Midterm

WeekLectures
7 Assignment 1due
L13: Midterm Exam
L14: Field Extensions coming

Part II: Fields & Galois Theory (Weeks 8–12)

WeekLectures
8 L15: Algebraic Extensions coming
L16: Finite Fields coming
9 L17: Field Automorphisms I coming
L18: Field Automorphisms II coming
10 L19: Isomorphism Extension coming
L20: Separable Extensions I coming
11 L21: Separable Extensions II coming
L22: Galois Theory I coming
12 L23: Galois Theory II Quiz 2
L24: Applications of Galois Theory coming

Weeks 13–14: Ring Theory & Review

WeekLectures
13 L25: Ring Theory: UFDs, PIDs, Euclidean Domains Assignment 2 due
L26: Tutorial coming
14 L27: Review coming
L28: Reserve / Q&A

Textbook: Fraleigh, A First Course in Abstract Algebra
Game: Abstract Algebra Game