18.704 (Seminar in Algebra and Number Theory), Spring 2006

The topic for the course this spring will be representation theory of finite groups and symmetric groups. This includes basics of representations, character theory, induction, Mackey theory, etc.

More course information (such as about about assignments and grading) is available on the course information sheet.

The main course textbook will be Serre's Linear representations of finite groups. The focus will be on the first two sections.

Lecture assignments
DateFirst lecturerSecond lecturer
February 9Nidhi Shrivastava1.1, 1.2Matthew Ellis1.2, 1.3
February 14Yiwen Chu1.3, 1.4Nhan Nguyen1.5
February 16Jonathan Campbell1.6, 2.1Melissa Shin2.2
February 21MONDAY SCHEDULE - no class
February 23T. L.Misc.Thu Duong2.3
February 28Benjamin Lantos2.2, 2.3Li-Mei Lim2.4, 2.5
March 2Jared Kubler2.5Dale Winter3.1, 3.2
March 7Antoni Rangachev3.2, 3.3Nhan Nguyen3.3
March 9------Jared Kubler5.1, 5.7
March 14Jonathan Campbell3.3Li-Mei LimS_4
March 16Nidhi ShrivastavaRingsMelissa Shin6.2
March 21Matthew EllisModulesDale Winter6.4
March 23Benjamin Lantos6.5Thu Duong6.3
March 28, 30Spring break - no class
April 4Antoni RangachevTensoringYiwen Chu7.3
April 6Thu Duong7.1Jonathan Campbell7.2
April 11Li-Mei Lim7.4Dale WinterMore S_4
April 13Yiwen Chu8.1, 8.3Jared Kubler8.2
April 18Patriots Day - no class
April 20T. L.Misc.Melissa Shin9.1
April 25Matthew Ellis9.2Antoni Rangachev8.5
April 27Nidhi Shrivastava9.3Jonathan Campbell9.4
May 2Benjamin LantosFieldsDale WinterLie algebras
May 4Matthew Ellis12.1Thu DuongSU(2)
May 9Yiwen ChuPhysicsMelissa ShinHistory
May 11Antonio RangachevNormal basisNidhi ShrivastavaDouble cosets
May 16Benjamin Lantos13.2Jared Kubler13.2
May 18Jonathan CampbellGroup cohomologyLi-Mei LimMurnaghan-Nakayama

Assignments

There will be six problem sets, one due every 2 weeks.

Problem Set 1. Solutions.

Problem Set 2. Solutions. This includes a typesetting question: here is example1.tex.

Problem Set 3. Solutions.

Problem Set 4. Solutions.

Problem Set 5 (corrected).

Major project

A list of topics for your writing project is now available.

Notes

Here are some notes written by the student lecturers.

Here are some more notes on an algorithm for constructing character tables of symmetric groups.

Here are more notes working towards explaining why this algorithm works.

Contact information

I can be contacted as follows.