Applications of abstract algebra with Maple:
"Abstract Algebra Applications with Maple opens the door to cryptography, coding, Polya counting theory, and the many other areas dependent on abstract algebra. The authors have carefully integrated Maple V throughout the text, enabling readers to see realistic examples of the topics discussed...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2000
|
| Series: | Discrete mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Abstract Algebra Applications with Maple opens the door to cryptography, coding, Polya counting theory, and the many other areas dependent on abstract algebra. The authors have carefully integrated Maple V throughout the text, enabling readers to see realistic examples of the topics discussed without struggling with the computations. It includes a first-chapter review of the mathematics required - groups, rings, and finite fields - and a Maple tutorial in the appendix along with detailed treatments of coding, cryptography, and Polya theory applications."--BOOK JACKET. |
| Item Description: | 2. Aufl. u.d.T.: Klima, Richard E.: Applications of abstract algebra with Maple and MATLAB |
| Physical Description: | XII, 256 S. graph. Darst. |
| ISBN: | 0849381703 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804127593584132096 |
|---|---|
| adam_text | Contents
Preface v
1 Preliminary Mathematics 1
1.1 Permutation Groups 1
1.2 Cosets and Quotient Groups 6
1.3 Rings and Euclidean Domains 9
1.4 Finite Fields 13
1.5 Finite Fields with Maple 16
1.6 The Euclidean Algorithm 18
2 Block Designs 27
2.1 General Properties of Block Designs 27
2.2 Hadamard Matrices 31
2.3 Hadamard Matrices with Maple 33
2.4 Difference Sets 36
2.5 Difference Sets with Maple 39
3 Error Correcting Codes 43
3.1 General Properties of Codes 43
3.2 Hadamard Codes 46
3.3 Reed Muller Codes 48
ix
x CONTENTS
3.4 Reed Muller Codes with Maple 48
3.5 Linear Codes 53
3.6 Hamming Codes with Maple 60
4 BCH Codes 67
4.1 Construction of BCH Codes 67
4.2 Error Correction in BCH Codes 70
4.3 BCH Codes with Maple 77
4.3.1 Construction of the Generator Polynomial 78
4.3.2 Error Correction 80
5 Reed Solomon Codes 91
5.1 Construction of Reed Solomon Codes 91
5.2 Error Correction in Reed Solomon Codes 93
5.3 Proof of Reed Solomon Error Correction 97
5.4 Binary Reed Solomon Codes 101
5.5 Reed Solomon Codes with Maple 102
5.5.1 Construction of the Codewords 103
5.5.2 Error Correction 105
5.6 Reed Solomon Codes in Voyager 2 Ill
6 Algebraic Cryptography 115
6.1 Some Elementary Cryptosystems 115
6.2 The Hill Cryptosystem 119
6.3 The Hill Cryptosystem with Maple 124
6.4 Generalizations of the Hill Cryptosystem 129
6.5 The Two Message Problem 131
7 The RSA Cryptosystem 139
7.1 Mathematical Prerequisites 140
CONTENTS xi
7.2 RSA Encryption and Decryption 142
7.3 The RSA Cryptosystem with Maple 147
7.4 A Note on Modular Exponentiation 150
7.5 A Note on Primality Testing 152
7.6 A Note on Integer Factorization 153
7.7 A Note on Digital Signatures 154
7.8 The Diffie Hellman Key Exchange 155
8 Elliptic Curve Cryptography 163
8.1 The ElGamal Cryptosystem 163
8.2 The ElGamal Cryptosystem with Maple 166
8.3 Elliptic Curves 168
8.4 Elliptic Curves with Maple 175
8.5 Elliptic Curve Cryptography 178
8.6 Elliptic Curve Cryptography with Maple 182
9 Polya Theory 189
9.1 Group Actions 190
9.2 Burnside s Theorem 192
9.3 The Cycle Index 195
9.4 The Pattern Inventory 198
9.5 The Pattern Inventory with Maple 203
9.6 Switching Functions 205
9.7 Switching Functions with Maple 208
Appendices
A Basic Maple Tutorial 213
A.I Introduction to Maple 213
A.2 Arithmetic 214
xii CONTENTS
A.3 Defining Variables and Functions 216
A.4 Algebra 217
A.5 Case Sensitivity 218
A.6 Help File 219
A.7 Arrays and Loops 219
A.8 Conditional Statements 221
A.9 Maple Procedures 223
B Some Maple Linear Algebra Commands 225
C User Written Maple Procedures 231
C.I Chapter 5 Procedures 231
C.2 Chapter 7 Procedures 234
C.3 Chapter 8 Procedures 235
C.4 Chapter 9 Procedures 236
Hints and Solutions to Selected Written Exercises 243
Index 248
|
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| author | Klima, Richard E. 1970- Sigmon, Neil P. Stitzinger, Ernest 1940- |
