Stanford Math 122
Modules and Group Representations
Course Information
Lecture: Monday, Wednesday, Friday 10:30am–11:20am
Building 380 (Sloan Hall), Room 380-D (Basement Floor, Room D)
Course Webpage: http://web.stanford.edu/~jchw/2018Math122
Grades will be made available through Canvas.
Previous years’ webpages:
(2017) http://web.stanford.edu/~jchw/2017Math122
(2016) http://web.stanford.edu/~jchw/2016Math122
(2015) http://web.stanford.edu/~jchw/2015Math122
Textbook: Dummit–Foote, Abstract Algebra
Suggested Reading: Fulton–Harris, Representation Theory (pdf at SpringerLink)
Professor: Jenny Wilson
Email: jchw@stanford.edu
Office Hours: Wednesdays 1–4pm
Office: Building 380 (Sloan Hall), Room 382-H (Second Floor, Room H)
Course Assistant: Nikolas Kuhn
Email: nkuhn "at" stanford.edu
Office Hours: Tuesdays 10–11am and Thursdays 1–3pm
Office: Building 380 (Sloan Hall), Room 381-K (First Floor, Room K)
Course Description: Modules over PID. Tensor algebra. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite: Math 120. Also recommended: 113.
Syllabus: We will follow Dummit & Foote Chapters 10, 12, 18, and parts of 19 as time permits.
| Grading Scheme: | |
| Homework | 50% |
| Midterm I | 15% |
| Midterm II | 15% |
| Final | 20% |
Students with documented disabilities: Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (723-1066, http://studentaffairs.stanford.edu/oae).
Affordability of course materials: Stanford University and its instructors are committed to ensuring that all courses are financially accessible to all students. If you are an undergraduate who needs assistance with the cost of course textbooks, supplies, materials and/or fees, you are welcome to approach your instructor directly. If you would prefer not to approach your instructor directly, please note that you can ask the Diversity & First-Gen Office for assistance by completing their questionnaire on course textbooks & supplies or by contacting Joseph Brown, the Associate Director of the Diversity and First-Gen Office (jlbrown "at" stanford.edu; Old Union Room 207). Dr. Brown is available to connect you with resources and support while ensuring your privacy.
Homework policy: Homework assignments will be posted to the course webpage. Homework is due Fridays, and collected at the beginning of lecture. Late homework is generally not accepted except under extenuating circumstances. Your homework solutions should be neat, legible, and stapled . You may work in groups and discuss homework problems with other students, but your solutions must be written up independently and in your own words.
Each student's lowest homework score will be dropped.
You are welcome to use other texts and online resources to review the mathematical theory and computational techniques we cover. You may not, however, seek out solutions to specific homework problems. Outside sources should be used to improve your understanding of the material, not as a shortcut to finish assignments with an incomplete understanding. Use your discretion.
You are encouraged to discuss the homework with classmates and work on difficult problems in groups. You must, however, write your own homework solutions, and you are responsible for understanding what you've written. The homework is your foremost resource for practice with the course material, and for feedback on your work. Doing the homework thoughtfully is essential to your success in this class.
Grading systems: I discourage students from taking Math 122 on a CR/NC basis. Please talk to me if you are considering this option.
Honour Code: The Stanford Honour Code is available through Stanford's Office of Community Standards.
Homework
| Homework 1 | Due: Friday 6 April 2018 |
and the (non-anonymous) midterm availability survey
| Homework 2 | Due: Friday 13 April 2018 |
| Homework 3 | Due: Friday 20 April 2018 |
| Homework 4 | Due: Friday 27 April 2018 |
| Homework 5 | Due: Monday 7 May 2018 |
| Homework 6 | Due: Friday 11 May 2018 |
| Homework 7 | Due: Friday 18 May 2018 |
| Homework 8 | Due: Friday 25 May 2018 |
| Homework 9 | Due: Monday 4 June 2018 |
Exams
The course will have two closed-book midterm exams.
The exams are designed to take one hour, but you may take up to two hours to write them. No books, notes, calculators, cell phones, or other electronic aids are permitted.
Midterm I: Thursday 3 May, 7–9pm
Location: Building 380 (Math department), room 380-X (Basement room X)
Alternate time (opt-in) 8–10pm in room 380-Y (Basement room Y)
Doors to the basement are locked at 5pm. Please enter the building through the first floor front doors after this time.
Midterm I will cover material from the Week 1 to Week 4.
Midterm I and solutions are available here:
| Midterm I Solutions |
Midterm II: Tuesday 29 May, 7–9pm
Location: Building 380 (Math department), room 380-Y (Basement room Y)
Alternate time (opt-in) 8–10pm in room 380-X (Basement room X)
Doors to the basement are locked at 5pm. Please enter the building through the first floor front doors after this time.
Midterm II will cover material from the Week 4 to Week 8.
Midterm II and solutions are available here:
| Midterm II Solutions |
A take-home final exam will be due during the exam week. Details to follow.
Outside Reading
The following reading is strictly optional: it is not related to the course material and will not be discussed in the course. These are articles on math education and learning psychology which may be of interest to math students.