Information is an important feature of the modern world. Mathematical techniques underlie the devices that we use to handle it, for example, mobile phones, digital cameras, and personal computers.
This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest mathematical background is assumed, the mathematical theory being introduced at a level that enables the basic problems to be stated carefully, but without unnecessary abstraction. Other features include:
clear and careful exposition of fundamental concepts, including optimal coding, data compression, and public-key cryptography
concise but complete proofs of results
coverage of recent advances of practical interest, for example in encryption standards, authentication schemes, and elliptic curve cryptography
numerous examples and exercises, and a full solutions manual available to lecturers from www.springer.com
This modern introduction to all aspects of coding is suitable for advanced undergraduate or postgraduate courses in mathematics, computer science, electrical engineering, or informatics. It is also useful for researchers and practitioners in related areas of science, engineering and economics.
Norman Biggs is an Emeritus Professor of Mathematics at LSE.
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'This undergraduate textbook is a pleasure to read. ... The author has a sense of humor, and he is not afraid to use it. The examples are very well chosen. ... This very enjoyable book deserves many readers.'
Miklós Bóna, The Mathematical Association of America