Cryptography, Information Theory, and Error-Correction

Wiley Series in Discrete Mathematics and Optimization

Book 68
Sold by John Wiley & Sons
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Discover the first unified treatment of today's most essential information technologies— Compressing, Encrypting, and Encoding

With identity theft, cybercrime, and digital file sharing proliferating in today's wired world, providing safe and accurate information transfers has become a paramount concern. The issues and problems raised in this endeavor are encompassed within three disciplines: cryptography, information theory, and error-correction. As technology continues to develop, these fields have converged at a practical level, increasing the need for a unified treatment of these three cornerstones of the information age.

Stressing the interconnections of the disciplines, Cryptography, Information Theory, and Error-Correction offers a complete, yet accessible account of the technologies shaping the 21st century. This book contains the most up-to-date, detailed, and balanced treatment available on these subjects. The authors draw on their experience both in the classroom and in industry, giving the book's material and presentation a unique real-world orientation.

With its reader-friendly style and interdisciplinary emphasis, Cryptography, Information Theory, and Error-Correction serves as both an admirable teaching text and a tool for self-learning. The chapter structure allows for anyone with a high school mathematics education to gain a strong conceptual understanding, and provides higher-level students with more mathematically advanced topics. The authors clearly map out paths through the book for readers of all levels to maximize their learning.

This book:

  • Is suitable for courses in cryptography, information theory, or error-correction as well as courses discussing all three areas
  • Provides over 300 example problems with solutions
  • Presents new and exciting algorithms adopted by industry
  • Discusses potential applications in cell biology
  • Details a new characterization of perfect secrecy
  • Features in-depth coverage of linear feedback shift registers (LFSR), a staple of modern computing
  • Follows a layered approach to facilitate discussion, with summaries followed by more detailed explanations
  • Provides a new perspective on the RSA algorithm

Cryptography, Information Theory, and Error-Correction is an excellent in-depth text for both graduate and undergraduate students of mathematics, computer science, and engineering. It is also an authoritative overview for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, entrepreneurs, and the generally curious.

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About the author

AIDEN A. BRUEN, PHD, is a Professor of Mathematics and Statistics at the University of Calgary in Calgary, Alberta, Canada. He has over 100 published articles in refereed journals and has served for many years on the Editorial Board of Designs, Codes and Cryptography. His research interests include error-correcting codes, number theory, algebraic geometry, algebra finite geometries, information theory, and cryptography.

MARIO A. FORCINITO, PHD, is a professional engineer with over ten years' experience as an industrial consultant. He is President of SUR Consultants in Engineering Science Inc., a member of the IEEE Computer Society, and has published extensively in peer-reviewed journals. Dr. Forcinito has experience lecturing on cryptography and numerical methods at several technical meetings.

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Additional Information

Publisher
John Wiley & Sons
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Published on
Sep 28, 2011
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Pages
496
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ISBN
9781118031384
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Best For
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Language
English
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Genres
Mathematics / Applied
Mathematics / General
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Content Protection
This content is DRM protected.
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Reading information

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Praise from the Second Edition

"...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002)

"A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002)

Explore the latest applications of optimization theory and methods

Optimization is central to any problem involving decision making in many disciplines, such as engineering, mathematics, statistics, economics, and computer science. Now, more than ever, it is increasingly vital to have a firm grasp of the topic due to the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and networks. Fully updated to reflect modern developments in the field, An Introduction to Optimization, Third Edition fills the need for an accessible, yet rigorous, introduction to optimization theory and methods.

The book begins with a review of basic definitions and notations and also provides the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and practitioners.

Additional features of the Third Edition include:

New discussions of semidefinite programming and Lagrangian algorithms

A new chapter on global search methods

A new chapter on multipleobjective optimization

New and modified examples and exercises in each chapter as well as an updated bibliography containing new references

An updated Instructor's Manual with fully worked-out solutions to the exercises

Numerous diagrams and figures found throughout the text complement the written presentation of key concepts, and each chapter is followed by MATLAB exercises and drill problems that reinforce the discussed theory and algorithms. With innovative coverage and a straightforward approach, An Introduction to Optimization, Third Edition is an excellent book for courses in optimization theory and methods at the upper-undergraduate and graduate levels. It also serves as a useful, self-contained reference for researchers and professionals in a wide array of fields.

The companion book to COURSERA®'s wildly popular massive open online course "Learning How to Learn"

Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
 
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. The learning strategies in this book apply not only to math and science, but to any subject in which we struggle. We all have what it takes to excel in areas that don't seem to come naturally to us at first, and learning them does not have to be as painful as we might think!


From the Trade Paperback edition.
Praise for the Third Edition ". . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail."  —MAA Reviews 

Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus. 

This new edition explores the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. The authors also present an optimization perspective on global search methods and include discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm.  Featuring an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, the Fourth Edition also offers: 
A new chapter on integer programming   Expanded coverage of one-dimensional methods   Updated and expanded sections on linear matrix inequalities   Numerous new exercises at the end of each chapter   MATLAB exercises and drill problems to reinforce the discussed theory and algorithms   Numerous diagrams and figures that complement the written presentation of key concepts   MATLAB M-files for implementation of the discussed theory and algorithms (available via the book's website)   Introduction to Optimization, Fourth Edition is an ideal textbook for courses on optimization theory and methods. In addition, the book is a useful reference for professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.
Praise for the First Edition

“This excellent text should prove a useful accoutrement for any developing mathematics program . . . it’s short, it’s sweet, it’s beautifully written.” —The Mathematical Intelligencer

“Erickson has prepared an exemplary work . . . strongly recommended for inclusion in undergraduate-level library collections.” —Choice

Featuring a modern approach, Introduction to Combinatorics, Second Edition illustrates the applicability of combinatorial methods and discusses topics that are not typically addressed in literature, such as Alcuin’s sequence, Rook paths, and Leech’s lattice. The book also presents fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise questions and observations.

Many important combinatorial methods are revisited and repeated several times throughout the book in exercises, examples, theorems, and proofs alike, allowing readers to build confidence and reinforce their understanding of complex material. In addition, the author successfully guides readers step-by-step through three major achievements of combinatorics: Van der Waerden’s theorem on arithmetic progressions, Pólya’s graph enumeration formula, and Leech’s 24-dimensional lattice.  Along with updated tables and references that reflect recent advances in various areas, such as error-correcting codes and combinatorial designs, the Second Edition also features:

Many new exercises to help readers understand and apply combinatorial techniques and ideas A deeper, investigative study of combinatorics through exercises requiring the use of computer programs Over fifty new examples, ranging in level from routine to advanced, that illustrate important combinatorial concepts Basic principles and theories in combinatorics as well as new and innovative results in the field

Introduction to Combinatorics, Second Edition is an ideal textbook for a one- or two-semester sequence in combinatorics, graph theory, and discrete mathematics at the upper-undergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.

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