MATH 5111 (Advanced Algebra I)

Teaching Site

Class schedule

Lecture
Time Mon, Wed 10:30 – 11:50
Venue Rm 2612A, Lift 31–32
Instructor Guowu Meng
Office 3422
Phone 2358-7451

Textbook

Cover of Lang's Algebra

Serge Lang, Algebra, 3rd revised edition.
Graduate Texts in Mathematics 211.

Course contents

A large part of Chapters I–V and Chapter XVI will be covered.

  1. Group theory — basic facts
  2. Categories — basic facts
  3. Group actions
  4. Sylow theory
  5. Sums and products
  6. Finite abelian groups
  7. Commutative rings — basic facts
  8. Localizations
  9. Modules — basic facts
  10. Exact sequences
  11. Free modules
  12. Hom, projective modules, and Ext
  13. PIDs, UFDs, and Euclidean domains
  14. Finitely generated modules over PIDs
  15. Polynomial rings
  16. Tensor products
  17. Field theory — basic facts

Homework

There are numerous exercise problems in the textbook, and you may do as many of them as you wish. To keep your workload to a minimum, do the exercises assigned in class.

Grading policy

Your final grade will be determined by the two exams.

Extra tool

ChatGPT or an equivalent.