It explains what algorithms do, how they are used, the risks associated with using them, and why governments should be concerned. Important areas arehighlighted, such as Stream Ciphers, block ciphers, public key algorithms, digital signatures, and applications such as e-commerce. This book highlights the explosive impact of cryptography on modern society, with, for example, the evolution of the internet and the introduction of more sophisticatedbanking methods.

    E. Moore, and Ludwig Wittgenstein in the four decades around the turn of the twentieth century, analytic philosophy established itself in various forms in the 1930s. After the Second World War, it developed further in North America, in the rest of Europe, and is now growing in influence as the dominant philosophical tradition right across the world, from Latin America to East Asia.In this Very Short Introduction Michael Beaney introduces some of the key ideas of the founders of analytic philosophy by exploring certain fundamental philosophical questions and showing how those ideas can be used in offering answers. Considering the work of Susan Stebbing, he also explores the application of analytic philosophy to critical thinking, and emphasizes the conceptual creativity that lies at the heart of fruitful analysis. Throughout, Beaney illustrates why clarity of thinking, precision of expression, and rigour of argumentation are rightly seen as virtues of analytic philosophy.

    An authoritative introduction to "fuzzy logic" brings readers up to speed on the "smart" products and computers that will change all of our lives in the future.

    The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality.Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

    In 1935, aged 22, he developed the mathematical theory upon which all subsequent stored-program digital computers are modeled.At the outbreak of hostilities with Germany in September 1939, he joined the Government Codebreaking team at Bletchley Park, Buckinghamshire and played a crucial role in deciphering Engima, the code used by the German armed forces to protect their radio communications. Turing's work on the versionof Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as Fish, which were used by the German High Command for the encryption of signals during the latter part of the war. His contribution helped toshorten the war in Europe by an estimated two years.After the war, his theoretical work led to the development of Britain's first computers at the National Physical Laboratory and the Royal Society Computing Machine Laboratory at Manchester University.Turing was also a founding father of modern cognitive science, theorizing that the cortex at birth is an unorganized machine which through training becomes organized into a universal machine or something like it. He went on to develop the use of computers to model biological growth, launchingthe discipline now referred to as Artificial Life.The papers in this book are the key works for understanding Turing's phenomenal contribution across all these fields. The collection includes Turing's declassified wartime Treatise on the Enigma; letters from Turing to Churchill and to codebreakers; lectures, papers, and broadcasts which opened upthe concept of AI and its implications; and the paper which formed the genesis of the investigation of Artifical Life.

    It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena. In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology.

    A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years.

    One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.