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Applied Mathematics for K-12 Textbooks

Edition: 00

Copyright: 2000

Publisher: Mathematical Association of America

Published: 2000

International: No

Copyright: 2000

Publisher: Mathematical Association of America

Published: 2000

International: No

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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.

Whether a reader is interested in cryptology, mathematics, or computer science, he or she will discover engaging and delightful material in this volume.

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Summary

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.

Whether a reader is interested in cryptology, mathematics, or computer science, he or she will discover engaging and delightful material in this volume.

Publisher Info

Publisher: Mathematical Association of America

Published: 2000

International: No

Published: 2000

International: No

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.

Whether a reader is interested in cryptology, mathematics, or computer science, he or she will discover engaging and delightful material in this volume.