Math 100A - Abstract Algebra I (Fall 2022)

Special note: due to the UC-wide academic strike that began in week 8, many of these policies have had to be adjusted. See Zulip for details.

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 2022, there will be two parallel lectures of Math 100A; these will be distinct but highly coordinated, and this syllabus applies equally to both lectures. Both 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. To get the link for Zulip, complete the Checklist survey 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.

If you are an enrolled UCSD student and wish to audit the course, contact an instructor to be added to Canvas.



Lectures: Kedlaya: MWF 9-9:50am in Peterson 102; Greenfeld: MWF 10-10:50am in Warren Lecture Hall 2205. Please attend only your assigned lecture; you may watch recordings of both lectures in Canvas. Masks will be required in lecture as long as campus guidelines require it.

Sections: McGlade: Wed 6-6:50pm or 7-7:50pm in Warren Lecture Hall 2112; Hu: Thu 8-8:50am or 9-9:50am in APM B402A. You may attend any section (of either lecture) as long as you make space for all students assigned to that section.

Office hours: These will be moved or augmented some weeks; watch Zulip for announcements.

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; the same text will be used for 100B and 100C this year.

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

Homework: Weekly assignments, submitted via Gradescope, due Fridays at 11:59pm. There will be no homework due in week 9 (Thanksgiving); homeworks due the week of a midterm will be shorter than usual, but will count equally in the course grade. Homework due in week 1 is not for credit. No extensions will be granted; however, there will be opportunities to submit revisions to bring selected assignments up to 80% total credit.

Midterm exams: Friday, October 14 and Wednesday, November 9 in class. No makeup exams will be given, nor remote exams except as provided for by course policy (see below). However, for each midterm there will be one opportunity to submit revised work for up to 90% total credit.

Final exam: Kedlaya: Wednesday, December 7, 8-11am, Peterson 102; Greenfeld: Friday, December 9, 8-11am, Warren Lecture Hall 2205. You may request in advance to switch to the exam time for the other lecture; otherwise, no makeup exam will be given, nor a remote exam except as provided for by course policy (see below). See also UCSD exam policies.

Grading: 45% homework (including revisions, not counting week 1); 15% each midterm (including revisions); 25% final exam. Each assignment (whether long or short) will be weighted equally; the lowest homework assignment (after revisions) will be dropped. 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.


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 total 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:

For each midterm, there will be an opportunity to submit one revision for up to 90% total credit; the closed-book policy also applies during the revision process.

Exam accommodations will be made only in the following cases.

All accommodation requests must be made with sufficient advance notice, preferably by the end of week 1. No accommodations are available for homework assignments except for the revision process (see above).

No makeup exams will be given. A missed midterm exam will score 0, subject to revision (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 (including revisions). 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. The correspondence between dates and topics may differ slightly between the two lectures. Listings for future dates are subject to adjustment based on how far we get in class.