Applied Abstract Algebra with Mapletm and Matlab (3rd Edition) by Richard E Klima; Neil P Sigmon; Ernest Stitzinger
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Applied Abstract Algebra with Mapletm and Matlab (3rd Edition) written by
Richard E Klima, Appalachian State University, Boone, North Carolina, USA
Neil P Sigmon, Radford University, Radford, Virginia, USA and
Ernest Stitzinger, North Carolina State University, Raleigh, North Carolina, USA.
Applied Abstract Algebra with MapleTM and MATLAB(R)provides an in-depth introduction to real-world abstract algebraic problems. This popular textbook covers a variety of topics including block designs, coding theory, cryptography, and counting techniques, including Polya's and Burnside's theorems. The book also includes a concise review of all prerequisite advanced mathematics. The use of sophisticated mathematical software packages such as MapleTM and MATLAB(R) allows students to work though realistic examples without having to struggle with extensive computations. Notable additions to the third edition include expanded contemporary applications, coverage of the two-message problem, and a full chapter on symmetry in Western music. Several other parts of the book were also updated, including some MATLAB sections due to their adoption of the MuPAD computer algebra system since the last edition. This edition also contains more than 100 new exercises. This new edition includes the two most widely used mathematical software packages. It builds upon the successful previous editions, favored by instructors and students alike.
Applied Abstract Algebra with Mapletm and Matlab (3rd Edition) written by
Richard E Klima,
Neil P Sigmon and
Ernest Stitzinger
cover the following topics.
1. Preliminary Mathematics
1.1 Permutation Groups
1.2 Cosets and Quotient Groups
1.3 Rings and Euclidean Domains
1.4 Finite Fields
1.5 Finite Fields with Maple
1.6 Finite Fields with MATLAB
1.7 The Euclidean Algorithm
Exercises
2. Block Designs
2.1 General Properties
2.2 Hadamard Matrices
2.3 Hadamard Matrices with Maple
2.4 Hadamard Matrices with MATLAB
2.5 Difference Sets
2.6 Difference Sets with Maple
2.7 Difference Sets with MATLAB
Exercises
3. Error-Correcting Codes
3.1 General Properties
3.2 Hadamard Codes
3.3 Reed-Muller Codes
3.4 Reed-Muller Codes with Maple
3.5 Reed-Muller Codes with MATLAB
3.6 Linear Codes
3.7 Hamming Codes with Maple
3.8 Hamming Codes with MATLAB
Exercises
4. BCH Codes
4.1 Construction
4.2 Error Correction
4.3 BCH Codes with Maple
4.3.1 Construction
4.3.2 Error Correction
4.4 BCH Codes with MATLAB
4.4.1 Construction
4.4.2 Error Correction
Exercises
5. Reed-Solomon Codes
5.1 Construction
5.2 Error Correction
5.3 Error Correction Method Proof
5.4 Reed-Solomon Codes with Maple
5.4.1 Construction
5.4.2 Error Correction
5.5 Reed-Solomon Codes with MATLAB
5.5.1 Construction
5.5.2 Error Correction
5.6 Reed-Solomon Codes in Voyager 2
Exercises
6. Algebraic Cryptography
6.1 Two Elementary Cryptosystems
6.1.1 Shift Ciphers
6.1.2 Affine Ciphers
6.2 Shift and Affine Ciphers with Maple
6.2.1 Shift Ciphers
6.2.2 Affine Ciphers
6.3 Shift and Affine Ciphers with MATLAB
6.3.1 Shift Ciphers
6.3.2 Affine Ciphers
6.4 Hill Ciphers
6.5 Hill Ciphers with Maple
6.6 Hill Ciphers with MATLAB
6.7 The Two-Message Problem
Exercises
7. Vigen`ere Ciphers
7.1 Encryption and Decryption
7.2 Cryptanalysis
7.2.1 The Index of Coincidence
7.2.2 Determining the Keyword Length
7.2.3 Determining the Keyword
7.3 Vigen`ere Ciphers with Maple
7.3.1 Encryption and Decryption
7.3.2 Cryptanalysis
7.4 Vigen`ere Ciphers with MATLAB
7.4.1 Encryption and Decryption
7.4.2 Cryptanalysis
Exercises
8. RSA Ciphers
8.1 Preliminary Mathematics
8.2 Encryption and Decryption
8.3 RSA Ciphers with Maple
8.4 RSA Ciphers with MATLAB
8.5 Efficiency and Security Issues
8.5.1 Primality Testing
8.5.2 Integer Factorization
8.5.3 Modular Exponentiation
8.5.4 Digital Signatures
8.6 The Diffie-Hellman Key Exchange with RSA
8.7 Discrete Logarithms with Maple
8.8 Discrete Logarithms with MATLAB
Exercises
9. Elliptic Curve Cryptography
9.1 ElGamal Ciphers
9.2 ElGamal Ciphers with Maple
9.3 ElGamal Ciphers with MATLAB
9.4 Elliptic Curves
9.5 Elliptic Curves with Maple
9.6 Elliptic Curves with MATLAB
9.7 Elliptic Curve Cryptography
9.8 Elliptic Curve Cryptography with Maple
9.9 Elliptic Curve Cryptography with MATLAB
Exercises
10. The Advanced Encryption Standard
10.1 Text Setup
10.2 The S-Box
10.3 Key Generation
10.3.1 The Initial Key
10.3.2 The Key Schedule
10.4 Encryption
10.5 The AES Layers
10.5.1 ByteSub
10.5.2 ShiftRow
10.5.3 MixColumn
10.5.4 AddRoundKey
10.6 Decryption
10.7 AES with Maple
10.7.1 Construction of Initial Parameters
10.7.2 The Encryption Layers
10.7.3 The Decryption Layers
10.7.4 Encryption and Decryption
10.8 AES with MATLAB
10.8.1 Construction of Initial Parameters
10.8.2 The Encryption Layers
10.8.3 The Decryption Layers
10.8.4 Encryption and Decryption
Exercises
11. P´olya Theory
11.1 Group Actions
11.2 Burnside’s Theorem
11.3 The Cycle Index
11.4 The Pattern Inventory
11.5 The Pattern Inventory with Maple
11.6 The Pattern Inventory with MATLAB
11.7 Switching Functions
Exercises
12. Graph Theory
12.1 The Cycle Index of Sn
12.2 The Cycle Index of Sn with Maple
12.3 The Cycle Index of Sn with MATLAB
12.4 Counting Undirected Graphs
12.5 Counting Undirected Graphs with Maple
12.6 Counting Undirected Graphs with MATLAB
Exercises
13. Symmetry in Western Music
13.1 Introduction
13.2 Group Actions and Scales
13.3 Group Actions and Chords
13.4 Group Actions and Chords with Maple
13.5 Group Actions and Chords with MATLAB
13.6 Cayley Graphs for Z12
13.7 Twelve-Tone Rows
13.8 Twelve-Tone Rows with Maple
13.9 Twelve-Tone Rows with MATLAB
Exercises
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