Instructor: Lucas Buzaglo.
Location of lectures: PETER 104.
Office hours in AP&M 1230:
- Tuesday 4-5pm.
- Wednesday 4-5pm.
- Friday 12-1pm.
TA: David Cavender will hold discussion sections on Thursdays 3-3:50pm or 4-4:50pm in AP&M B412.
Course website: Canvas.
Lecture notes: Link.
Recommended textbook: J. Fraleigh, N. Brand, A First Course in Abstract Algebra, 8th edition, Pearson, 2021.
Course description: The aim of this course learn the basics of group theory. 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
| Week | Lecture dates | Material to be covered | Deadlines | Homework |
|---|---|---|---|---|
| 1 | Jan 6, Jan 8, Jan 10 |
Introduction. Sets and relations. Binary operations. |
Jan 10: Homework 0 is due. | Homework 0 |
| 2 | Jan 13, Jan 15, Jan 17 |
Groups and group isomorphisms. Modular arithmetic. |
Jan 17: Homework 1 is due. | Homework 1 |
| 3 |
Jan 22, Jan 24 No class on Jan 20 (Martin Luther King, Jr. Holiday) |
Permutations and symmetric groups. | Jan 24: Homework 2 is due. | Homework 2 |
| 4 |
Jan 27, Jan 29 Midterm on Jan 31 |
Subgroups. Review lecture. |
Jan 31: Midterm 1 during lecture time. Jan 31: Deadline to drop class without W. |
No homework due this week. |
| 5 | Feb 3, Feb 5, Feb 7 |
Dihedral groups. Cyclic groups. |
Feb 7: Homework 3 is due. | Homework 3 |
| 6 | Feb 10, Feb 12, Feb 14 |
Cyclic groups. Generating sets. |
Feb 14: Homework 4 is due. Feb 14: Deadline to drop class without F. |
Homework 4 |
| 7 |
Feb 19, Feb 21 No class on Feb 17 (Presidents' Day) |
Cayley graphs. Homomorphisms. |
Feb 21: Homework 5 is due. | Homework 5 |
| 8 |
Feb 24, Feb 26 Midterm on Feb 28 |
Groups of permutation. Review lecture. |
Feb 28: Midterm 2 during lecture time. | No homework due this week. |
| 9 | Mar 3, Mar 5, Mar 7 |
Cosets and Lagrange's theorem. Quotient groups. |
Mar 9: Homework 6 is due. | Homework 6 |
| 10 | Mar 10, Mar 12, Mar 14 |
Simple groups. Review lecture. |
Mar 14: Homework 7 is due. | Homework 7 |
| Finals week | Final exam on Mar 17 |
Mar 17: FINAL EXAM. Time: 11:30am-2:30pm. Room: PETER 104. |