Instructor: Sebastien Vasey
Office: Science Center 321H
Email: sebv (at) math (dot) harvard (dot) edu
Course assistants: Forrest Flesher (forrestflesher (at) college) and Garrett Brown (garrettbrown (at) college)
Lectures: Wednesday and Friday, 9AM-10h15AM
Course syllabus
The class is now over and there will be no more office hours. Good luck with the exam!
The midterm is cancelled. All class meetings and office hours will take place via Zoom from now on (March 10). Regular class meetings will be recorded. You can find links to all the meetings by clicking on "Zoom" on the left hand side Canvas menu. Here is a direct link. Please do not share the links to these recordings with anyone outside of class. If you have privacy concerns, you may use a pseudonym (but please email me what it is!) or turn off your webcam. Please talk to me if you have any questions regarding the recordings.
Unless noted otherwise, chapter and section numbers are from David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd edition, Wiley, 2004.
| Week | Reading | Assignment | Other documents, and things to do |
|---|---|---|---|
| Jan 27-31 | The syllabus and Sections 7.1-7.3. | Assignment 1 due Tuesday, Feb. 4, 11h59pm. Latex source Solution Questionnaire. |
|
| Feb 3-7 | Sections 7.3-7.4 (for Wednesday), 7.4-7.6 (for Friday). | Assignment 2 due Tuesday, Feb. 11, 11h59pm. Latex source Solution. | Just for fun: read Bjorn Poonen's article on why all rings should have a 1. |
| Feb 10-14 | Chapter 8 (for Wednesday), Sections 9.1-9.4 (for Friday). | Assignment 3 due Tuesday, Feb. 18, 11h59pm. Latex source Solution. | Just for fun: check out the Database of ring theory. |
| Feb 17-21 | Sections 10.1-10.3 (for Wednesday), Section 12.1 (for Friday). | Assignment 4 due Tuesday, Feb. 25, 11h59pm. Latex source Solution. | |
| Feb 24-28 | Section 12.1 (for Wednesday), Sections 12.2-12.3 (for Friday; no need to read about how to convert to the normal forms). | Assignment 5 due Tuesday, Mar. 3, 11h59pm. Latex source Solution. | Read about Emmy Noether. Her contributions go far beyond Noetherian rings: she invented abstract algebra as we know it. |
| Mar 2-6 | Section 13.1 (for Wednesday) and 13.2 (for Friday). | Assignment 6 due Tuesday, Mar. 24, 11h59pm. Latex source Solution. | Read the information on the midterm (Updated 3/6) and attempt the sample midterm (here is the solution). |
| Mar 9-13 | Section 13.2 for Wednesday. Section 13.3 for Friday. | Assignment 7 due Friday, Mar. 27, 11h59pm. Latex source Solution. |
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| Mar 23-27 | Section 13.4 and 13.5 (up to Corollary 34) for Wednesday. Rest of 13.5 and 13.6 for Friday. | Assignment 8 due Tuesday, Mar. 31, 11h59pm. Latex source Solution. | Slides: Wednesday Friday. |
| Mar 30-Apr 3 | Section 14.1 for Wednesday. Section 14.2 for Friday. | Assignment 9 due Tuesday, April 7, 11h59pm. Latex source Solution. | Slides: Wednesday Friday. |
| Apr 6-Apr 10 | Section 14.2, 14.3 for Wednesday. Section 14.4 for Friday. | Assignment 10 due Tuesday, April 14, 11h59pm. Latex source Solution. | Slides: Wednesday Friday. |
| Apr 13-Apr 17 | Section 14.4 (primitive element theorem), 14.5 (before constructibility of the n-gon) for Wednesday. Rest of section 14.5 and proofs of fundamental theorem of algebra in 14.6 for Friday. | Assignment 11 due Friday, April 24, 11h59pm. Latex source Solution. | Slides: Wednesday Friday. |
| Apr 20-Apr 24 | Section 14.6 for Wednesday and 14.7 for Friday. | No more assignments, yay! Optional: peer review a problem of your choice from assignment 11. | Slides: Wednesday Friday. Read the information on the last exam (Updated 4/24) and attempt the sample last exam. Here is the Solution. |
| Apr 27-May 1 | End of 14.6 and 14.7 (computation of Galois groups of small degree polynomials and Cardano's formula). | Last exam, due Friday, May 1, before 2pm, Eastern time (send it to me by email and I will reply with a confirmation). Here is the solution. | Slides for Wednesday. No class on Friday, May 1. |