Applied Abstract AlgebraSpringer Science & Business Media, 14 mars 2013 - 488 pages 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. |
Table des matières
Applications of Lattices | 55 |
Finite Fields and Polynomials | 95 |
13 | 125 |
14 | 144 |
Factorization of Polynomials over Finite Fields | 166 |
Linear Codes | 200 |
XV | 215 |
19 | 221 |
Notes | 329 |
29 | 342 |
30 | 350 |
32 | 356 |
35 | 388 |
37 | 404 |
95 | 406 |
39 | 434 |
20 | 229 |
Notes | 236 |
62 | 271 |
24 | 284 |
26 | 292 |
27 | 303 |
40 | 447 |
Bibliography | 459 |
| 475 | |
| 476 | |
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Expressions et termes fréquents
a₁ abelian algorithm applications automata b₁ b₂ BCH code binary blocks Boolean algebra C₁ called cipher ciphertext codewords coefficients column construct coset cryptography cyclic code cyclotomic deciphering decoding defined Definition denote Determine enciphering equations equivalent errors Example Exercise factors field F finite field Fq[x function given Gröbner basis Hadamard matrix Hamming code Hence homomorphism ideal input integer irreducible polynomial isomorphic Latin squares lattice Let F Let G linear recurring sequence mathematics minimal polynomial minimum distance monic monoid multiplication near-ring nonzero nth root obtain orthogonal p₁ parameters parity-check matrix plaintext polynomial ƒ polynomial of degree prime primitive element problem Proof public key cryptosystem representation ring root of unity S₁ semigroup Show splitting field subset switching symmetry t₁ Theorem theory transform unique vector space x²+x+1 zero