Math 503 Home Page, Spring 2012

Instructor: Ching-Li Chai
Office: DRL 4N36, Ext. 8-8469.
Office Hours: WF 11:05-11:55
Email:chai@math.upenn.edu

Teaching Assistant: Paul Levande
Office: 3N2D DRL
Office Hours:

WWW tip: Click on the "Reload" button to make sure you are seeing the most up-to-date version of this (or any) page!

Evolving log: what have been explained/done in class, and plan for the next few lectures.

Notes and Homework Assignment

General Information about Math 503:

• Lecture class meetings are Mondays, Wednesdays and Fridays, from 12:00 to 12:50 in DRL 4C8.
• First Meeting: Wednesday, January 11, 2012.
• Lab sessions are on Tuesdays from 6:30 to 8:30 p.m. in DRL 3C2. The lab is an integral part of this course; attendance is required.
• This is the second half of a year-long course on algebra, followed by Math 503. A similar, but less theoretical, sequence is Math 370-Math 371.
• Rigor is a basic tenet of this course. The students are expected to learn the language of rigorous mathematics, and to differentiate complete proofs from arguments with gaps. The ability to write coherent mathematical proofs is necessary to achieve a passing grade .
• Text book: Basic Algebra, vol. I, II, second edition, by Nathan Jacobson, 2009 Dover reprint.
• A list of other textbooks on abstract algebra. If you find any of them more understandable than the designated textbook, go ahead and read it instead.
  • Michael Artin, Algebra.
  • Dummit and Foote, Abstract Algebra.
  • I. N. Herstein, Topics in Algebra.
  • Jacobson, Lectures in Abstract Algebra (3 volumes)
  • Serge Lang, Undergraduate Algebra.
  • Serge Lang, Algebra.
  • J-P. Serre, Linear Representations of Finite Groups.
  • B. L. van der Waerden, Modern Algebra (2 volumes, a timeless classic).
• The lectures will be self-contained and will not follow the textbook closely. You are encouraged to read the textbook and compare it with the presentation in class. If you find a different proof yourself, do come to my office and show off.
• The materials include factorization, notherian rings and modules, field theory (including Galois theory), representation theory for finite groups, contained in chapter 4 of volume 1 and chapters 3, 5, 8 of volume 2 of Jacobson's book.
• Announcement, homework assignment, notes, sample problems, solutions will all be posted on web. No hard copies will be distributed. Please check this page frequently for the most updated information. Remember to use to Reload button of your browser.

Basic Ground Rules:

• The course grade is based on: Final Exam (40%), Midterm Exam (20%) and everything else (40%). "Everything else" consists of regular homework, participation and performance in the lab sessions.
• Homeworks
  • Homeworks will be assigned each week. They are due in class on Monday the following week. Follow this link to see the assigned problems.
  • Your works should contain complete, rigorous and logically correct proofs. (A reminder: The usual rules of English grammar also apply in mathematical writing.)
  • You are encourage to work in groups and discuss with each other. But the work you hand in MUST BE YOUR OWN WRITE-UP.
  • Homeworks will be spot graded and returned in the following lab session. Answers to selected problems will be posted.
  • LATE WORK will NEVER be accepted.
• Lab Sessions
  • The lab session is an integral part of this course. Attendance is required.
  • Students will be required to present their works during the lab sessions. This is a part of the training to construct and communicate mathematically correct proofs.

Grading notes: At the end of the semester, everyone who has not withdrawn from the class will get a grade. Incompletes will not be given to avoid F's.

Semester Calendar:

• First Day of Classes: Wednesday, January 11, 2012.
• Course selection period ends: Monday, January 30, 2012.
• Drop period ends: Friday, February 17, 2012.
• Spring break: Saturday, March 3 -- Sunday, March 11, 2012.
• Midterm: Wednesday, March 13 (tentative)
• Last day to withdraw: Friday, March 30, 2012.
• Last day of classes: Tuesday, April 24, 2012.
• Reading days: Wednesday, April 25 -- Friday, April 27, 2012.
• Final Exam: Tuesday, May 1, 9:00 -- 11:00AM (tentative)

Exams:

• Midterm: Wednesday, March 13 (tentative)
• Final Exam: Tuesday, May 1, 9:00 -- 11:00AM (tentative)

Homework Assignment