Graduate Algebra

Instructor:Guanghua Ji

Classroom and Time:C701; 2-4, Monday.

Prerequisites:Chapter 1-3 in Ash's book.

Grading:The course grade will be based on attendance(10%), homework(10%), midterm exam(30%) and final exam(50%).

References:

1, M. Artin, Algebra, Addison Wesley, 2010.

2, R. B. Ash, Basic abstract algebra, Dover Publications, 2006.

3, B. Hall, Lie Groups, Lie Algebras, and Representations, GTM 222, 2004.

4, D. S. Dummit and R. M. Foote, Abstract algebra(3rd), John Wiley and Sons

5, A. W. Knapp, Basic Algebra, Advanced Algebra, Birkhauser.

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Syllabus:

1, Advanced groups theory:See Ash: chapter 5; Or Artin: chapter 6.

2, Linear lie groupsSee Hall: chapter 1-3.

3, Basic representation theory:Homework

4, Module theory:See Ash: chapter 4; Or Artin: chapter 12

5, Galois theory:See Ash: chapter 6; Or Artin: chapter 14

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If time permits, we will also consider the following topics:

6, Introducing algebraic number theory:see Ash: chapter 7; or Knapp: chapter V

7, Introducing algebraic geometry:see Ash: chapter 8

8, Introduction to homological algebra and group cohomology:see Ash: chapter 10; Or Dummit: chpater 17.

Other online resources

All are welcome!