## Course summary

• Type MOOC course
• Period Always open
• Learning Time Study freely
• Course approval method Automatic approval
• Certificate Issue Online
http://www.edwith.org/abstract-algebra-1
Thumb up 27 Learner 219 ### Instructor Introduction

• 박지훈 교수

- POSTECH 수학과 (정수론과 산술기하 전공) 부교수
- 전, 캐나다 McGill 대학 박사후연구원
- 전, 미국 Clay liftoff fellow
- 미국 보스톤 대학 수학과 박사학위 (2007)
- The modular j-function and homotopy Lie theory (Proceedings of AMS, 2018)
- Abelian arithmetic Chern-Simons theory (International Mathematical Research Notices,2017)
- Enhanced homotopy theory of period integrals (Communications in Number theory and physics, 2016)

### Lecture plan

강의
1. CHAPTER 1: Definition of a group and a group homomorphism
1. 학습자료 & 주차목표
1. definition of groups and basic examples
1. properties of a group and a homomorphism
1. dihedral group and group presentation
1. Quiz 1-1
1. Quiz 1-2
1. Quiz 1-3
2. CHAPTER 2: Examples of groups
1. 학습자료 & 주차목표
1. symmetric group
1. more examples
1. group action and its property
1. Quiz 2-1
1. Quiz 2-2
1. Quiz 2-3
3. CHAPTER 3: Subgroups
1. 학습자료 & 주차목표
1. subgroups and related examples
1. cyclic group and group generators
1. lattice diagram of subgroups
1. Quiz 3-1
1. Quiz 3-2
1. Quiz 3-3
4. CHAPTER 4: Quotient groups and isomorphism theorems
1. 학습자료 & 주차목표
1. cosets, normal subgroup and quotient group
1. Lagrange’s theorem
1. isomorphism theorems
1. Quiz 4-1
1. Quiz 4-2
1. Quiz 4-3
5. CHAPTER 5: Group actions and Cayley’s theorem
1. 학습자료 & 주차목표
1. cycle decomposition
1. Cayley’s theorem and symmetric group
1. class equation
1. Quiz 5-1
1. Quiz 5-2
1. Quiz 5-3
6. CHAPTER 6: Sylow’s theorem
1. 학습자료 & 주차목표
1. automorphisms of groups
1. Sylow’s theorem I
1. Sylow’s theorem II
1. Quiz 6-1
1. Quiz 6-2
1. Quiz 6-3
7. CHAPTER 7: semi-direct products and solvable groups
1. 학습자료 & 주차목표
1. semi-direct products
1. p-groups and nilpotent groups
1. solvable groups
1. Quiz 7-1
1. Quiz 7-2
1. Quiz 7-3
8. CHAPTER 8: Definition of a ring and its homomorphism
1. 학습자료 & 주차목표
1. definition of rings and basic examples
1. Units of a ring and integral domains
1. More examples and ring homomorphism
1. Quiz 8-1
1. Quiz 8-2
1. Quiz 8-3
9. CHAPTER 9: The ring isomorphisms and localization
1. 학습자료 & 주차목표
1. ring isomorphism theorems
1. properties of rings
1. rings of fractions
1. Quiz 9-1
1. Quiz 9-2
1. Quiz 9-3
10. CHAPTER 10: Euclidean domain (ED) and discrete valuation ring (DVR)
1. 학습자료 & 주차목표
1. Chines remainder theorem
1. Euclidean domain (ED)
1. discrete valuation ring (DVR)
1. Quiz 10-1
1. Quiz 10-2
1. Quiz 10-3
11. CHAPTER 11: principal ideal domain (PID) and unique factorization domain (UFD)
1. 학습자료 & 주차목표
1. principal ideal domain (PID)
1. unique factorization domain (UFD)
1. polynomial rings I
1. Quiz 11-1
1. Quiz 11-2
1. Quiz 11-3
12. CHAPTER 12: Polynomial rings
1. 학습자료 & 주차목표
1. polynomial rings II
1. Irreducibility: the Eisenstein criterion
1. polynomial rings over a field and summary
1. Quiz 12-1
1. Quiz 12-2
1. Quiz 12-3