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| author_sort | Klima, Richard E. 1970- |
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| ctrlnum | (OCoLC)41674338 (DE-599)BVBBV012907170 |
| dewey-full | 512/.02/02855369 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| genre_facet | Maple 5.0 |
| id | DE-604.BV012907170 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:49Z |
| institution | BVB |
| isbn | 0849381703 |
| language | English |
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| physical | XII, 256 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Discrete mathematics and its applications |
| spelling | Klima, Richard E. 1970- Verfasser (DE-588)135945402 aut Applications of abstract algebra with Maple Richard E. Klima ; Neil Sigmon ; Ernest Stitzinger Boca Raton [u.a.] CRC Press 2000 XII, 256 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications 2. Aufl. u.d.T.: Klima, Richard E.: Applications of abstract algebra with Maple and MATLAB "Abstract Algebra Applications with Maple opens the door to cryptography, coding, Polya counting theory, and the many other areas dependent on abstract algebra. The authors have carefully integrated Maple V throughout the text, enabling readers to see realistic examples of the topics discussed without struggling with the computations. It includes a first-chapter review of the mathematics required - groups, rings, and finite fields - and a Maple tutorial in the appendix along with detailed treatments of coding, cryptography, and Polya theory applications."--BOOK JACKET. Maple (Computer file) Datenverarbeitung Algebra, Abstract Data processing Algebra (DE-588)4001156-2 gnd rswk-swf Algebraische Codierung (DE-588)4141834-7 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Maple V (DE-588)4276266-2 gnd rswk-swf Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Maple V 5.0 (DE-588)4499931-8 gnd rswk-swf Maple 5.0 gnd rswk-swf Algebraische Codierung (DE-588)4141834-7 s Kryptologie (DE-588)4033329-2 s Maple 5.0 f DE-604 Algebra (DE-588)4001156-2 s Universelle Algebra (DE-588)4061777-4 s Maple V 5.0 (DE-588)4499931-8 s Maple V (DE-588)4276266-2 s DE-188 Sigmon, Neil P. Verfasser aut Stitzinger, Ernest 1940- Verfasser (DE-588)135945542 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008785456&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klima, Richard E. 1970- Sigmon, Neil P. Stitzinger, Ernest 1940- Applications of abstract algebra with Maple Maple (Computer file) Datenverarbeitung Algebra, Abstract Data processing Algebra (DE-588)4001156-2 gnd Algebraische Codierung (DE-588)4141834-7 gnd Kryptologie (DE-588)4033329-2 gnd Maple V (DE-588)4276266-2 gnd Universelle Algebra (DE-588)4061777-4 gnd Maple V 5.0 (DE-588)4499931-8 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4141834-7 (DE-588)4033329-2 (DE-588)4276266-2 (DE-588)4061777-4 (DE-588)4499931-8 |
| title | Applications of abstract algebra with Maple |
| title_auth | Applications of abstract algebra with Maple |
| title_exact_search | Applications of abstract algebra with Maple |
| title_full | Applications of abstract algebra with Maple Richard E. Klima ; Neil Sigmon ; Ernest Stitzinger |
| title_fullStr | Applications of abstract algebra with Maple Richard E. Klima ; Neil Sigmon ; Ernest Stitzinger |
| title_full_unstemmed | Applications of abstract algebra with Maple Richard E. Klima ; Neil Sigmon ; Ernest Stitzinger |
| title_short | Applications of abstract algebra with Maple |
| title_sort | applications of abstract algebra with maple |
| topic | Maple (Computer file) Datenverarbeitung Algebra, Abstract Data processing Algebra (DE-588)4001156-2 gnd Algebraische Codierung (DE-588)4141834-7 gnd Kryptologie (DE-588)4033329-2 gnd Maple V (DE-588)4276266-2 gnd Universelle Algebra (DE-588)4061777-4 gnd Maple V 5.0 (DE-588)4499931-8 gnd |
| topic_facet | Maple (Computer file) Datenverarbeitung Algebra, Abstract Data processing Algebra Algebraische Codierung Kryptologie Maple V Universelle Algebra Maple V 5.0 Maple 5.0 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008785456&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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