Abstract Algebra

A Gentle Introduction
1. Auflage 2016
ISBN: 978-1-4822-5006-0
Verlag: Taylor & Francis

Buch, Englisch, 214 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 453 g

Reihe: Textbooks in Mathematics

Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra.

Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors

who need to have an introduction to the topic.

As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic.

Features

- Groups before rings approach

- Interesting modern applications

- Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers.

- Numerous exercises at the end of each section

- Chapter "Hint and Partial Solutions" offers built in solutions manual

Autoren/Hrsg.

Mullen, Gary L.

Sellers, James A.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Elementary Number Theory
Divisibility

Primes and factorization

Congruences

Solving congruences

Theorems of Fermat and Euler

RSA cryptosystem

Groups
Definition of a group

Examples of groups

Subgroups
Cosets and Lagrange's Theorem

Rings
Definition of a ring

Subrings and ideals

Ring homomorphisms

Integral domains
Fields

Definition and basic properties of a field
Finite Fields

Number of elements in a finite field

How to construct finite fields
Properties of finite fields
Polynomials over finite fields
Permutation polynomials

Applications

Orthogonal latin squares
Die/Hellman key exchange
Vector Spaces
De nition and examples
Basic properties of vector spaces

Subspaces

Polynomials
Basics
Unique factorization

Polynomials over the real and complex numbers
Root formulas
Linear Codes
Basics
Hamming codes
Encoding
Decoding
Further study
Exercises
Appendix
Mathematical induction
Well-ordering Principle

Sets
Functions
Permutations
Matrices

Complex numbers
Hints and Partial Solutions to Selected Exercises

Über Autor(innen)

Gary Mullen is Professor of Mathematics, The Pennsylvania State University, where he earned his Ph.D. His main interest is finite fields, and is founder of the journal "Finite Fields and Their Introduction." He is also the Editor of The Handbook of Finite Fields published by CRC Press.

James Sellers is Professor and Associate Head for Undergraduate Mathematics, The Pennsylvania State University, where he also earned his Ph.D. He has published many research articles and won awards related to his efforts to advance mathematics education.