Math 721-- Abstract Algebra II

Spring 2017,  TuTh 10:15 - 11:30, SAS 1220

Instructor: Seth Sullivant, office: 3114 SAS Hall, email:

Syllabus: Syllabus

Office Hours: Tu 11:30 - 12:30, Tu 4:30-5:30, W 3:00-4:00, Or by appointment

Text: David Dummit and Richard Foote, Abstract Algebra (Third Edition), Pearson, ISBN-13:978-0-321-79477-2

Prerequisites: MA 521 (First semester graduate abstract algebra.)

Course Description: This course is part of a two course qualifying exam sequence on abstract algebra, covering major topics of interest necessary for study in nearly all areas of mathematics research.

The first course assumes a solid foundation in undergraduate abstract algebra. After brief review of undergraduate level material the course will cover the following topics: quotient groups, group actions and the Sylow theorems, quotient rings, factorization, principal ideal domains, fields, Galois theory.

The second course will cover module theory, tensor products and multilinear algebra, structure theory of modules over a PID, some homological algebra, and representation theory.

A more detailed breakdown of the topics that will be covered over the two semesters is availabe here.

Learning Objectives (This document will be updated throughout the course and can be used as a study guide.)

Schedule: Is available here.

Homework: Homework will be roughly assigned weekly and is due in class on Thursday, unless otherwise indicated.

A file explaining how to prepare your homework can be found here. Homework assignments can be found here.

Policy on Late Homework: Homework is due in class on Thursdays, unless otherwise indicated. Late homework will be accepted up to Friday at 5 PM on the week it was due, and will received 80% of the points. Each student may turn in at most 2 late homework assignments during the semester for credit. If you must miss a class on the day a homework is due and you want full credit, it is your responsibility to get the homework to me by 5PM on Friday. I do not accept scans or photos of homework but if you prepare your homeowrk in LateX you can send me a pdf.

LaTeX Assignment: LaTeX is a powerful text editing and typesetting tool for preparing mathematical writing. If you are getting a PhD in mathematics you must learn to prepare LaTeX documents. There will be one homework assignment that must be prepared in LaTeX. You will be graded on both the math content and for correctly preparing the LaTeX and typesetting a number of mathematical elements. The LaTeX assignment will be due on March 16th.

Exams: There will be an in-class 75-minute midterm exam and a comprehensive final exam. The midterm will be worth 20% of the grade and the final is worth 40% of the grade. The midterm is on March 2nd. The final is on May 4th, in the usual classroom from 8 AM to 11 AM.

Grades: Grades will be based on Homework (35%), LaTex Assignment(5%), Midterm (20%), and Final Exam (40%). Grades are based on the following scale:   A : (> 85%), B: (70-85 %) C: (60-70%) D-F: (<60%).


LateX Resources: