Eliminating the need for heavy number-crunching, sophisticated
mathematical software packages open the door to areas like
cryptography, coding theory, and combinatorics that are dependent on
abstract algebra. "Applications of Abstract Algebra with Maple and
MATLAB, Second Edition" explores these topics and shows how to apply
the software programs to abstract algebra and its related fields.
Carefully integrating Maple and MATLAB, this book provides an in-depth
introduction to real-world abstract algebraic problems. The first
chapter offers a concise and comprehensive review of prerequisite
advanced mathematics. The next several chapters examine block designs,
coding theory, and cryptography, while the final chapters cover
counting techniques, including Plya's and Burnside's theorems. Other
topics discussed include the Rivest, Shamir, and Adleman (RSA)
cryptosystem, digital signatures, primes for security, and elliptic
curve cryptosystems. New to the Second Edition are: three new chapters
on Vigenre ciphers, the Advanced Encryption Standard (AES), and graph
theory as well as new MATLAB and Maple sections; expanded exercises and
additional research exercises; Maple and MATLAB files and functions
available for download online and from a CD-ROM. With the incorporation
of MATLAB, this second edition further illuminates the topics discussed
by eliminating extensive computations of abstract algebraic techniques.
The clear organization of the book as well as the inclusion of two of
the most respected mathematical software packages available make the
book a useful tool for students, mathematicians, and computer
scientists.