Math 120: Groups and Rings
In Spring 2018 I am teaching Math 120 at Stanford University.
For questions about the material and class discussions, we will use
the Math 120 Piazza page.
Lectures are MWF 11:30–12:20 in 380-X, in the basement of the math building.
Office hours: Prof. Church (383-Y) Mon 4–5, Wed 3–4:30, Thurs 2–3, Fri 12:30–1:30. Xiaoyu (381-D) Mon 1–3, Thurs 4–6, and by appointment.
Exams:
- Homework 1, due Saturday, April 7 (solutions)
- Homework 2, due Thursday, April 12 (solutions)
- Homework 3, due Thursday, April 19 (solutions)
- Homework 4, due Thursday, April 26 (solutions)
- Homework 5, due Thursday, May 3 (solutions)
- Homework 6, due Thursday, May 10 (solutions)
- Homework 7, due Friday, May 18 (solutions)
- Homework 8, due Thursday, May 24 (solutions)
- Homework 9, due Wednesday, June 6 (solutions)
Material covered:
Sections in (parentheses) were covered in reading;[brackets] are plans for upcoming lectures
- Week 1: 1.1, 1.6, 2.1, (1.4)
- Week 2: 1.6, 2.4, 2.3, 1.3, 3.2
- Week 3: 3.1, 3.3, 5.1, 1.7, 6.3, (1.2, 1.5)
- Week 4: 4.1, 4.2, 4.3, 4.4, 4.5
- Week 5: 4.5, 5.4, 5.5, 2.2, 4.5
- Week 6: 5.2, 4.5, 7.1, 7.3
- Week 7: 7.3, 7.4
- Week 8: [7.2, 8.1, 8]
- Week 9:
- Week 10:
- WIM paper: 3.5, 4.6
- not covered: 2.5, 3.4, 5.3, 6.1, 6.2
Exams + paper schedule (subject to minor perturbations, but not major ones):
- Midterm due Monday May 14 at 11:59pm (handed out ~ Wed May 9)
- WIM paper first draft due Monday May 21 at 11:59pm
- WIM paper final draft due Monday June 4 at 11:59pm
- Final exam due Wednesday June 13 at 11:30AM [note this is NOT midnight]
WIM paper topics: 1) alternating group An is simple for n≥5, or 2) Banach–Tarski paradox. For alternating group: definition of An is 3.5, definition of simple group is on p102, simplicity of A5 is Theorem 4.3.12, simplicity for general n is 4.6 (there are other proofs, you can use another argument if you like). Source for Banach–Tarski: Brief exposition by Terry Tao, also sketch of the proof on Wikipedia (you can use other references if you like).
The full syllabus for the course is available here.
Textbook: Dummit and Foote, Abstract Algebra (3rd ed), required.
Further resources:
- Statement from the Registrar concerning students with documented disabilities: "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC 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 being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."
- Stanford's Honor Code and Fundamental Standard.