Abstract Algebra II

Fall 2009




Instructor:            Dr. Cordero                                                                                                               

Office:                  486 Pickard Hall

Telephone:          817-272-5062

Office hours:       MW 10-11:30 a.m.  or by appointment.


Class webpage


About the course:  In this course we will study fields, in particular finite fields in depth. We will begin the semester with a review of groups, rings and fields, in general. Then we will study field extensions, the Fundamental Theorem of Galois Theory, and splitting fields.  The last half of the semester we will investigate the structure of finite fields and factorization of polynomials over finite fields. We will conclude with a look at some theoretical applications of finite fields.


The material is covered in the following books:

Abstract Algebra, David S. Dummit and Richard M. Foote

Algebra, Thomas W. Hungerford

Introduction to finite fields and their applications, Revised Edition, Rudolf Lidl and Harald Niederreiter  



Homework and informal class presentations (60%)

Final Research Presentation (40%)


Tentative schedule:

Weeks 1-3       Algebraic foundations

Weeks 4-6       Field extensions and Galois Theory

Weeks 7-13     Finite fields and polynomials over finite fields

Weeks 14-15   Research presentations








University Information


Americans with Disabilities Act

The University of Texas at Arlington is on record as being committed to both the spirit and letter of federal equal opportunity legislation; reference Public Law 93112  The Rehabilitation Act of 1973 as amended.  With the passage of new federal legislation entitled Americans with Disabilities Act - (ADA), pursuant to section 504 of the Rehabilitation Act, there is renewed focus on providing this population with the same opportunities enjoyed by all citizens. As a faculty member, I am required by law to provide reasonable accommodation to students with disabilities, so as not to discriminate on the basis of that disability.  Student responsibility primarily rests with informing faculty at the beginning of the semester and in providing authorized documentation through designated administrative channels.


Academic Dishonesty

It is the philosophy of The University of Texas at Arlington that academic dishonesty is a completely unacceptable mode of conduct and will not be tolerated in any form.  All persons involved in academic dishonesty will be disciplined in accordance with University regulations and procedures.  Discipline may include suspension or expulsion from the University.

Scholastic dishonesty includes but is not limited to cheating, plagiarism, collusion, the submission for credit of any work or materials that are attributable in whole or in part to another person, taking an examination for another person, any act designed to give unfair advantage to a student or the attempt to commit such acts. (Regents Rules and Regulations, Part One, Chapter VI, Section 3, Subsection 3.2, Subdivision 3.22).



Student Disruption

The University reserves the right to impose disciplinary action for an infraction of University policies.  For example, engagement in conduct, alone or with others, intended to obstruct, disrupt, or interfere with, or which in fact obstructs, disrupts, or interferes with, any function or activity sponsored, authorized by or participated in by the University.