Information appearing below is subject to revision until the first lecture.
Math 100A/B/C is a rigorous three-quarter introduction to the methods and basic structures of abstract algebra. While Math 100A concentrates on groups, while Math 100B focuses on rings and fields, Math 100C explores ways that these structures can be used to study each other. Topics include: representation theory of finite groups; Galois theory of fields; applications to constructions in Euclidean geometry; solvability of polynomial equations.
Instructor: Kiran Kedlaya, kedlaya [at] ucsd [etcetera].
TA: Nik Castro, n1castro [at] ucsd [etcetera].
Lectures: MWF 9:00-9:50am in Peterson 102. No lectures on the following university holidays: Monday, May 25 (Memorial Day). Lectures will be recorded and made available via Zulip (see below).
Sections: Tue 5:00-5:50pm or 6:00-6:50pm in APM 6402. You may attend either section; however, students attending their registered section have priority in case the room is full.Office hours: Kedlaya: Wed 12-1pm, APM 7202 and Thu 7-8pm, online; Castro: Fri 1:30-3:30pm, HSS 5086. See Zulip for one-off adjustments to the schedule. Note: I am bad with names, so I will probably ask for a reminder when you come to office hours.
Communication: All communication regarding the course will take place on the Zulip platform; we will not be using Canvas. An invite link to Zulip will be sent to all enrolled students. You must use your UCSD email address to sign into Zulip, but please indicate your preferred name and pronouns.
Prerequisites: Math 100B (taken at any time) or consent of instructor. Students wishing to proceed from 103B to 100C should contact the instructor.
Homework: weekly assignments, due Fridays at 11:59pm via Gradescope. You will not be added to Gradescope automatically; use the entry code provided on Zulip to join. No extensions will be given, but the lowest assignment will be dropped. The week 1 assignment is a survey that is not for credit, but please submit it anyway to check your Gradescope setup. You may submit handwritten or typed assignments; if typed, use of LaTeX is encouraged.
Doing the homework problems is crucial to understanding the material in this course (including preparing for the quizzes and the final exam). You are expected to write your solutions logically, using mathematical rigor and clear exposition, and cite relevant results from lecture or the textbook. As this is a 4-credit class, you are expected to spend 8-12 hours per week outside of class on reading, studying, and completing the homework problems.
You are strongly encouraged to collaborate with other students in the course on the homework! You may also consult other materials such as textbooks, websites, and LLMs. However, you should submit your own solutions written in your own words; in particular, beware of text generated by LLMs as it may include convincing but wrong arguments (and will probably not align with the structure of the lectures either).
Exams: in class on Monday, April 20; Friday, May 15; and Friday, June 5 (last day of class). Exams will not be cumulative. Make-up exams must be for a documented reason (e.g., a sporting event) and must be arranged in advance (preferably by the end of week 1). See UCSD exam policies as well as course-specific policies (to be added later).
Final exam: None.
Text: Algebra by Michael Artin, first or second edition (required). You may use hardcover, softcover, and eBook format. This is the same text that was used for 100A/B in fall 2025/winter 2026 and in some previous terms (which might make it easier to find a used copy). The material for 100C will be drawn primarily from chapters 10, 15, and 16.
Grading: 40% homework (dropping one assignment); 20% each exam. Regarding the conversion of raw percentages into letter grades, 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- |
Accommodations: The Office for Students with Disabilities is tasked with identifying and documenting student disabilities and determining reasonable accommodations to be made in academic settings. Please consult OSD if you may be affected in such a way as to require accommodations; I only promise to handle accommodations based on notification from OSD received by the end of week 1 (beyond that is at my discretion). Note that accommodations affecting exam administration are handled by the Math Front Office, so contact them directly. Remember that accommodations are meant for those with genuine documented needs; receipt of accommodations under false pretenses constitutes a violation of academic integrity (see below).
AI policy: AI (academic integrity) matters even in the age of AI (artificial intelligence)! There is no formal prohibition on use of large language models, but as noted above you must submit homework written in your own words (not generated directly from an LLM). Also, you must cite all sources (including collaborators, static websites, LLMs, etc.) and retain logs of all relevant chatbot transcripts; we reserve the right to request these transcripts.
Absolutely no collaboration or use of outside sources is allowed for exams. Please keep all Internet-enabled devices (phones, smart watches, smart glasses) stored out of use during these sessions. In case of suspected volations of AI policy, we reserve the right to request additional consultation (i.e., you come and explain your work to us in your own words); zero out affected scores; and/or institute official disciplinary action.
Other violations of AI policy include plagiarism, bullying, harassment, or inappropriate behavior. This covers both in-person settings and online spaces.
Recommendation letters: Experience suggests that many students in this class may ask me for recommendation letters afterward. If you are likely to do this, it is strongly advised that you make this request shortly after the end of the course so that I can make some contemporary notes. (I will not be on campus during summer or fall 2026 and will have trouble remembering much if I don't write it down right away.) I also suggest reading this page to see what I will ask for when it comes time to actually write a letter.