Math 100A - Abstract Algebra I (Fall 2021)

Warning: It may be necessary to make adjustments during the term as the pandemic and UCSD's policies in response continue to evolve, but we will keep these to a minimum.

All times are local to San Diego; this is PDT (UTC-7) until November 6 and thereafter PST (UTC-8).

Course syllabus

Math 100A/B/C is a rigorous three-quarter introduction to the methods and basic structures of higher algebra. 100A will focus on group theory. Topics include: groups, subgroups and factor (quotient) groups, homomorphisms, permutation groups, matrix groups, and some advanced topics as time permits (e.g., the Sylow theorems).

UCSD also offers a two-quarter algebra sequence, Math 103A/B (offered fall/winter, winter/spring, and in summer sessions). Between the two, Math 100 offers a greater emphasis on concepts and mathematical rigor, as well as some advanced topics not covered in Math 103 (e.g., Galois theory). Math 100 is recommended for students planning further study in pure mathematics, while Math 103 is recommended for most other students; however, any student interested in exploring these topics at a deeper level is welcome!

Students may not receive credit for both Math 100A and Math 103A. While 100A is a valid prerequisite for 103B, 103A is not a valid prerequisite for 100B without permission of the 100B instructor. (If you took 103A and want to audit 100A, contact an instructor for assistance.)

During fall 2021, there will be two parallel lectures of Math 100A; the two lectures will be coordinated, with the same homework, exams, and course policies. Both 100A lectures are equally valid prerequisites for 100B.

Most communication about the course will take place on the Zulip platform; in particular, all Zoom links will be posted there. An invitation link for Zulip is posted on Canvas.

All course activities will be available for remote participation except for the two midterms and the final exam. See the course policies below for the allowed accommodations.

Instructors:

TAs: Jack (JJ) Garzella, jgarzell [at] ucsd [etcetera]; Nathaniel (Tanny) Libman, nlibman [at] ucsd [etcetera]; Alex Mathers, amathers [at] ucsd [etcetera]; Baiming Qiao, bqiao [at] ucsd [etcetera].

Lectures: MWF 9-9:50am (Alberts) or MWF 10-10:50am (Kedlaya), in Peterson 102. A reminder about campus policies:

All lectures (by both instructors) will be recorded and made available via Canvas. In case it becomes necessary, we are prepared to shift some lectures to Zoom; details will be announced on Zulip. If you have a disability that interferes with compliance with these requirements, please request a disability accommodation (see below).

Sections: Monday 5-5:50pm (Qiao) over Zoom; Monday 6-6:50pm (Libman) in APM B412; Tuesdays 2-2:50pm (Mathers) in APM 2402; Tuesday 4-4:50pm (Garzella) in APM 2402. You may attend any of these sections; however, in case of too many students in the room, students enrolled in that section will have priority. Sections will not be recorded; if you wish to participate remotely, attend the Zoom section (which has no capacity limit).

Office hours (in-person):

Remote office hours (see Zulip for Zoom links):

Text: Algebra by Michael Artin, second edition (required). The hardcover, softcover, and eBook versions of the text are all interchangeable. For 100A, only chapters 1-7 will be used.

Prerequisites: Math 31CH or Math 109 or consent of instructor.

Homework: Weekly assignments, submitted via Gradescope, due Thursdays at 11:59pm. There will be no homeworks due in weeks 1 or 9 (Thanksgiving); homeworks due the week of a midterm will be shorter than usual, but will count equally in the course grade. No extensions will be granted; however, there will be opportunities to submit revisions to bring selected assignments up to 80% credit.

Midterm exams: Wednesday, October 20 and November 10, 8:00-8:50pm in Cognitive Sciences 001 (for students in the 9am lecture) and Cognitive Sciences 002 (for students in the 10am lecture). Note that these are outside of usual class hours, and not in the same location! (These rooms are significantly bigger, which will help with social distancing.) No makeup exams will be given, nor remote exams except as provided for by course policy (see below).

Final exam: Saturday, December 4, 3-6pm, location TBA. No makeup exam will be given (except to accommodate the Putnam competition; see below), nor a remote exam except as provided for by course policy (see below). See also UCSD exam policies.

Grading: 45% homework (including revisions); 15% first midterm; 15% second midterm; 25% final exam. Each assignment (whether long or short) will be weighted equally; the lowest homework assignment (after revisions) will be dropped. The lowest midterm score will be replaced with the final exam score if this is to your benefit. All grades will appear in Gradescope, not Canvas.

The conversion of raw percentages into letter grades will be made in order to maintain a grade distribution comparable with historical averages for this course. However, the following minima are guaranteed:
Percentage 97 93 90 87 83 80 77 73 70
Minimum grade A+ A A- B+ B B- C+ C C-
Additionally, any score in at least the 90th percentile or higher is guaranteed an A grade, while any score in the 70th percentile or higher is guaranteed a B grade.

Notwithstanding the above, to receive a passing grade, you must fulfill the following conditions.

Policies

No extensions will be given for homework assignments, but the lowest homework assignment will be dropped. In addition, there will be an opportunity at the end of the term to submit revisions for credit of up to 80% on each assignment.

Students who join the course from the waitlist, or who transfer between the two lectures, will be responsible for all homework from the start of the term. If you are on the waitlist, contact a member of course staff in order to get access to Gradescope and Zulip.

At the top of each homework assignment, you must specify all outside resources that you consulted, or write "None" if none were used. You do not need to report use of the main textbook; any materials posted to Canvas; your own notes from lecture; or consultations with course staff (including discussions during sections or office hours). You do need to report use of any other textbooks; any materials found online (in a precise fashion; e.g., for Wikipedia you must specify particular articles); and any consultation with anyone other than course staff (including study group partners). You are welcome and encouraged to collaborate with other 100A students (in either lecture), but you must write up your solutions in your own words; copying solutions verbatim from another student or other source is a violation of academic integrity (see below).

All exams will be closed-book: no outside materials may be consulted. This includes the textbook, lecture notes, the Internet, and anyone other than the exam proctor(s). We reserve the right to:

Exam accommodations will be made only in the following cases.

No makeup exams will be given (except for the Putnam, see above). A missed exam will be scored 0 and handled in accordance with the course grading scheme (see above).

A request for an Incomplete grade will only be granted in accordance with UCSD policies. In particular, you must be on track to receive a passing grade based on your submitted homework and midterm results (without the final exam substitution). To convert an incomplete into a final grade, you must provide to the instructor proper documentation of the circumstances leading to the Incomplete, and arrange with the instructor to complete all outstanding course requirements no later than the end of the subsequent quarter.

Violations of UCSD's academic integrity policies (cheating, plagiarism, etc.) will be handled by the instructor using UCSD administrative measures. In addition, the instructor reserves the right to assign a 0 score to any homework or exam affected by a violation. If you suspect a violation, please bring it to the attention of the instructor and/or TA immediately.

Topics by date

All numbering refers to Artin. Listings for future dates are subject to adjustment based on how far we get in class.