MAT205: Abstract Algebra II

Ma, Jia-Jun — Xiamen University Malaysia

Part I: Advanced Group Theory (Weeks 1–7)

Week	Lectures
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	Assignment 1 due Monday, 18 May 2026, 5:00pm Solutions Midterm Exam
7	L11: Fraction Fields, Localization & Root Boundslive PDF

Part II: Fields & Galois Theory (Weeks 8–13)

Week	Lectures
8	L12: Field Extensions & Roots of Polynomialslive PDF L12b: Algebraic Closure via Zorn's Lemmalive PDF
9	Holiday
10	L13: Conjugate Elements and the Isomorphism Extension Theoremlive PDF
11	L14: Finite Fieldslive PDF L15: Splitting Fields and Normal Extensionslive PDF
12	L16: Finite Galois Theory — The Fundamental Theoremlive PDF L17A: The Primitive Element Theoremlive PDF
13	L17: Constructions by Straightedge and Compasslive PDF L18: Solvability of Equationslive PDF

Week 14: Quiz & Review

Week	Lectures
14	Assignment 2 due Monday, 6 July 2026, 5:00pm Solutions Quiz 2 live Solutions L19: Course Reviewlive PDF

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