Syllabus for Math 6121
Algebra I
Fall 2011

This is a graduate-level course in abstract algebra. The principal aim is to lead students to a mastery of the parts of algebra that every mathematician should know. Successfully attaining that goal will prepare students for the comprehensive exam in algebra required for the PhD program in Mathematics.

Instructor:

• Douglas Ulmer, Professor and Chair, School of Mathematics
• Office: Skiles 118B
• E-mail: ulmer@math.gatech.edu
• Web site: http://www.math.gatech.edu/~ulmer
• Office hours: Mondays and Tuesdays 3:00 - 4:00, or by appointment. Check my web site for changes.

Course info:

• Title: Algebra I
• Number: 6121-A (81169)
• Course Meetings: MWF 2:05 - 2:55 in Skiles 169
• Objectives: Master the theories of groups, rings, modules, and fields at the graduate level.
• Audience: PhD students in Mathematics and related fields. Others with a need to know algebra at the graduate level.
• Prerequisites: An undergraduate course in algebra (at the level of texts such as Herstein, Hungerford, Artin, etc.), for example Georgia Tech Math 4107/4108.
• Topics:
  • Groups
  • Rings
  • Modules
  • Fields
  • Advanced topics in Linear Algebra

Resources:

• Text: “Abstract Algebra” (third edition) by Dummit and Foote
• Alternates: The “Algebra” texts of Lang, Rotman, Jacobson, and Knapp are also recommended
• TA/grader: TBA

Requirements and grades:

• Homework will be assigned regularly, collected, and graded.
• There will be two in-class exams: on Friday, September 30 and Friday, November 7. (Dates subject to change)
• The final exam will Monday, December 12, 11:30 - 2:20, in Skiles 169. The in-class final may be replaced with a (harder, more interesting) take-home final if students' performance on the previous exams is sufficiently strong.
• Grades will be based on the percentage of possible points earned. The-in class exams will each count for 20% of the grade, the final will count for 30%, and homework will count for 30%.
• Cutoff percentages for A, B, C, D are 90%, 80%, 70%, and 60% respectively.

Other important policies and tips:

• There will be no make-up exams. If an in-class exam is missed for an acceptable and documented reason (severe illness, death in the famiy, etc.), the score on that exam will be replaced with the score on the corresponding part of the final exam. A test missed for unacceptable or undocumented reasons will receive a score of 0. Arrangements for extensive absences (e.g., for extracurricular activities) must be made by the end of the first week of classes.
• Collaboration and plagiarism: Discussing ideas and homework exercises with your peers is not only acceptable, it is a good idea. However, you must write your own solutions and proofs in your own words. Copying another's words or otherwise passing off someone else's work as your own is plagiarism and will result in a score of 0 on the entire assigmemnt in question. Egregious cases will be dealt with more harshly. ASK if you have any questions whatsoever about this
• Homework is due at the beginning of class, usually on Mondays. Late homework is strongly discouraged. It will be accepted up to 48 hours after the due time and will be assessed a 20% penalty.
• The Georgia Tech Honor Code applies 100% without exception. Know it and live it.
• Experience shows that attendance in class is very much to the student's benefit. It is strongly encouraged and offers the opportunity to earn quiz points.
• Class time will be used to discuss difficult ideas, points of confusion, etc., not to go over basics in the text. Read assignments before class and come prepared with questions.