Math 125: Quaternion algebras
Spring 2014
Course Info:
- Lectures: Monday, Wednesday, Friday, 10A (10:00 - 11:05 a.m.)
- x-period: Thursday, 12:00 noon - 12:50 p.m.
- Dates: 24 March 2014 - 28 May 2014
- Room: 004 Kemeny
- Instructor: John Voight
- Office: Kemeny Hall, Room 240
- E-mail: jvoight@gmail.com
- Office hours: Monday 1:00 - 2:30 p.m., Wednesday 2:00 - 3:30 p.m., or just make an appointment!
- Course Web Page: http://www.math.dartmouth.edu/~jvoight/125/
- Prerequisites: See course description.
- Required Texts: None (text below).
- Grading: For undergraduates, grade will be based on weekly homework.
Syllabus:
[PDF] Syllabus
Text:
Please see the latest book draft.
Homework:
The homework assignments will be assigned on a varying basis and will be posted below. Homework is required for undergraduates and optional but strongly encouraged for graduate students. In general, it is due in one week, but late homework will be accepted.
Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, you must write the solution up on your own.
Plagiarism, collusion, or other violations of the Academic Honor Principle, after consultation, will be referred to the The Committee on Standards.
| 1 | 24 Mar | (M) | Introduction | |
| 2 | 26 Mar | (W) | Chapter 2: Beginnings | 2.1-2.10 (pick 3) |
| 3 | 28 Mar | (F) | Chapter 3: Involutions | |
| 4 | 31 Mar | (M) | Chapter 3 | 3.1-3.13 (pick 3) |
| 5 | 2 Apr | (W) | Chapter 4: Quadratic forms | |
| 6 | 4 Apr | (F) | Chapter 6: Simple algebras | |
| 7 | 7 Apr | (M) | Chapter 6 | 6.1-6.14 (pick 2) |
| 8 | 9 Apr | (W) | Chapter 4 | 4.1-4.15 (pick 2) |
| * | 10 Apr | (R) | Chapters 2-4, algorithmic aspects | |
| 9 | 11 Apr | (F) | Chapter 8: Orders | |
| 10 | 14 Apr | (M) | Chapter 9: Hurwitz order | |
| 11 | 16 Apr | (W) | Chapter 9 | 9.1-9.6 (pick 2) |
| 12 | 18 Apr | (F) | Chapter 10: Quaternion algebras over local fields | |
| 13 | 21 Apr | (M) | Chapter 10 | 10.1-10.15 (pick 3) |
| 14 | 23 Apr | (W) | Chapter 11: Lattices and localization | |
| 15 | 25 Apr | (F) | Chapter 11 | 11.1-11.4 (pick 1) |
| - | 28 Apr | (M) | NO CLASS (JV at Yale) | |
| 16 | 30 Apr | (W) | Chapter 13: Quaternion algebras over global fields | |
| 17 | 1 Apr | (R) | Chapter 13 | |
| 18 | 2 May | (F) | Chapter 13 | 13.1-13.8 (pick 3) |
| 19 | 5 May | (M) | Chapter 12: Discriminants | |
| 20 | 7 May | (W) | Chapter 12: Discriminants | 12.1-12.7 (pick 1) |
| 21 | 9 May | (F) | Chapter 14: Quaternion ideals over Dedekind domains | |
| 22 | 12 May | (M) | Chapter 14 | |
| 23 | 14 May | (W) | Chapter 14 | 14.1-14.15 (pick 2) |
| 24 | 16 May | (F) | Chapter 14 | |
| 25 | 19 May | (M) | Chapter 14 | |
| 26 | 21 May | (W) | Chapter 17: Zeta functions and the mass formula | |
| 27 | 23 May | (F) | Chapter 17 | |
| 28 | 28 May | (W) | Vista |