Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.
Applied Abstract Algebra
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Inside This Book
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First Sentence:
In 1854, George Boole (1815-1864) introduced an important class of algebraic structures in connection with his research in mathematical logic. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
linear recurring sequence, cycle index polynomial, affine cipher, prime implicants, cyclic codes, recovery equations, coset leaders, orthomodular lattices, orthogonal maps, splitting field, generator polynomial, recurring sequences, primitive nth root, commutative ring with identity, linear shift registers, finite semigroup, linear recurrence relation, monic irreducible polynomials, generator matrix, minimal polynomial, initial state vector, companion matrix, free semigroup, algebraic coding theory, check symbols Key Phrases - Capitalized Phrases (CAPs): (learn more)
Chinese Remainder Theorem, Homomorphism Theorem, Proof Let, Some Group Theory, United States, Use Exercise, Fermat's Little Theorem, Kronecker's Theorem, Pólya's Theorem, Schur's Lemma, Zorn's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In 1854, George Boole (1815-1864) introduced an important class of algebraic structures in connection with his research in mathematical logic. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
linear recurring sequence, cycle index polynomial, affine cipher, prime implicants, cyclic codes, recovery equations, coset leaders, orthomodular lattices, orthogonal maps, splitting field, generator polynomial, recurring sequences, primitive nth root, commutative ring with identity, linear shift registers, finite semigroup, linear recurrence relation, monic irreducible polynomials, generator matrix, minimal polynomial, initial state vector, companion matrix, free semigroup, algebraic coding theory, check symbols Key Phrases - Capitalized Phrases (CAPs): (learn more)
Chinese Remainder Theorem, Homomorphism Theorem, Proof Let, Some Group Theory, United States, Use Exercise, Fermat's Little Theorem, Kronecker's Theorem, Pólya's Theorem, Schur's Lemma, Zorn's Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
cite this book:
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- Discrete Mathematics by Wiley in Back Matter (1), and Back Matter (2)
- A Course in Combinatorics by J. H. van Lint in Back Matter
- Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) by Charles C. Sims in Back Matter
- Introduction to Finite Fields and their Applications by Rudolf Lidl in Back Matter
- Group Theory and Physics by S. Sternberg in Back Matter
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- Introduction to Abstract Algebra by W. Keith Nicholson on page 64, page 152, and Back Matter
- Introduction to Cryptography (Undergraduate Texts in Mathematics) by Johannes Buchmann in Back Matter
- Introduction to Finite Fields and their Applications by Rudolf Lidl in Back Matter
- Introduction to the Mathematics of Finance: From Risk Management to Options Pricing (Undergraduate Texts in Mathematics) by Steven Roman in Back Matter
- Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan D. Bloch in Back Matter
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