Applied Abstract Algebra
1st Edition
Published on 15. January 2010
Book
Hardback
406 pages
978-1-58488-426-2 (ISBN)
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.
More details
Series
Language
English
Place of publication
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
College/higher education
Undergraduate
Illustrations
100 s/w Abbildungen
100 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
ISBN-13
978-1-58488-426-2 (9781584884262)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Persons
Content
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.