Instructor: Lucas Buzaglo.
Location of lectures: Peterson Hall 104.
Office hours in AP&M 1230:
- Monday 4:30-5:30pm.
- Tuesday 12:30-1:30pm.
- Thursday 12:30-1:30pm.
TA: Zehong Zhao will hold discussion sections on Wednesdays 2-2:50pm or 3-3:50pm in AP&M 2402.
Course Website: Canvas.
Textbook: J. Fraleigh, N. Brand, A First Course in Abstract Algebra, 8th edition, Pearson, 2021.
Course Description: The aim of this course will be to cover Chapters 1-3. Topics include: Sets, binary relations, groups, subgroups, cyclic groups, and generating sets.
Prerequisites: Math 31CH or Math 109 or consent of instructor.
Grading and homework policies can be found here.
Schedule - Link to Google Calendar
Click on the lecture dates to see the lecture notes
| Week | Lecture dates | Material to be covered | Deadlines | Description of homework |
|---|---|---|---|---|
| 0 | Sept 26 |
Introduction and Section 0: Sets and relations |
None. | No homework due this week. |
| 1 | Oct 1, Oct 3 |
Section 1: Binary operations. Section 2: Groups. |
Oct 4: Homework 1 is due. |
Homework 1 Section 0 (page 7) #6, 12, 16, 30. Section 1 (page 17) #3, 10, 27. Section 2 (page 28) #2. |
| 2 | Oct 8, Oct 10 |
Section 3: Abelian Examples. Section 4: Nonabelian examples. |
Oct 11: Homework 2 is due. |
Homework 2 Section 2 (page 28) #6, 18, 28, 31, 38. Section 3 (page 38) #26, 27. Section 4 (page 50) #11. |
| 3 | Oct 15, Oct 17 |
Section 5: Subgroups. Section 6: Cyclic groups. |
Oct 18: Homework 3 is due. |
Homework 3 Section 4 (page 50) #12, 26, 35. Section 5 #8, 22, 30, 56, 61. |
| 4 | Oct 22, Oct 24 |
Section 7: Generating sets and Cayley Digraphs. Catch up and review. |
Oct 24: Midterm 1 at 8pm. Room: Center Hall 212. Practice test Oct 25: Deadline to drop class without W. |
No homework due this week. |
| 5 | Oct 29, Oct 31 | Section 8: Groups of permutation. | Nov 1: Homework 4 is due. |
Homework 4 Section 6 #4, 18, 24c, 58. Section 7 #2, 10, 21. Section 8 #5. |
| 6 | Nov 5, Nov 7 |
Section 9: Finitely generated abelian groups. Section 10: Cosets and the theorem of Lagrange. |
Nov 8: Homework 5 is due. Nov 8: Deadline to drop class without F. |
Homework 5 Section 8 #2, 15, 37. Section 9 #3, 10, 15, 39. Section 10 #6. |
| 7 | Nov 12, Nov 14 | Section 12: Factor groups. | Nov 15: Homework 6 is due. |
Homework 6 Section 10 #16, 36, 47. Section 12 #8, 12, 28, 33, 36. |
| 8 | Nov 19, Nov 21 |
Section 13: Factor-group computations and simple groups. Catch up and review. |
Nov 21: Midterm 2 at 8pm. Room: Center Hall 212. |
No homework due this week. |
| 9 |
Nov 26 No class on Nov 28 (Thanksgiving) |
Section 13: Factor-group computations and simple groups. | None. | No homework due this week. |
| 10 | Dec 3, Dec 5 | Section 14: Group action on a set. |
Dec 6: Homework 7 is due. Dec 7: Final exam at 11:30am. Room: Peterson Hall 104. |
Homework 7 Section 13 #4, 7, 16, 41 (parts a, b, c), 42, 43. |