Syllabus

MATHEMATICS 3321 Abstract Algebra l

Fall 2008

  •     TTh 2:00-3:20 p.m.  Room 304 PKH
  •    Problem session Thursdays 1:00-1:50 p.m. Room 304 PKH

Instructor:           Dr. Cordero

Office:                  425 Pickard Hall

Telephone:          817-272-5062

Office hours:      Wednesdays 1:00-3:00 p.m.; Tuesdays and Thursdays 1:00-1:50     p.m. and by appointment.

E-mail:                  cordero@uta.edu

Textbook:          A First Course in Abstract Algebra,  7th Edition By John B. Fraleigh

Evaluation: Three in-class examinations (60 %), Homework (15 %) and a comprehensive final examination (25%) on the following dates (subject to change):

Test # 1Tuesday, September 23
Test # 2Thursday, October 30
Test # 3Tuesday, November 25
Final examinationTuesday, December 9th
 2:00-4:30 p.m.


Learning Outcomes:

Upon completion of Math 3321, students will be able to perform the following three tasks, where “statement in Abstract Algebra I” refers to a statement about concepts introduced in the course that the student may or may not have seen before.

  1. Students will be able to determine whether statements in Abstract Algebra I are true or false.
  2. Students will be able to create examples or counter-examples and apply them appropriately to prove or disprove statements in Abstract Algebra I.
  3. Students will be able to construct correct and rigorous mathematical arguments based on definitions and theorems to prove true statements in Abstract
    Algebra I.

About the course

  • Introductory Abstract Algebra consists mainly of a study of mathematical structures-specifically groups, rings, fields, and a few others.
  • This semester we will concentrate on what is in some ways the simplest of these and in other ways the richest and most complex: the theory of groups.
  • The most fundamental concept in Abstract Algebra is that of an operation on a set. Indeed, the “function” concept is an indispensable tool in all of modern mathematics. The words “function” and “mapping” are synonymous. We are accustomed to using the word “function” in calculus; our context for mappings will be more general than that in Calculus and we use “mapping” rather than “function”. We start our study of Abstract Algebra by looking at mappings and operations. An overview of the course is:

I. Mappings and operations-one-to-one and onto mappings- composition, invertible mappings- properties of operations-composition as an operation 
II. Introduction to groups-definition, examples-permutations-subgroups-groups of symmetry 
III. Equivalence relations and congruence-in this chapter we will study some elementary facts about the integers 
IV. Groups-here we study groups more in depth and prove some general theorems about groups. The important topic of isomorphism is introduced and discussed 
V. Group homomorphisms-operations between groups. The material on this chapter is rather advanced. 

What’s in Abstract Algebra II? More complex algebraic structures: rings, fields, etc.

References:

  • Fraleigh: A first course in Abstract Algebra,
  • Herstein: Algebra,
  • Hungerford: Abstract Algebra, An Introduction

Applications of Abstract Algebra

Here are a few links to provide an introduction to some applications of Abstract Algebra.  

  • Ethnomathematics: A Multicultural View of Mathematical Ideas by Marcia Ascher   includes a chapter on using group theory to model kinship relations in Australian aborigines.


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 IV, Section 3, Subsection 3.2, Subdivision 3.22)

Grade Replacement Policy: Upon receiving a grade of D or F in a course, a student may, after filing an intent to do so, replace the grade by repeating the course. The second grade earned, whether higher or lower, will be used in calculating the grade point average unless the second grade is a W. This policy applies only the second time the course is attempted. Both grades received will be shown on the student’s transcript. This policy will apply to a maximum of 10 credit hours at U.T. Arlington. Students must file their intention to replace a grade with the registrar by the Census Date (Feb. 4th). All withdrawals after Census Date will be considered an attempt, and the initial grade will be used. This policy will not apply to courses that may be repeated for credit or courses taken on a pass/fail basis. This policy is not applicable to graduate students and is not retroactive in that a grade in a course taken prior to adoption may be replaced but a grade earned in a course prior to adoption may not be used as a replacement. Individual colleges and schools may limit this policy.

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.

Drop for Non-Payment of Tuition: If you are dropped from this class for non-payment of tuition, you may secure an Enrollment Loan through the Bursar’s Office.