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