Math 602/3, Algebra, fall 2020 and spring 2021

Instructor: Ching-Li Chai

Office Hours: M 3:15-3:45 pm on days with no Algebra Seminar, and M 5:30-6:00 pm on days with Algebra Seminar, and by appointments.

Email: chai@math.upenn.edu

Grader : Yao-Rui Yeo Email: yeya@math.upenn.edu spring 2021; Souparna Purohit Email: soupur@sas.upenn.edu fall 2020

Exercises

Evolving plan for the coming lecture(s)

Notes

General Information

• Synchronous Zoom sessions: MF 1:30-3:00 pm.
  Meeting URL https://upenn.zoom.us/j/92988879794?pwd=ZDJma29FRC95Z0ZIVFQzVjZCZHBqdz09
  Passcode: 320519
• Students are encouraged to use Piazza as a platform for discussions, posing and answering questions. You can sign up following link to the Piazza signup page.
  
  
• Course Prospectus
  
  
• Homeworks/Exercises will be assigned regularly. This is the most important part of this course; see the first paragraph of "For the Student" in Shatz and Gallier
  • Completed assignments are to be submitted, in the pdf format, to the Canvas page for this course.
  • At least one problem in each assignment should be done with TeX/LaTeX. The rest can be hand-written and scanned. (There are a number of apps which allow you to use a smartphone as a scanner.)
  • Penn Math Department TeX resources page, TeX resources on the web
  
  
• Textbook: Algebra by Gallier and Shatz, developed from decades of lectures by Shatz at Penn. The heart of the book is the Problems section. Working out these problems was a rite of passage for generations math graduate students at Penn.
  The authors have kindly granted permission for students in Math 602/3 to download this book for personal use. Here are the files of individual chapters: problems, chapter 1, chapter 2, chapter 3, chapter 4, chapter 5, bibliography. Please report to me all errors/typos/inaccuracies you find.
  
  
• References: You are encouraged to study one of the standard textbooks for graduate algebra, such as items 1-5 below. Van der Waerden's book is a timeless classic. Bourbaki's treatment is the most comprehensive, and the problems are delicious. But it's not a "textbook". References 7-10 are for specific topics.
  1. Serge Lang, Algebra.
  2. Nathan Jacobson, Algebra I, II.
  3. Michael Artin, Algebra.
  4. Dummit and Foote, Abstract Algebra.
  5. van der Waerden, Algebra I, II.
  6. Bourbaki, Algebre.
  7. M. F. Atiyah and I. G. MacDonald, Commutative Algebra.
  8. Ernst Kunz, Introduction to Commutative Algebra and Algebraic Geometry.
  9. Jean-Pierre Serre, Linear Representations of Finite Groups.
  10. I.-N. Herstein, Noncommutative Rings.
  
  
• Sample of past exams: Math 602 midterm exam fall 2016, Math 602 final exam fall 2010
  
  
• Course Grade: Homework 50%, presentation (=explaining your work during zoom meetings) 20%, take-home exams 30%.
  
  
• academinc calender, spring 2021:
  • first meeting: Friday 1/22
  • course selection period ends: 2/02
  • engagement day (no class) Friday 2/12
  • drop period ends: 3/01
  • spring break: Wednesday 3/10-Thursday 3/11
  • last day to withdraw: 3/29
  • engagement day (no class) Tuesday 3/30
  • engagement day (no class) Monday 4/12
  • last day of classes: Thursday 4/29
  • final exam (take-home): Friday 4/30 (whole day)