Updated: 05/07/07, 11:20pm
What is new: File size reduced: Algebra II, 2007, combined HW,

Syllabus

• The book will be Serge Lang "Algebra," 4th edition. (Contents, page numbers and layout are identical to the 3rd edition as far as I can tell. Introduction and references are different.)
• We will cover the following topics:
  1. Homological algebra (Chapter XX)
  2. Commutative algebra (Chap VIII-X, XII)
  3. Noncommutative algebra (Chap XVII)
  4. Representations of finite groups (Chap XVIII)
• There will be no quizzes or tests. The grade is based on HW and ``class participation.'' You will get a letter grade for each homework.

Instructor

• Kiyoshi Igusa
• Goldsmith 305
• Office hours (subject to change): MWR 11-12, MW 3:30-4 and by appointment.
• Phone 63062.

Notes

• Notes and HW in one document
• Part A: Homological algebra (41pp= pp1-36 with extra pp17-19 plus cover page and table of contents)
• Part B: Commutative algebra (48pp with cover page and table of contents)
• Part C: Semisimplicity (13pp with cover page and table of contents)
• Part D: Representations of finite groups (46pp with cover page and table of contents)
  • Part D1a: Representation of groups (pp2-5) (handed out in class)
  • Part D1b: The group ring k[G] (pp6-8) (thursday's lecture)
  • Part D1: Representations (pp2-9)
• Part D2: Characters
  • Part D2a:Basic properties of characters (pp10-12)
  • Part D2b:Irreducible characters (pp13-18)
  • Part D2c:Character table (pp19-22)
  • Part D2d:Orthogonality relations (pp23-28)
  • Part D2e:Column orthogonality (pp29-30)
• Part D3: Induction
  • Part D3a: Induced characters (pp31-35)
  • Part D3b: Induced representations (pp36-41)
  • Part D3c: Artin's induction theorem (pp42-45)

HW and answers in one file

• Homework 01, answers
• Homework 02, answers
• Homework 03, answers
• Homework 04, answers
• Homework 05, answers
• Homework 06, answers
• Homework 07, answers
• Homework 08, answers
• Homework 09, answers
• Homework 10, answers