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Mathematicians and Their Gods af Snezana Lawrence; Mark McCartney
To open a newspaper or turn on the television it would appear that science and religion are polar opposites - mutually exclusive bedfellows competing for hearts and minds. There is little indication of the rich interaction between religion and science throughout history, much of whichcontinues today. From ancient to modern times, mathematicians have played a key role in this interaction. This is a book on the relationship between mathematics and religious beliefs. It aims to show that, throughout scientific history, mathematics has been used to make sense of the 'big' questions of life, and that religious beliefs sometimes drove mathematicians to mathematics to help them make senseof the world. Containing contributions from a wide array of scholars in the fields of philosophy, history of science and history of mathematics, this book shows that the intersection between mathematics and theism is rich in both culture and character. Chapters cover a fascinating range of topics including theSect of the Pythagoreans, Newton's views on the apocalypse, Charles Dodgson's Anglican faith and Godel's proof of the existence of God.
Modern Cryptography af Chuck Easttom
A Practical Guide to Cryptography Principles and Security Practices Employ cryptography in real-world security situations using the hands-on information contained in this book. InfoSec expert Chuck Easttom lays out essential math skills and fully explains how to implement cryptographic algorithms in today's data protection landscape. Find out how to use ciphers and hashes, generate random keys, handle VPN and WiFi security, and encrypt VoIP, Email, and Web communications. Modern Cryptography: Applied Mathematics for Encryption and Information Security covers cryptanalysis, steganography, and cryptographic backdoors. Learn the necessary number theory, discrete math, and algebra Employ symmetric ciphers, including Feistel and substitution-permutation ciphers Understand asymmetric cryptography algorithms Design s-boxes that maximize output non-linearity Deploy cryptographic hashes Create cryptographic keys using pseudo random number generators Encrypt Web traffic using SSL/TLS Secure VPN, WiFi, and SSH communications Work with cryptanalysis and steganography Explore government, military, and intelligence agency applications
From Mathematics to Generic Programming af Alexander A. Stepanov; Daniel E. Rose
In this substantive yet accessible book, pioneering software designer Alexander Stepanov and his colleague Daniel Rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based, helping you write code that is both simpler and more powerful. If you're a reasonably proficient programmer who can think logically, you have all the background you'll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem. As you read this book, you'll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You'll also gain deep insight into the value of mathematics to programming--insight that will prove invaluable no matter what programming languages and paradigms you use. You will learn about How to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiency Ancient paradoxes, beautiful theorems, and the productive tension between continuous and discrete A simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on it Powerful mathematical approaches to abstraction How abstract algebra provides the idea at the heart of generic programming Axioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structures Surprising subtleties of simple programming tasks and what you can learn from them How practical implementations can exploit theoretical knowledge