Algebra

Instructor: Vera Serganova
Email address: serganov@math
  • webpage:http://math.berkeley.edu/~serganov
  • Phone Number: 642-2150
  • Office hours: Tu 4:00-6:00 in 709 Evans
  • Text: S. Lang, Algebra.
  • Homework: Each Thursday problems will be posted on this webpage. Homework will be due the following Thursday
  • Grading policy: Your grade will be computed according to the following rule: 70% for your homework, 30% for the take-home final.
  • Course outline
  • Integral Ring Extensions (Chapter VII)
  • Transcendental Extensions (Chapter VIII)
  • Algebraic Spaces (Chapter IX)
  • Noetherian Rings and Modules (Chapter X)
  • Tensor Product (Chapter XVI)
  • Semisimple Modules and Rings (Chapter XVII)
  • Alternating Product (Chapter XIX)
  • Complexes and Derived Functors (Chapter XX)
  • Week 1. Lang VII.1,2. Problem set #1
  • Week 2. Lang VII.3, VIII.1. Problem set #2
  • Notes on exchange property
  • Week 3. Lang VIII.2, IX.1,2 Problem set #3
  • Week 4. Lang IX.3,4 Problem set #4
  • Week 5. Lang IX.5, X.1,2 Problem set #5
  • Week 6. Lang X.3,4,7 Problem set #6
  • Week 7. Lang X.5,6 Problem set #7
  • Week 8. Lang XVI.1,2,5 Problem set #8
  • Week 9. Lang XVI.3,4 Problem set #9
  • Week 10. Lang XVI.6,7,8 Problem set #10
  • Week 11. Lang XIX.4, XVII.1,2,3 Problem set #11
  • Extra credit exercises
  • Notes on Weyl and Clifford algebras
  • Week 12. Lang XVII.4,5,6
  • Week 13. Lang XX.1,2,3 Problem set #12
  • Take home final exam