Math 503, Bridge to Algebra
Time: M/W/F 1230-120
Location: MATH 215
Office hours: MWF 1130-1230
Book: I do not plan to have an official textbook for the class. Every book has strengthens and weaknesses. In particular, it is usually best to have several different references. The following books are all fairly standard textbooks.
- Abstract Algebra by Dummit-Foote.
- Algebra by Lang.
- Advanced Modern Algebra by Rotman.
- Basic Algebra I, II, III by Jacobson.
- Algebra I, II by Bourbaki.
- Algebra by Hungerford
- Topics in Algebra by Hernstein.
There are other books as well that you could reference. I suggested finding two or three different references.
Class Lectures: The class lecture notes can be viewed below. They will be editing throughout the term and so I strongly suggest that you DO NOT print them out.
Problem sets: I will post weekly problem sets here in .pdf format. The due date for the problem sets will be in class on Wednesdays.
Grades: A combination of your performance of the problem sets and the exams will be used to calculate your grade. The grades are based on your ranking in the class.
Class announcements:
- August 26: Problem set 1 has been posted. There are a lot more problems than I was expecting to give but the problems are all relatively easy.
- September 5: Problem Set 2, problem 5 (b) had a typo that has now been fixed. It should have said $H_1 \leq H_3$.
- September 10: Problem Set 3 has been posted. It is due on September 20 (this is a Wednesday). From now on, the problem sets will be due on Wednesdays.
- September 13: Problem 4 (b) on Pset 3 was changed. The old version was silly.
- September 26: Problem 6 (b) on Pset 3. The problem has a typo. The points x_1 and x_2 need to be in the same G-orbit, say O_x. It is false for x_1 and x_2 merely in X.
- October 23: Fixed a few typos in on Problem Set 6/Practice exam.
Class Lectures:
The lecture schedule with topic is below (this is tentative):
- Lecture 0. August 21. Class Overview.
- Lecture 1. August 23. Sets and Functions.
- Lecture 2. August 25. Mathematical Overview.
- Lecture 3. August 28. Algebraic Structures (1.1 in the class notes).
- Lecture 4. August 30. Algebraic Subobjects (1.2 in the class notes).
- Lecture 5. September 1. Morphisms (1.3 in the class notes) Pset 1 due.
- September 4. Holiday. No class.
- Lecture 6. September 6. Quotients, Part 1 (1.4 in the class notes).
- Lecture 7. September 8. Quotients, Part 2 (1.4 in the class notes).
- Lecture 8. September 11. Quotients, Part 3 (1.4 in the class notes). Pset 2 due.
- Lecture 9. September 13. Isomorphism Theorems (1.5 in the class notes).
- Lecture 10. September 15. Isomorphism Theorem (1.5 in the class notes).
- Lecture 11. September 18. Commutative Diagrams (1.6 in the class notes).
- Lecture 12. September 20. Group Actions. Pset 3 due.
- Lecture 13. September 22. Group Actions.
- Lecture 14. September 25. Group Actions.
- Lecture 15. September 27. Group Actions. Pset 4 due.
- Lecture 16. September 29. Group Actions.
- Lecture 17. October 2. Group Actions.
- Lecture 18. October 4. Group Actions.
- Lecture 19. October 6. Group Theory Overview.
- October 9. Fall Break. No class.
- Lecture 20. October 11. Group Theory.
- Lecture 21. October 13. Group Theory.
- Lecture 22. October 16. Group Theory.
- Lecture 23. October 18. Group Theory. Pset 5 due.
- Lecture 24. October 20. Group Theory.
- Lecture 25. October 23. Group Theory.
- Lecture 26. October 25. Group Theory.
- Lecture 27. October 27. Midterm 1. Pset 6/Practice Exam due.
- Lecture 28. October 30. Ring Theory.
- Lecture 29. November 1. Ring Theory.
- Lecture 30. November 3. Ring Theory
- Lecture 31. November 6. Ring Theory.
- Lecture 32. November 8. Polynomial Rings.
- Lecture 33. November 10. Polynomial Rings.
- Lecture 34. November 13. Polynomial Rings.
- Lecture 35. November 15. Fields.
- Lecture 36. November 17. Fields.
- Lecture 37. November 20. Fields.
- November 22. Holiday. No class.
- November 24. Holiday. No class.
- Lecture 38. November 27. Fields.
- Lecture 39. November 29. Fields.
- Lecture 40. December 1. Midterm 2.
- Lecture 41. December 4.
- Lecture 42. December 6.
- Lecture 43. December 8.