Math 103A, Modern Algebra I, Fall 2021

Instructor: Andrew Suk (Section A), Ming Zhang (Section B), Aranya Lahiri (Section C), Reuven Hodges (Section D)
Course Website: Canvas.
Syllabus: here (Please read carefully).
Textbook: J. Fraleigh, N. Brand, A First Course in Abstract Algebra, 8th edition, Pearson, 2021.

Schedule

Sept 24: Introduction and Section 0: Sets and relations.

Sept 27. Section 1: Binary operations.
Sept 29. Section 2: Groups.
Oct 1. Section 2: Groups. Homework 1 is due. Section 0 (page 7) #6, 12, 16, 30. Section 1 (page 17) #3, 10, 27. Section 2 (page 28) #2.

Oct 4. Section 3: Abelian Examples.
Oct 6. Section 4: Nonabelian examples.
Oct 8. Section 4: Nonabelian examples. Homework 2 is due. Section 2 (page 28) #6, 18, 28, 31, 38. Section 3 (page 38) #26, 27. Section 4 (page 50) #11.

Oct 11. Section 5: Subgroups.
Oct 13. Section 6: Cyclic groups.
Oct 15. Section 6: Cyclic groups. Homework 3 is due. Section 4 (page 50) #12, 26, 35. Seciton 5 #8, 22, 30, 56, 61.

Oct 18. Section 7: Generating sets and Cayley Digraphs.
Oct 20. Catch up and review.
Oct 22. Midterm 1. No homework due.

Oct 25. Section 8: Groups of permutation.
Oct 27. Section 8: Groups of permutation.
Oct 29. Section 9: Finitely generated abelian groups. Homework 4 is due. Section 6 #4, 18, 24c, 58. Section 7 #2, 10, 21. Section 8 #5.

Nov 1. Section 9: Finitely generated abelian groups.
Nov 3. Section 10: Cosets and the theorem of Lagrange.
Nov 5. Section 10: Cosets and the theorem of Lagrange. Homework 5 is due. Section 8 #3, 15, 37. Section 9 #3, 10, 15, 39. Section 10 #6.

Nov 8. Section 12: Factor groups.
Nov 10. Section 12: Factor groups.
Nov 12. Section 12: Factor-groups. Homework 6 is due. Section 10 #16, 36, 47. Section 12 #8, 12, 28, 33, 36.

Nov 15. Section 12: Factor groups.
Nov 17. Catch up and review. Review.
Nov 19. Midterm 2. No homework due.

Nov 22. Section 13: Factor-group computations and simple groups.
Nov 24. Catch up and review.
Nov 26. No class (Thanksgiving).

Nov 29. Section 13: Factor-group computations and simple groups.
Dec 1. Section 14: Group action on a set.
Dec 3. Catch up and review. Homework 7 is due. TBA on Canvas.