Applications of abstract algebra with Maple and MATLAB:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2007
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Discrete mathematics and its applications
|
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/toc/ecip0611/2006010706.html http://www.loc.gov/catdir/enhancements/fy0661/2006010706-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014874811&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | 1. Aufl. u.d.T.: Klima, Richard E.: Applications of abstract algebra with Maple |
| Umfang: | 505 S. 1 CD-ROM (12 cm) |
| ISBN: | 9781584886105 1584886102 |
Internformat
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| 630 | 0 | 4 | |a MATLAB |
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Datensatz im Suchindex
| _version_ | 1819287139214426112 |
|---|---|
| adam_text | Titel: Applications of abstract algebra with Maple and MATLAB
Autor: Klima, Richard E
Jahr: 2007
Contents
Preliminary Mathematics 1
1.1 Permutation Groups...................... 1
1.2 Cosets and Quotient Groups.................. 6
1.3 Rings and Euclidean Domains................. 8
1.4 Finite Fields .......................... 12
1.5 Finite Fields with Maple.................... 16
1.6 Finite Fields with MATLAB.................. 17
1.7 The Euclidean Algorithm................... 20
Exercises ............................... 25
Computer Exercises ......................... 28
Block Designs 29
2.1 General Properties....................... 29
2.2 Hadamard Matrices ...................... 33
2.3 Hadamard Matrices with Maple................ 35
2.4 Hadamard Matrices with MATLAB.............. 38
2.5 Difference Sets......................... 41
2.6 Difference Sets with Maple .................. 44
2.7 Difference Sets with MATLAB................. 47
Exercises ............................... 50
Computer Exercises ......................... 52
Research Exercises.......................... 52
Error Correcting Codes 53
3.1 General Properties....................... 53
3.2 Hadamard Codes........................ 56
3.3 Reed-Muller Codes....................... 58
3.4 Reed-Muller Codes with Maple................ 59
3.5 Reed-Muller Codes with MATLAB.............. 64
3.6 Linear Codes.......................... 70
3.7 Hamming Codes with Maple ................. 77
3.8 Hamming Codes with MATLAB................ 82
Exercises ............................... 88
Computer Exercises......................... 90
Research Exercises.......................... 91
BCH Codes 93
4.1 Construction.......................... 93
4.2 Error Correction........................ 96
4.3 BCH Codes with Maple.................... 103
4.3.1 Construction...................... 103
4.3.2 Error Correction.................... 108
4.4 BCH Codes with MATLAB.................. 114
4.4.1 Construction...................... 114
4.4.2 Error Correction.................... 120
Exercises ............................... 130
Computer Exercises......................... 132
Research Exercises.......................... 133
Reed-Solomon Codes 135
5.1 Construction.......................... 135
5.2 Error Correction........................ 138
5.3 Error Correction Method Proof................ 142
5.4 Reed-Solomon Codes with Maple............... 145
5.4.1 Construction...................... 145
5.4.2 Error Correction.................... 148
5.5 Reed-Solomon Codes with MATLAB............. 153
5.5.1 Construction...................... 153
5.5.2 Error Correction.................... 156
5.6 Reed-Solomon Codes in Voyager 2.............. 163
Exercises ............................... 164
Computer Exercises......................... 166
Research Exercises.......................... 167
Algebraic Cryptography 169
6.1 Two Elementary Cryptosystems................ 169
6.1.1 Shift Ciphers...................... 170
6.1.2 Affine Ciphers ..................... 173
6.2 Shift and Affine Ciphers with Maple............. 175
6.2.1 Shift Ciphers...................... 176
6.2.2 Affine Ciphers ..................... 179
6.3 Shift and Affine Ciphers with MATLAB........... 184
6.3.1 Shift Ciphers...................... 185
6.3.2 Affine Ciphers ..................... 188
