Applied Abstract Algebra

Applied Abstract Algebra

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Description

With a clear focus on compulsory algebra for undergraduates, Applied Abstract Algebra includes many significant and exciting applications. The author addresses the key topics in algebra while leaving out topics usually covered in advanced courses. This tradeoff allows the book to cover more interesting and realistic applications. The core set of examples and applications are in cryptography, coding theory, linear recurrences, and control theory. Applications include the Advanced Encryption Standard, decoding of BCH codes, and convolutional codes. The material for these topics is developed systematically, allowing students a taste of real-life, cutting edge applications.show more

Product details

  • Hardback | 406 pages
  • 155.58 x 234.95mm
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • United States
  • English
  • 100 black & white illustrations
  • 1584884266
  • 9781584884262

Table of contents

Integers mod n. Finite fields GF(p). Matrix algebra. Vector Spaces. Linear codes. Linear transformations. Invariant subspaces. Groups. Permutation groups (groups acting on structures). Determinants. Rings . Structure of finite commutative rings. Rings of polynomials and rings of power series, Groebner bases, symmetric functions. Resultants, factorizing polynomials. Rings of fractions, partial fractions; approximating power series by rational functions. Extension fields, basic structure of finite fields; discrete log, theorem of algebra. Automorphisms of GF(q); trace; normal bases, optimal normal bases and fast hardware. Cyclic codes, BCH codes, Golay code, Reed-Solomon codes. p-adic numbers, lifting factorizations mod p to factorizations mod pn. Discrete Fourier transform, applications to cylic codes, Kronecker product and fast transforms. Linear systems and control theory.show more