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klima r applications abstract algebra maple 1999

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Textbook in PDF format The mathematical concepts of abstract algebra may indeed be considered abstract, but its utility is quite concrete and continues to grow in importance. Unfortunately, the practical application of abstract algebra typically involves extensive and cumbersome calculations-often frustrating even the most dedicated attempts to appreciate and employ its intricacies. Now, however, sophisticated mathematical software packages help obviate the need for heavy number-crunching and make fields dependent on the algebra more interesting-and more accessible. Applications of Abstract Algebra with Maple opens the door to cryptography, coding, Polya counting theory, and the many other areas dependent on abstract algebra. Preliminary Mathematics Permutation Groups Cosets and Quotient Groups Rings and Euclidean Domains Finite Fields Finite Fields with Maple The Euclidean Algorithm Block Designs General Properties of Block Designs Hadamard Matrices Hadamard Matrices with Maple Difference Sets Difference Sets with Maple Error-Correcting Codes General Properties of Codes Hadamard Codes Reed-Muller Codes Reed-Muller Codes withMapl e Linear Codes Hamming Codes withMaple BCH Codes Construction of BCH Codes Error Correction in BCH Codes BCH Codes withMapl e Construction of the Generator Polynomial Error Correction Reed-Solomon Codes Construction of Reed-Solomon Codes Error Correction in Reed-Solomon Codes Proof of Reed-Solomon Error Correction Binary Reed-Solomon Codes Reed-Solomon Codes withMapl e Construction of the Codewords Error Correction Reed-Solomon Codes in Voyager2 Algebraic Cryptography Some Elementary Cryptosystems The Hill Cryptosystem The Hill Cryptosystem with Maple Generalizations of the Hill Cryptosystem The Two-Message Problem The RSA Cryptosystem Mathematical Prerequisites RSA Encryption and Decryption The RSA Cryptosystem with Maple A Note on Modular Exponentiation A Note on Primality Testing A Note on Integer Factorization A Note on Digital Signatures The Diffie-Hellman Key Exchange Elliptic Curve Cryptography The ElGamal Cryptosystem The ElGamal Cryptosystem with Maple Elliptic Curves Elliptic Curves withMaple Elliptic Curve Cryptography Elliptic Curve Cryptography with Maple Polya Theory Group Actions Burnside’s Theorem The Cycle Index The Pattern Inventory The Pattern Inventory with Maple Switching Functions Switching Functions with Maple Appendices Basic Maple Tutorial Introduction to Maple Arithmetic Defining Variables and Functions Algebra Case Sensitivity Help File Arrays and Loops Conditional Statements Maple Procedures Some Maple Linear Algebra Commands User-Written Maple Procedures Chapter 5 Procedures Chapter 7 Procedures Chapter 8 Procedures Chapter 9 Procedures Hints and Solutions to Selected Written Exercises

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klima r applications abstract algebra maple 1999

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