Math 653 (Section 600) -- Fall 2012

Algebra I

TuTh 12:45-2:00
CE 222


Course Description:

Topics of Study: This is a first semester course in abstract algebra, which will introduce students to the fundamental objects of groups, rings, fields, modules, and vector spaces. We will cover most of Chapters I-III and parts of Chapter IV from Hungerford, going through the following topics as time permits:
  • basic group theory
  • solvable groups
  • finitely generated abelian groups
  • Sylow theorems & aspects of the classification of finite groups
  • free groups and inverse limits
  • definitions of rings, integral domains, and fields
  • basic ring theory and ideals
  • commutative rings & the Chinese remainder theorem
  • polynomial rings
  • localization
  • principal ideal domains and unique factorization domains
  • power series and power series rings
  • introduction to modules
  • exact sequences
  • free modules and vector spaces
Prerequisites: Math 415-416 or equivalents. Students should be familiar with material from a year-long course in undergraduate algebra and with concepts from linear algebra.

Course Information:

Instructor: Matthew Papanikolas

Office Hours: Wed. 3:00-4:00, Thurs. 2:00-3:00; also by appointment

Office: 321 Milner


Textbook: Algebra, by Thomas W. Hungerford, Springer, 1974, ISBN 0-387-90518-9

Prerequisites: Math 415-416 (groups, rings, fields, and vector spaces); or equivalents

Course Webpage:

Course Work and Grades:

Reading: Reading the sections in the book we are covering will be crucial throughout the semester. There will not be enough time to cover all important topics in class, and some topics will only be covered in the reading or exercises.

Homework: There will be regular homework assignments, and each assignment will include written problems to be turned in for a grade. Homework assignments can be found at the link Late homework will not be accepted, except as provided by University rules on missed work.

Group Work: It is perfectly fine for students to work together on finding solutions for out of class assignments. However, each student must write up the solutions of problems to be turned in on his or her own. Consulting web sites or other problem solution sources (other than the textbook) is not allowed.

Exams: Midterm Exam in class on Thursday, October 18.
Final Exam in our usual classroom on Wednesday, December 12, 8:00-10:00 AM.

Grades: The components contributing to your grade in the course are weighted as follows: Homework (1/3), Midterm Exam (1/3), Final Exam (1/3).

Page maintained by Matt Papanikolas, Dept. of Mathematics, Texas A&M University.