Description 
1 online resource 
Series 
Open textbook library 

Open Textbook Library

Contents 
Preliminaries  The Integers  Groups  Cyclic Groups  Permutation Groups  Cosets and Lagrange's Theorem  Introduction to Cryptography  Algebraic Coding Theory  Isomorphisms  Normal Subgroups and Factor Groups  Homomorphisms  Matrix Groups and Symmetry  The Structure of Groups  Group Actions  The Sylow Theorems  Rings  Polynomials  Integral Domains  Lattices and Boolean Algebras  Vector Spaces  Fields  Finite Fields  Galois Theory 
Summary 
This text is intended for a one or twosemester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects 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 the subject 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 single semester. Certainly there is adequate material for a twosemester course, and perhaps more; however, for a onesemester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical onesemester course might cover groups and rings while briefly touching on field theory, using Chapters 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 twosemester 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 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.) 
Notes 
Mode of access: World Wide Web 

Free Documentation License (GNU) 
Subject 
Mathematics  Textbooks.

Genre/Form 
Textbooks.

Form 
Electronic book

Author 
Judson, Thomas, active 15811600, author


Open Textbook Library, distributor

ISBN 
9781944325022 
