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Abstract algebra: a gentle introduction

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Bibliographic Details
Main Authors:	Mullen, Gary L. 1947- (Author), Sellers, James (Author)
Format:	Book
Language:	English
Published:	Boca Raton CRC Press [2017]
Series:	Textbooks in mathematics A Chapman & Hall book
Subjects:	Algebra, Abstract > Textbooks Algebra > Textbooks Universelle Algebra Einführung
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	X, 203 Seiten
ISBN:	9781482250060

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MARC


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Record in the Search Index

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adam_text	Contents Preface ix 1 Elementary Number Theory 1 1.1 Divisibility ................................................ 1 1.2 Primes and factorization .................................... 6 1.3 Congruences ................................................ 11 1.4 Solving congruences ........................................ 15 1.5 Theorems of Fermat and Euler................................ 20 1.6 RSA cryptosystem............................................ 28 2 Groups 33 2.1 Definition of a group ...................................... 33 2.2 Examples of groups ......................................... 34 2.3 Subgroups .................................................. 43 2.4 Cosets and Lagrange’s Theorem .............................. 49 3 Rings 55 3.1 Definition of a ring ....................................... 55 3.2 Subrings and ideals ........................................ 61 3.3 Ring homomorphisms ......................................... 63 3.4 Integral domains............................................ 65 4 Fields 67 4.1 Definition and basic properties of a field............... 67 5 Finite Fields 73 5.1 Number of elements in a finite field ....................... 73 5.2 How to construct finite fields.............................. 75 5.3 Properties of finite fields ................................ 82 5.4 Polynomials over finite fields ............................. 86 5.5 Permutation polynomials .................................... 89 5.6 Applications .............................................. 91 5.6.1 Orthogonal Latin squares............................. 91 5.6.2 Diffie/Hellman key exchange.......................... 94 vii viii Contents 6 Vector Spaces 99 6.1 Definition and examples................................... 99 6.2 Basic properties of vector spaces........................ 103 6.3 Subspaces................................................ 109 7 Polynomials 111 7.1 Basics................................................... Ill 7.2 Unique factorization..................................... 115 7.3 Polynomials over the real and complex numbers ........... 117 7.4 Root formulas ........................................... 118 8 Linear Codes 127 8.1 Basics................................................... 129 8.2 Hamming codes ........................................... 132 8.3 Encoding................................................. 134 8.4 Decoding ................................................ 137 8.5 Further study ........................................... 143 8.6 Exercises . ........................................ 145 9 10 9 Appendix 149 9.1 Mathematical induction.................................... 149 9.2 Well-ordering Principle .................................. 152 9.3 Sets...................................................... 154 9.4 Functions................................................. 158 9.5 Permutations.............................................. 160 9.6 Matrices ................................................. 163 9.7 Complex numbers .......................................... 165 10 Hints and Partial Solutions to Selected Exercises 167 Bibliography 195 Index 199
any_adam_object	1
author	Mullen, Gary L. 1947- Sellers, James
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isbn	9781482250060
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series2	Textbooks in mathematics A Chapman & Hall book
spelling	Mullen, Gary L. 1947- Verfasser (DE-588)123964059 aut Abstract algebra a gentle introduction Gary L. Mullen, James A. Sellers Boca Raton CRC Press [2017] © 2017 X, 203 Seiten txt rdacontent n rdamedia nc rdacarrier Textbooks in mathematics A Chapman & Hall book Includes bibliographical references and index Algebra, Abstract Textbooks Algebra Textbooks Universelle Algebra (DE-588)4061777-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Universelle Algebra (DE-588)4061777-4 s DE-604 Sellers, James Verfasser (DE-588)1044332700 aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029438551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Mullen, Gary L. 1947- Sellers, James Abstract algebra a gentle introduction Algebra, Abstract Textbooks Algebra Textbooks Universelle Algebra (DE-588)4061777-4 gnd
subject_GND	(DE-588)4061777-4 (DE-588)4151278-9
title	Abstract algebra a gentle introduction
title_auth	Abstract algebra a gentle introduction
title_exact_search	Abstract algebra a gentle introduction
title_full	Abstract algebra a gentle introduction Gary L. Mullen, James A. Sellers
title_fullStr	Abstract algebra a gentle introduction Gary L. Mullen, James A. Sellers
title_full_unstemmed	Abstract algebra a gentle introduction Gary L. Mullen, James A. Sellers
title_short	Abstract algebra
title_sort	abstract algebra a gentle introduction
title_sub	a gentle introduction
topic	Algebra, Abstract Textbooks Algebra Textbooks Universelle Algebra (DE-588)4061777-4 gnd
topic_facet	Algebra, Abstract Textbooks Algebra Textbooks Universelle Algebra Einführung
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