Abstract algebra: a gentle introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press
[2017]
|
| Schriftenreihe: | Textbooks in mathematics
A Chapman & Hall book |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | X, 203 Seiten |
| ISBN: | 9781482250060 |
Internformat
MARC
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| 245 | 1 | 0 | |a Abstract algebra |b a gentle introduction |c Gary L. Mullen, James A. Sellers |
| 264 | 1 | |a Boca Raton |b CRC Press |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a X, 203 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Textbooks in mathematics | |
| 490 | 0 | |a A Chapman & Hall book | |
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| 650 | 4 | |a Algebra |v Textbooks | |
| 650 | 0 | 7 | |a Universelle Algebra |0 (DE-588)4061777-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1804177034626203648 |
|---|---|
| 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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| callnumber-first | Q - Science |
| callnumber-label | QA162 |
| callnumber-raw | QA162 |
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| callnumber-sort | QA 3162 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 SK 230 |
| ctrlnum | (OCoLC)988298113 (DE-599)BVBBV044031288 |
| dewey-full | 512/.02 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.02 |
| dewey-search | 512/.02 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T07:41:40Z |
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| isbn | 9781482250060 |
| language | English |
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| 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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