6.4 Hill Ciphers........................... 194
6.5 Hill Ciphers with Maple.................... 200
6.6 Hill Ciphers with MATLAB.................. 206
Exercises ............................... 213
Computer Exercises ......................... 215
Research Exercises.......................... 217
Vigenere Ciphers 219
7.1 Encryption and Decryption.................. 219
7.2 Cryptanalysis.......................... 222
7.2.1 The Index of Coincidence............... 222
7.2.2 Determining the Keyword Length .......... 224
7.2.3 Determining the Keyword............... 226
7.3 Vigenere Ciphers with Maple................. 230
7.3.1 Encryption and Decryption.............. 231
7.3.2 Cryptanalysis...................... 232
7.4 Vigenere Ciphers with MATLAB ............... 240
7.4.1 Encryption and Decryption.............. 241
7.4.2 Cryptanalysis...................... 243
Exercises ............................... 254
Computer Exercises ......................... 257
Research Exercises.......................... 258
The RSA Cryptosystem 259
8.1 Preliminary Mathematics................... 260
8.2 Encryption and Decryption.................. 262
8.3 The RSA Cryptosystem with Maple............. 267
8.4 The RSA Cryptosystem with MATLAB ........... 271
8.5 A Note on Modular Exponentiation ............. 277
8.6 A Note on Primality Testing ................. 278
8.7 A Note on Integer Factorization................ 279
8.8 A Note on Digital Signatures................. 280
8.9 The Diffie-Hellman Key Exchange .............. 281
8.10 Discrete Logarithms with Maple ............... 284
8.11 Discrete Logarithms with MATLAB.............. 285
Exercises ............................... 286
Computer Exercises ......................... 289
Research Exercises.......................... 291
Elliptic Curve Cryptography 293
9.1 The ElGamal Cryptosystem.................. 293
9.2 The ElGamal Cryptosystem with Maple........... 296
9.3 The ElGamal Cryptosystem with MATLAB......... 298
9.4 Elliptic Curves......................... 301
9.5 Elliptic Curves with Maple .................. 309
9.6 Elliptic Curves with MATLAB................. 312
9.7 Elliptic Curve Cryptography ................. 317
9.8 Elliptic Curve Cryptography with Maple........... 321
9.9 Elliptic Curve Cryptography with MATLAB......... 324
Exercises ............................... 329
Computer Exercises ......................... 331
Research Exercises.......................... 333
10 The Advanced Encryption Standard 335
10.1 Alphabet Assignment and Text Setup............ 335
10.2 The S-Box............................ 338
10.3 Key Generation......................... 341
10.3.1 The Initial Key..................... 341
10.3.2 The Key Schedule................... 342
10.4 Encryption........................... 346
10.5 The AES Layers ........................ 347
10.5.1 ByteSub......................... 347
10.5.2 ShiftRow........................ 348
10.5.3 MixColumn....................... 349
10.5.4 AddRoundKey..................... 350
10.6 Decryption........................... 350
10.7 A Note on Security....................... 355
10.8 AES with Maple........................ 356
10.8.1 Construction of Initial Parameters.......... 356
10.8.2 The Encryption Layers................. 361
10.8.3 The Decryption Layers................. 363
10.8.4 Encryption and Decryption.............. 366
10.9 AES with MATLAB ...................... 369
10.9.1 Construction of Initial Parameters.......... 369
10.9.2 The Encryption Layers................. 374
10.9.3 The Decryption Layers................. 376
10.9.4 Encryption and Decryption.............. 379
Exercises ............................... 383
Computer Exercises......................... 385
Research Exercises.......................... 388
11 Polya Theory 389
11.1 Group Actions......................... 389
11.2 Burnside s Theorem...................... 392
11.3 The Cycle Index........................ 395
11.4 The Pattern Inventory..................... 398
11.5 The Pattern Inventory with Maple.............. 403
11.6 The Pattern Inventory with MATLAB............ 406
11.7 Switching Functions...................... 410
Exercises ............................... 413
