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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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