Abstract algebra with applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2019
|
| Schriftenreihe: | Cambridge mathematical textbooks
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030773145&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xix, 310 Seiten Illustrationen, Diagramme |
| ISBN: | 1107164079 9781107164079 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819355538432983040 |
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| adam_text | Contents List of Figures Preface ix xiii PARTI GROUPS 1 Preliminaries______________________________________________________________ 3 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Introduction Sets The Integers Mathematical Induction Divisibility, Greatest Common Divisor, Primes, and Unique Factorization Modular Arithmetic, Congruences Relations Functions, the Pigeonhole Principle, and Binary Operations 2 Groups: A Beginning______________________________________________________ 43 2.1 2.2 2.3 2.4 2.5 What is a Group? Visualizing Groups More Examples of Groups and Some Basic Facts Subgroups Cyclic Groups are Our Friends 3 Groups: There s More_____________________________________________________ 81 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Groups of Permutations Isomorphisms and Cayley’s Theorem Cosets, Lagrange’s Theorem, and Normal Subgroups Building New Groups from Old, I: Quotient or Factor Groups G/Я Group Homomorphism Building New Groups from Old, II: Direct Product of Groups Group Actions 4 Applications and More Examples of Groups_________________________________ 124 4.1 4.2 4.3 4.4 4.5 Public-Key Cryptography Chemistry and the Finite Fourier Transform Groups and Conservation Laws in Physics Puzzles Small Groups 3 6 9 14 19 26 30 34 43 52 56 64 72 81 89 93 98 102 108 114 124 129 135 142 146
Abstract Algebra with Applications PARTII RINGS 5 Rings: A Beginning_______________________________________________________ 157 5.1 5.2 5.3 5.4 5.5 5.6 Introduction What is a Ring? Integral Domains and Fields are Nicer Rings Building New Rings from Old: Quotients and Direct Sums of Rings Polynomial Rings Quotients of Polynomial Rings 6 Rings: There s More______________________________________________________ 189 6.1 6.2 6.3 6.4 Ring Homomorphisms The Chinese Remainder Theorem More Stories about F[x Including Comparisons with Z Field of Fractions or Quotients 7 Vector Spaces and Finite Fields____________________________________________ 206 7.1 7.2 7.3 7.4 7.5 7.6 Matrices and Vector Spaces over Arbitrary Fieldsand Rings like Z Linear Functions or Mappings Determinants Extension Fields: Algebraic versus Transcendental Subfields and Field Extensions of Finite Fields Galois Theory for Finite Fields 8 Applications of Rings_____________________________________________________244 8.1 8.2 8.3 8.4 8.5 Random Number Generators Error-Correcting Codes Finite Upper Half Planes and Ramanujan Graphs Eigenvalues, Random Walks on Graphs, and Google Elliptic Curve Cryptography References Index 157 158 166 173 180 185 189 193 198 202 206 218 224 229 233 239 244 256 265 272 282 299 305
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-12-20T18:25:52Z |
| institution | BVB |
| isbn | 1107164079 9781107164079 |
| language | English |
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| physical | xix, 310 Seiten Illustrationen, Diagramme |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge mathematical textbooks |
| spellingShingle | Terras, Audrey 1942- Abstract algebra with applications Universelle Algebra (DE-588)4061777-4 gnd |
| subject_GND | (DE-588)4061777-4 |
| title | Abstract algebra with applications |
| title_auth | Abstract algebra with applications |
| title_exact_search | Abstract algebra with applications |
| title_full | Abstract algebra with applications Audrey Terras, University of California, San Diego, CA, USA |
| title_fullStr | Abstract algebra with applications Audrey Terras, University of California, San Diego, CA, USA |
| title_full_unstemmed | Abstract algebra with applications Audrey Terras, University of California, San Diego, CA, USA |
| title_short | Abstract algebra with applications |
| title_sort | abstract algebra with applications |
| topic | Universelle Algebra (DE-588)4061777-4 gnd |
| topic_facet | Universelle Algebra |
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