Brand new. We distribute directly for the publisher. Cryptological Mathematics introduces the reader to elementary yet rigorous mathematics from several different branches of the ...subject including number theory, abstract algebra, matrix algebra, probability, and statistics, all of which play a role in enciphering and deciphering secret messages. And it does so in a light-hearted fashion, thanks to the carryings-on of the book's three main characters, Beth, Stephanie, and Molly.The book can be used at several different levels. Those interested in learning how to encipher messages using a variety of symmetric and asymmetric schemes will learn those techniques in this volume. Those interested in learning the mathematical foundations of these techniques will learn how and why the enciphering schemes actually work. And those who are looking for some challenging computer programming exercises will also find exercises in this book to keep them busy. So, the book may be used profitably by amateur cryptographers, motivated liberal arts students, and mathematics or computer science majors alike.The book begins by considering simple monoalphabetic substitution ciphers (additive, multiplicative, affine and keyword) and then moves through a polyalphabetic substitution cipher (the Vignere Square) and on to polygraphic substitution ciphers (including Hill's system). Finally the RSA Public Key Encryption System is introduced along with several of its variations. At each step the mathematics required to understand these systems is introduced in a thorough yet gentle manner.The book also invites those readers who may be interested to program the algorithms it describes. Some exercises can be done using a simple spreadsheet program; others are best handled by a symbolic algebra system.In addition, the book contains biographical sketches of some lesser-known yet fascinating personalities who had been involved with cryptography. Read moreShow Less
This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. Challenging computer programming exercises are also included. The book is written in an engaging style which will appeal to all, and also includes historical background on some of the founders of the subject. It will be of interest both to students wishing to learn cryptology per se, and also to those searching for practical applications of seemingly abstract mathematics.
This book is written with careful attention to the challenge of motivating a humanities or business major. An impressive amount of the mathematics that might make a standard "math for poets" course-mathematical induction, elementary number theory, probabilities, matrices-is presented through the vehicle of cryptography.
—American Mathematical Monthly
A textbook for a one-semester undergraduate course for students who will or will not go on to more advanced mathematics. Lewant (Groucher College, Baltimore) draws together elementary mathematics from number theory, abstract algebra, matrix algebra, probability, and statistics. The point is not so much to learn to encode and decode, but to use cryptology as a fun way to learn the math itself. Annotation c. Book News, Inc., Portland, OR (booknews.com)