Mathematics 551 Information

• Text Readings: Hungerford, 1.7, 1.1-1.3
• Week 1 Problem set 1

• Text Readings: Hungerford, 1.4-1.6
• Week 2 Problem set 2
• Week 2 expository reading:
  • Read When is one thing equal to some other thing? by B. Mazur

• Text Readings: Hungerford, 1.7-1.9
• Week 3 Problem set 3
• Week 3 expository reading:
  • Read sections 1-3 of this article by Baez and Dolan which discusses categorification.
  • There are textbooks on category theory freely available online which may be useful in finding a definition or proposition. For example The Joy of Cats by Adamek, Herrlich and Strecker is a more than 500 page text containing many examples and theorems of category theory.

• Text Readings: Hungerford, 2.1-2.4
• Week 4 Problem set 4

• Text Readings: Hungerford, 2.5-2.8
• Week 5 Problem set 5
• Week 5 expository reading:
  • Read the notes on colimits and limits which provide examples about the notions discussed in class.
  • Read the short note concerning the Burnside, Cauchy-Frobenius method for counting orbits in a group action.

• Text Readings: Hungerford, 3.1-3.2
• Week 6 Problem set 6
• Week 6 expository reading:
  • Read the expository article on classifying finite simple groups
  • Read the short one-page article which explains how to solve problem 4c of week 4.

Oral midterm exam signup information 11/3-11/9

• Text Readings: Hungerford, 3.3-3.4
• Week 7 Problem set 7

• Text Readings: Hungerford, 3.5-3.6
• Week 8 Problem set 8

• Text Readings: Hungerford, 4.1-4.3
• Week 9 Problem set 9
• Week 9 expository reading:
  • Read the brief introduction to adjoint functors

• Text Readings: Hungerford, 4.4-4.7
• Week 10 Problem set 10
• Week 10 expository reading:
  • Read the notes on projective and injective modules .

• Text Readings: Hungerford, 7.1-7.5
• Week 11 Problem set 11
• Week 11 expository reading:
  • Read the notes on the dimension of the space of intertwining operators .

• The final exam problem set has been posted.
• Check by periodically to see if there are any changes, misprint corrections, etc.
• The record of changes will be detailed here and at the beginning of the PDF file
  • Initial posting 1:05 PM 12/11/06
  • Added n > 0 to problem 8 12:04 AM 12/14/06
  • Changed b) to a) in last part of problem 2 11:31 PM 12/14/06
  • Added "with entries in a field" to problem 7 11:41 PM 12/14/06
  • Removed "Let F and E be fields" from problem 2 9:45 PM 12/19/06
• It will be due at 11:59 AM on 12/21/06