Computer Exercises ......................... 416
Research Exercises.......................... 416
12 Graph Theory 417
12.1 The Cycle Index of Sn..................... 417
12.2 The Cycle Index of Sn with Maple.............. 421
12.3 The Cycle Index of Sn with MATLAB............ 424
12.4 Counting Undirected Graphs................. 429
12.5 Counting Undirected Graphs with Maple .......... 437
12.6 Counting Undirected Graphs with MATLAB......... 439
Exercises ............................... 442
Computer Exercises ......................... 443
Research Exercises.......................... 444
Appendices 445
A User-Written Maple Functions 445
A.5 Functions Used in Chapter 5 ................. 445
A.6 Functions Used in Chapter 6 ................. 447
A.7 Functions Used in Chapter 7 ................. 448
A.8 Functions Used in Chapter 8 ................. 449
A.9 Functions Used in Chapter 9 ................. 450
A.10 Functions Used in Chapter 10................. 452
A.12 Functions Used in Chapter 12................. 459
B User-Written MATLAB Functions 461
B.4 Functions Used in Chapter 4 ................. 461
B.5 Functions Used in Chapter 5 ................. 461
B.6 Functions Used in Chapter 6 ................. 464
B.7 Functions Used in Chapter 7 ................. 465
B.8 Functions Used in Chapter 8 ................. 467
B.9 Functions Used in Chapter 9 ................. 467
B.10 Functions Used in Chapter 10................. 470
B.12 Functions Used in Chapter 12................. 477
Bibliography 481
Hints or Answers for Selected Exercises 485
Index 493
|
| any_adam_object | 1 |
| author | Klima, Richard E. 1970- Sigmon, Neil P. Stitzinger, Ernest 1940- |
| author_GND | (DE-588)135945402 (DE-588)135945542 |
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| classification_rvk | SK 220 ST 601 |
| ctrlnum | (OCoLC)263740867 (DE-599)BVBBV021660303 |
| dewey-full | 512/.02 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.02 |
| dewey-search | 512/.02 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV021660303 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T12:38:48Z |
| institution | BVB |
| isbn | 9781584886105 1584886102 |
| language | English |
| lccn | 2006010706 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014874811 |
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| owner_facet | DE-29T DE-355 DE-BY-UBR DE-824 |
| physical | 505 S. 1 CD-ROM (12 cm) |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Discrete mathematics and its applications |
| spellingShingle | Klima, Richard E. 1970- Sigmon, Neil P. Stitzinger, Ernest 1940- Applications of abstract algebra with Maple and MATLAB Maple (Computer file) MATLAB Datenverarbeitung Algebra, Abstract Data processing MATLAB (DE-588)4329066-8 gnd Maple Programm (DE-588)4209397-1 gnd Universelle Algebra (DE-588)4061777-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4209397-1 (DE-588)4061777-4 (DE-588)4128130-5 |
| title | Applications of abstract algebra with Maple and MATLAB |
| title_auth | Applications of abstract algebra with Maple and MATLAB |
| title_exact_search | Applications of abstract algebra with Maple and MATLAB |
| title_full | Applications of abstract algebra with Maple and MATLAB Richard E. Klima ; Neil P. Sigmon ; Ernest L. Stitzinger |
| title_fullStr | Applications of abstract algebra with Maple and MATLAB Richard E. Klima ; Neil P. Sigmon ; Ernest L. Stitzinger |
| title_full_unstemmed | Applications of abstract algebra with Maple and MATLAB Richard E. Klima ; Neil P. Sigmon ; Ernest L. Stitzinger |
| title_short | Applications of abstract algebra with Maple and MATLAB |
| title_sort | applications of abstract algebra with maple and matlab |
| topic | Maple (Computer file) MATLAB Datenverarbeitung Algebra, Abstract Data processing MATLAB (DE-588)4329066-8 gnd Maple Programm (DE-588)4209397-1 gnd Universelle Algebra (DE-588)4061777-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Maple (Computer file) MATLAB Datenverarbeitung Algebra, Abstract Data processing Maple Programm Universelle Algebra Numerisches Verfahren |
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