Math 654 (Section 600) – Spring 2017

Algebra II

MWF 12:40 – 1:30
BLOC 161


Course Description:

Topics of Study: This is a second semester course in abstract algebra, which will continue the study of fundamental objects of groups, rings, fields, modules, and vector spaces that began in Math 653. We will cover material from Chapters I–VI, IX, XIII, XIV, XVI from Lang, going through the following topics as time permits:
  • categories and functors
  • modules, free modules, and vector spaces
  • exact sequences
  • localizations of modules
  • projective and injective modules
  • tensor products
  • left & right exact functors
  • modules over principal ideal domains
  • field extensions
  • splitting fields, normality, and separability
  • Fundamental Theorem of Galois Theory
  • finite fields
  • cyclic, cyclotomic, and radical extensions
  • decompositions of linear transformations
  • characteristic polynomials, eigenvectors, and eigenvalues
  • chain conditions
  • noetherian rings and modules
  • Hilbert Nullstellensatz
Prerequisites: Math 653 or equivalent.

Course Information:

Instructor: Matthew Papanikolas

Office Hours: Mon. & Wed. 10:30-11:30; also by appointment

Office: Blocker 641H


Textbook: Algebra, 3rd ed., by Serge Lang, Springer, 2002, ISBN 0-387-95385-X

Prerequisites: Math 653 or equivalent

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.

Alternate Texts: We will mostly follow the exposition of Lang in class, but other texts you may find useful:
  • Abstract Algebra by Dummit and Foote
  • Algebra by Hungerford

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 textbooks above) is not allowed.

Exams: Midterm Exam in class on Wednesday, March 8.
Final Exam in BLOC 161 on Friday, May 5, 10:30AM–12:30PM.

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.