id: 05042896
dt: b
an: 2011a.00745
au: Klima, Richard E.; Sigmon, Neil P.; Stitzinger, Ernest L.
ti: Applications of abstract algebra with Maple and MATLAB. 2nd ed.
so: Discrete Mathematics and its Applications. Boca Raton, FL: Chapman \&
Hall/CRC (ISBN 1-58488-610-2/hbk). 505~p. (2007).
py: 2007
pu: Boca Raton, FL: Chapman \& Hall/CRC
la: EN
cc: H45 K25 R25
ut: linear algebra; Maple; MATLAB; designs; coding theory; cryptography; Pólya
theory
ci: Zbl 0948.00001
li:
ab: This book concentrates on the mathematical softwares {\tt Maple} and {\tt
MATLAB} which would certainly help in better understanding of several
topics dependent on abstract algebra like block designs, coding theory,
combinatorics, cryptography and graph theory, eliminating the need for
extensive computations. Beginning with a comprehensive and concise
review of all prerequisite advanced mathematics, the authors go on
examining block designs, coding theory, cryptography: RSA cryptosystem,
digital signatures, primes for security, elliptic curve cryptosystems;
finally dealing with counting techniques such as Pólya’s,
Burnside’s theorem, Pólya enumeration theorem, and counting
undirected graphs. This (second) edition incorporates some new
chapters which are on Vigenère ciphers, Advanced Encryption Standard
(AES) and graph theory, also including expanded exercises and
additional research exercises. The book provides a variety of codes
including Hadamard, Reed-Muller, Hamming, BCH, and Reed-Solomon;
exploers shift, affine, Hill, and Vigenère ciphers; describes how
elliptic curves can be incorporated into the El-Gamal cryptosystem;
presents a thorough treatment of AES. The book intends to give
students more exposure to basic algebraic concepts as well as their
practical uses. The inclusion of two mathematical software packages
available make the book a useful tool for students, mathematicians, and
computer scientists. {\tt Maple} and {\tt MATLAB} files and functions
are available for download online and from a CD-ROM with all the
programs and codes that are used in the book. The book can be used by
students having a course on linear and abstract algebra.
rv: Bal Kishan Dass (Delhi)