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박지훈 교수
박지훈 교수
  • Type MOOC course
  • Period Always open
  • Learning Time Study freely
  • Course approval method Automatic approval
  • Certificate Issue Online

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

Additional Info

교재: Dummit-Foote Abstract Algebra 4th edition