Algebra Seminar, Autumn and Winter 2012

 

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Coordinator: Wang Jun(王俊)
Email: WANSTEX AT GMAIL DOT COM
Textbook: Algebra, by Michael Artin

Schedule: 2012.09.23. - 2013.01.06. Sunday Afternoon, 13:30 - 16:30, 紫金港 6-415

09.23. 11.1  Definition of a ring
11.2  Polynomial ring
11.3  Homomorphisms and ideals
Speaker:
王俊

09.30. 11.4  Quotient rings
11.5  Adjoining elements
11.6  Product rings
11.7  Fractions
Speaker:
肖羚晏

10.14. 11.8  Maximal ideals
11.9  Algebraic geometry
Review of the exercises in Chapter 11
Speaker:
罗之麟

10.21. 12.1  Factoring integers
12.2  Unique factorization domains
12.3  Gauss’ Lemma
Speaker:
雷宇环

10.28. 12.4  Factoring integer polynomials
12.5  Gauss primes
Review of the exercises in Chapter 12
Speaker: 
刘远通

11.04. 13.1  Algebraic integers
13.2  Factoring algebraic integers
13.3  Ideals in Z[square root of (-5)]
13.4  Ideal multiplication
Speaker:
陈俊杰

11.18. 13.5  Factoring ideals
13.6  Prime ideals and prime integers
13.7  Ideal classes
13.8  Computing the class group
Review of the exercises in Chapter 13
Speaker:
徐曦磊

11.25. 13.9  Real quadratic fields
13.10  About lattices
Review of the exercises in Chapter 13
Speaker:
肖羚晏

12.02. 14.1  Modules
14.2  Free modules
14.3  Identities
Speaker:
陈俊杰

12.09. 14.4  Diagonalizing integer matrices
14.5  Generators and relations
14.6  Noetherian rings
14.7  Structure of abelian groups
Speaker:
肖羚晏

12.16. 14.8  Application to linear operators
14.9  Polynomial rings in several variables
Review of the exercises in Chapter 14
Speaker:
刘远通

12.23. 9.1  The classical groups
9.2  Interlude: Spheres
9.3  The special unitary group SU2
Speaker:
罗之麟

12.30. 9.4  The rotation group SO3
9.5  One-parameter groups
9.6  The Lie algebra
Speaker:
陈俊杰

01.06. 9.7  Translation in a group
9.8  Normal subgroups of SL2
Review of the exercises in Chapter 9
Speaker:
徐曦磊

 

If you want to participate in the seminar, please contact the coordinator.

Besides the reading and the presentations, it is important that at least one-third of the exercises in the book should be worked out and then discussed in the seminar.

 

Confirmed Participants:

 

For Freshmen and New-comers

Objectives of the seminar

On the presentations

1. Each presentation should be meticulously prepared, not only by the speaker, but also by the audience (in order to understand the talk).

2. Because of the time limit, you have to tailor the contents. Focus on the most central and essential ideas and leave out the secondary stuffs.

3. Definitions and theorems should always be stated clearly, precisely, and concisely.

4. Do not try to give all the details of a proof unless it involves useful techniques or it is very interesting. Just sketch the main line of thought.

5. Be prepared to answer and discuss any question posed by the audience.

6. For effective learning, English should be used as much as possible, at least for the blackboard writing.




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