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 (3.0 / 5.0) Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, and so forth. Users therefore should not only know how its techniques work, but they must also be able to estimate their efficiency and security. Based on courses taught by the author, this book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. This revised and extended edition includes new material on the AES encryption algorithm, the SHA-1 Hash algorithm, on secret sharing, as well as updates in the chapters on factoring and discrete logarithms.
Johannes A. Buchmann is Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and an Associate Editor of the Journal of Cryptology. In 1985, he received a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. He has also received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation (Deutsche Forschungsgemeinschaft). 
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$34.99 |
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 (5.0 / 5.0) From "Raising Rabbits" to "Prickly Pinecones", 24 easy-to-use, reproducible activities and projects introduce students to Fibonacci numbers and the golden ratio. Grades 4-8
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$18.97 |
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 (4.5 / 5.0) This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
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$101.60 |
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(4.5 / 5.0) Bridging the gap between elementary number theory and the systematic study of advanced topics, A CLASSICAL INTRODUCTION TO MODERN NUMBER THEORY is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical developement is stressed throughout, along with wide-ranging coverage of significant results with comparitively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
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 (3.5 / 5.0) It has been more than 20 years since this classic book on formal languages, automata theory, and computational complexity was first published. With this long-awaited revision, the authors continue to present the theory in a concise and straightforward manner, now with an eye out for the practical applications. They have revised this book to make it more accessible to today's students, including the addition of more material on writing proofs, more figures and pictures to convey ideas, side-boxes to highlight other interesting material, and a less formal writing style. Exercises at the end of each chapter, including some new, easier exercises, help readers confirm and enhance their understanding of the material.
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 (4.0 / 5.0) Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them.
In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered i in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.
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(3.5 / 5.0) Explore Fibonacci numbers, ratios and their occurrence in natural phenomena.
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$17.50 |
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(5.0 / 5.0) Number 9 tells the story of Enjil, a boy mathematician who is
challenged by a spirit to solve the riddle, What is the fixed point of the wind? As Enjil searches for the answer, he and the reader embark on a journey through myth, legend, and religion. Enjil s adventures lead readers to an appreciation of symmetry within asymmetry, classical ideas, and modern impulses. Along the way Balmond redefines arithmetic for the lay person and opens the gateway to further discoveries.
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(4.0 / 5.0) The reader of this book is probably about to teach or take a "first course in proof techniques." Students are taking this course because they like mathematics, and the authors hope to keep it that way. At this point, they have an intuitive sense of why things are true, but not the exposure to detailed and critical thinking necessary to survive in the mathematical world. The authors have written this book to bridge the gap. Often, students beginning this course have little training in rigorous mathematical reasoning; they need guidance. At the end, they are where they should be; on their own. The authors aim is to teach the students to read, write and do mathematics independently, and to do it with clarity, precision, and care.
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$42.00 |
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(4.0 / 5.0) This thoroughly revised and updated version of the popular textbook on abstract algebra introduces students to easily understood problems and concepts. John Humphreys and Mike Prest include many examples and exercises throughout the book to make it more appealing to students and instructors. The second edition features new sections on mathematical reasoning and polynomials. In addition, three chapters have been completely rewritten and all others have been updated. First Edition Pb (1990): 0-521-35938-4
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$44.26 |