General Logistics
| Instructor: | Angus Chung. You can call me by Angus. |
| Email: | k7chung (at) ucsd (dot) edu. Email is the best way to contact me. Do not send me messages on canvas, as canvas messages are not well-organized. In general, I will reply to emails as soon as I have time during work hours (9-5 weekdays). However, allow for a business day for a reply. In particular, please do not expect questions for homework being answered the night it is due. |
| Office: | AP&M 6442 |
| David Cavender | |
| Email: | dcavende (at) ucsd (dot) edu |
| Office: | HSS 6414 |
| Course Title: | Math 103A: Modern Algebra I |
| Textbook: | Abstract Algebra: Theory and Applications, written by Thomas Judson with Sage support by Rob Beezer, Version 2022 |
| Reference book (optional): | A Book of Abstract Algebra, by Charles Pinster, Second Edition |
| Reference book 2 (optional, a lot more theory based): | Abstract Algebra, by David Dummit and Richard Foote, Third Edition |
The textbook is free online, via the above link.
| Lecture Time: | MWF 3-4pm |
| Location | Ridge Walk Academic Complex 0121 |
| Midterms | Feb 1, Mar 1 (Wed), in class |
| Final Exam | Mar 22, 2023, 3-4:30pm (finalized), RWAC 0121 |
Syllabus PDF
Office Hour
My office hour: MWF 4-5pm at my office (location tentative)
If you are not sure what "office hour" is, it is an opportunity for you to talk to me about the class, seek help in topics you are unsure about, discuss the homework problems you are stuck at. A lot of students tend to be intimidated to talk to the instructor, fearing that they are judged for not knowing the material. The fact is, we are trying to help you succeed, and we do not evaluate student at all during office hours. A student who comes to office hours regularly will generally leave a good impression to the instructor, in contrast to the misbelief that the instructor would think such student is not performing well. So, if you need anything, come to office hours. Seek help soon, rather than later!
Class Format
The class will not be in a traditional "lecture-only" style. I will ask you to actively participate. This includes have you work and talk both as a small group in class, and in front of everyone. See "Reading" in Syllabus.pdf.
Attendance is not part of your grade, but it is required via oral presentation. If I pick a person to present and they are not in class, they get a 0 for the presentation.
Late Join Policy
If you wish to enroll in this class (e.g. you are currently on the waitlist), you should keep up with the class since day 1. In particular, you need to attend all lectures, submit all the homework on time and be present for progress checks.
(IMPORTANT) When you are finally officially enrolled to the class, please read the ''Welcome Message'' on Canvas Announcements, and complete everything it instructs you to do.
Homework
Please read the homework instructions before working on the homework.- HW 1: Ch 1.4 Q1 (no proof), 2 (no proof), 8, 17, 18, 22, 29. Ch 2.4 Q4, 15, 16
- HW 2: Ch 3.5 Q2 (give counterexamples to all prperties which are not fulfilled; no proof needed if it is a group), 4, 5, 6 (answer only), 7, 11, 15, 16, 39, 40 (39, 40: replace ''subgroup of ...'' by ''group''). Solution, note that there is a typo for Q16, g^2 should be CAB not CBA.
- HW 3: Ch 3.5 Q27, 31, 33, 44, 46, 47, 48, 53, 54. Ch 4.5 Q2abd. Solution.
- HW 4: Ch 4.5 Q1bd, 4acf, 7, 8, 11, 14, 23, 26, 27, 31. Solution.
- HW 5: Ch 5.4 Q2dfghij, 3cde, 5 (skip "list all subgroups of S4"), 17, 24, 26, 27, 30, 32, 36. Solution.
- HW 6: Ch 5.4 Q11, 25, 35, 37. Ch 6.5 Q1, 11 (Change (c) to g_2H \subseteq g_1H; One possible way is to show: (a) => (b), (b) => (a), (a) => (c), (c) => (d), (d) => (e), (e) => (a)), 12, 13, 17, 18. Solution.
- HW 7: Ch 9.4 Q2, 3, 8, 9 (skip ''Prove that G is a group'', we have done this in HW2 already), 11, 12, 24, 25, 34, 37. Solution.
- HW 8: Ch 9.4 Q20, 21, 22, 24, 26, 41, 42. Ch 13.4 Q2, 3, 7. Solution.
- HW 9: Ch 10.4 Q2, 5 , 7, 8, 12 (skip ''Show that C(g) is a subgroup''), 13, 14. Ch 11.4 Q2, 3, 12, 18. For Q5 and 13c, you only have to prove that the subgroup is normal, as we know those subsets are indeed subgroups from midterm 1 / HW2 respectively. Solution.
- HW 10: David's problem sheet, Q3, 4, 5. This problem sheet focuses on the new topics, but you should also review on the old topics, such as order, proofs about subgroup, Sn, etc.