Math 6320-001, Spring 2021: Modern Algebra II
Whiteboard links
Everybody
Group 1 (left, purple)
Group 2 (middle, red)
Group 3 (right, blue)
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This is the second course in the graduate algebra sequence; the main topics are groups, field extensions / Galois theory, and representation theory. Please consult the graduate bulletin for a more detailed description of the course contents.
Class info
- Spring 2021, Tu/Th 12:25pm-1:45pm (mountain)
- Office hours on Thursdays, 8:30pm-10:00pm (mountain)
- Class and office hours are in the gather.town link on Canvas. If you are auditing the class, please contact me via email for access information.
References and other resources
- Dummit and Foote - Abstract Algebra (3rd edition)
Exams
- Final · 5/03, 10:30am-12:30pm mountain time · links live 5/03 at approximately 10:30am mountain · PDF · TeX · answer key (T/F and short answer only)
- The exam will be administered on Zoom (not gather.town), in the same room we previously used for class and the midterm (details on Canvas).
- The midterm is open-book (Dummit and Foote) and open-notes, but no other sources or collaboration are allowed.
- You will be put into individual breakout rooms so that you can call me in to ask any questions.
- You will have 1 hour and 45 minutes for the exam, then 15 minutes to upload your answers Gradescope. Please stay logged in to Zoom until your exam is submitted on Gradescope so that I can assist if there are any techinical difficulties.
- The exam is cumulative, but the biggest emphasis will be on Galois theory.
- Questions:
- 15 true/false (1 pt each, no justification).
- 5 short answer (2 pts each, no justification).
- 1 proof (5 points). You will choose one of 3 questions; one in abstract group theory, one in Galois theory, and one in representation theory.
- Midterm (3/04) -- PDF · TeX · answer key
Weekly handouts / homework
- Week 13-15 (4/13, 4/15, 4/20, 4/22, 4/27). PDF · TeX · Homework due 4/29.
Updated 2021-04-27 at 10:15pm: Removed parts (2) and (3) in Exercise 3 -- I made a mistake in trying to organize a proof this way and the hint didn't work, sorry! Also, in Exercise 1, G is a finite group.
Updated 2021-04-25 at 1:05pm: Exercise 6 changed to bonus exercise.
Updated 2021-04-22 at 9:05pm: Exercise 4 corrected; changed K to characteristic zero since the normal basis theorem is only stated in characteristic zero.
Reminder: we are flipping the class for the remainder of the term -- lectures will be posted in advance on the website, and the class meeting will be on gather.town (see canvas for the access information).
- Week 11-12 (3/30, 4/01, 4/06, 4/08). PDF · TeX · Homework due 4/15 (extended from 4/13).
Optional reading on straight-edge and compass constructions for Problem 2
Updated 2021-04-13 at 2:20pm: Exercise 3-(2) corrected; there was a missing sign -- to fix it I've rewritten the statement to be more straightforward and given a hint.
- Week 10 (3/23, 3/25). PDF · TeX · Homework due 3/30.
Updated 2021-03-25 at 7:45pm: Exercise 4 -- ad-bc not = 0 (instead of 1), and the matrix was transposed
- Week 9 (3/16, 3/18). PDF · TeX · Homework due 3/23.
- Week 8 (3/09, 3/11). Spring Pause -- Class on 3/09 is optional; we will go over the answers to the midterm. Class on 3/11 will serve as office hours and the regular office hours are cancelled this week.
- Week 7 (3/02, 3/04). Review on 3/02; midterm on 3/04. Office hours moved to Tuesday 3/02, 8:30pm-10:00pm (mountain) this week. Problem rewrites for homeworks 1-5 should be submitted via Gradescope by March 4th at 11:59p (mountain).
- Week 6 (2/23, 2/25). PDF · TeX · Homework due 3/16.
Updated 2021-03-10 at 7:45pm: Exercise 1.(14) - (2 pi i) / k in the exponent meant to be (2 pi i k)/p
- Week 5 (2/16, 2/18). PDF · TeX · Homework due 2/23.
Updated 2021-02-18 at 2:25pm: Statement of Exercise 4 corrected: the group of *invertible* upper triangular 3x3 matrices.
- Week 4 (2/09, 2/11). PDF · TeX · Homework due 2/16.
Updated 2021-02-14 at 2:25pm: Statement of Exercise 4-(1) corrected: if K is infinite, you should assume the phi_i are injective. Because of how the problem was previously worded, it is fine if you write up your solution assuming either that K is finite or that the phi_i are always injective.
- Week 3 (2/02, 2/04). PDF · TeX · Homework due 2/09.
Updated 2021-02-07 at 2:35pm: Statement of Problem 2 corrected (n != 6).
- Week 2 (1/26, 1/28). PDF · TeX · Homework due 2/02.
Updated 2021-01-26 at 9:00pm: Statement of Problem 1 corrected (assume G finite).
- Week 1 (1/19, 1/21). PDF · TeX · Homework due 1/26.
Updated 2021-01-19 at 9:00pm: Statement of Problem 1 corrected (1,2,3 -> 1,2,3,4,6)
Class recordings and notes
Note: for student privacy, only the instructor's screenshare and audio is recorded.
- 2021-04-27, Class 24. whiteboard (PDF), notes, video (to be watched before class).
- 2021-04-22, Class 23. whiteboard (PDF), notes, video (to be watched before class).
- 2021-04-20, Class 22. whiteboard (PDF), notes, video (to be watched before class).
- 2021-04-15, Class 21. notes, video (to be watched before class).
- 2021-04-13. No notes or video -- just group exercises related to the homework.
Starting 2021-04-13, we switched to a flipped class.
- 2021-04-08, Class 20. Notes. Video.
- 2021-04-06, Class 19. Notes. Video.
- 2021-04-01, Class 18. Notes. Video.
- 2021-03-30, Class 17. Notes. Video.
- 2021-03-25, Class 16. Notes. Video.
- 2021-03-23, Class 15. Notes. Video.
- 2021-03-18, Class 14. Notes. Video.
- 2021-03-16, Class 13. Notes. Video.
- 2021-03-11, Class=Office Hours. (Spring Pause)
- 2021-03-09, Midterm solutions. Notes. Video. (Spring Pause)
- 2021-03-04, Midterm.
- 2021-03-02, Midterm Review. Notes. Video.
- 2021-02-25, Class 12. Notes. Video.
- 2021-02-23, Class 11. Notes. Video.
- 2021-02-18, Class 10. Notes. Video.
- 2021-02-16, Class 9. Notes. Video.
- 2021-02-11, Class 8. Notes. Video.
- 2021-02-09, Class 7. Notes. Video.
- 2021-02-04, Class 6. Notes. Video.
- 2021-02-02, Class 5. Notes. Video.
- 2021-01-28, Class 4. Notes. Video.
Notes updated 2021-02-07: The exercise at the end should have said G/Z(G) cyclic, not abelian!
- 2021-01-26, Class 3. Notes. Video.
- 2021-01-21, Class 2. Notes. Video.
- 2021-01-19, Class 1. Notes. Video.