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Abstract Algebra: A Gentle Introduction: Textbooks in Mathematics

Autor Gary L. Mullen, James A. Sellers
en Limba Engleză Paperback – 21 ian 2023
 

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




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Specificații

ISBN-13: 9781032476971
ISBN-10: 1032476974
Pagini: 214
Dimensiuni: 152 x 229 x 16 mm
Greutate: 0.29 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics

Locul publicării:Boca Raton, United States

Recenzii

As the subtitle implies, those seeking a standard undergraduate text in abstract algebra should look elsewhere. The authors provide readers with a very brief introduction to some of the central structures of algebra: groups, rings, fields, and vector spaces. As an example of the text’s brevity, its treatment of groups consists of definitions, examples, and a discussion of subgroups and cosets that culminates in LaGrange’s theorem. There is no mention of group homomorphisms, normal subgroups, or quotient groups. Nonetheless, various applications of the subject not often addressed in traditional texts are treated within this work. It appears that the intent is to provide enough content for readers to comprehend these applications. Just enough elementary number theory is presented to allow a discussion of the RSA cryptosystem. Sufficient material on finite fields is given for a discussion of Latin squares and the Diffie-Hellman public key exchange. Adequate linear algebra topics foster a discussion of Hamming codes. This text will be suitable for an algebra-based course introducing students to abstract mathematical thought or an algebra course with an emphasis on applications.
--D. S. Larson, Gonzaga University, Choice magazine 2016 

Cuprins

Elementary Number Theory


Divisibility 


Primes and factorization 


Congruences


Solving congruences 


Theorems of Fermat and Euler


RSA cryptosystem 


Groups


De nition of a group 


Examples of groups


Subgroups


Cosets and Lagrange's Theorem


Rings


Defiition 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


Definition 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

Notă biografică

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.

Descriere

This book introduces the basic notions of abstract algebra to sophomores and perhaps even junior mathematics majors who have a relatively weak background with conceptual courses. It introduces the material with many concrete examples and establishes a firm foundation for introducing more abstract mathematical notions.