of 442

Abstract Algebra: Theory and Applications | Group (Mathematics) | Field (Mathematics)

8 views
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Share
Description
This text is intended for a one- or two-semester undergraduate course in abstract algebra.Though there are no specific prerequisites for a course in abstract algebra, Students who have had other higher-level courses in mathematics will generally be more prepared than those who have not, because they will possess a bit more mathematical sophistication. Occasionally, we shall assume some basic linear algebra; that is, we shall take for granted an elementary knowledge of matrices and determinants.
Tags
Transcript
  Abstract Algebra Theory and Applications Thomas W. JudsonStephen F. Austin State UniversityMay 7, 2013  iiCopyright 1997 by Thomas W. Judson. Permission is granted to copy, distribute and/or modify this document underthe terms of the GNU Free Documentation License, Version 1.2 or any laterversion published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled “GNU Free Documentation License”.A current version can always be found via  abstract.pugetsound.edu .  Preface This text is intended for a one- or two-semester undergraduate course inabstract algebra. Traditionally, these courses have covered the theoreticalaspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in thesubject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly. Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation. This text contains more material than can possibly be covered in a singlesemester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentationof topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester coursemight cover groups and rings while briefly touching on field theory, usingChapters 1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters 1 through 6, 9, 10, 11, 13 through 18, 20, 21, 22 (the first part), and 23. On the other iii  iv  PREFACE  hand, if applications are to be emphasized, the course might cover Chapters 1 through 14, and 16 through 22. In an applied course, some of the more theoretical results could be assumed or omitted. A chapter dependency chart appears below. (A broken line indicates a partial dependency.)Chapter 23Chapter 22Chapter 21Chapter 18 Chapter 20 Chapter 19Chapter 17 Chapter 15Chapter 13 Chapter 16 Chapter 12 Chapter 14Chapter 11Chapter 10Chapter 8 Chapter 9 Chapter 7Chapters 1–6 Though there are no specific prerequisites for a course in abstract algebra,students who have had other higher-level courses in mathematics will generally be more prepared than those who have not, because they will possess a bit more mathematical sophistication. Occasionally, we shall assume some basic linear algebra; that is, we shall take for granted an elementary knowledge of matrices and determinants. This should present no great problem, since most students taking a course in abstract algebra have been introduced to matrices and determinants elsewhere in their career, if they have not already taken a sophomore- or junior-level course in linear algebra.
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks