Cryptography is vital to keeping information safe, in an era when the formula to do so becomes more and more challenging. Written by a team of world-renowned cryptography experts, this essential guide is the definitive introduction to all major areas of cryptography: message security, key negotiation, and key management. You'll learn how to think like a cryptographer. You'll discover techniques for building cryptography into products from the start and you'll examine the many technical changes in the field.After a basic overview of cryptography and what it means today, this indispensable resource covers such topics as block ciphers, block modes, hash functions, encryption modes, message authentication codes, implementation issues, negotiation protocols, and more. Helpful examples and hands-on exercises enhance your understanding of the multi-faceted field of cryptography.An author team of internationally recognized cryptography experts updates you on vital topics in the field of cryptography Shows you how to build cryptography into products from the start Examines updates and changes to cryptography Includes coverage on key servers, message security, authentication codes, new standards, block ciphers, message authentication codes, and more Cryptography Engineering gets you up to speed in the ever-evolving field of cryptography.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    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.

    Contains 640 problems including solutions; additional practice problems with answers; explanations of complex variable theory; coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions.

    Johnson. It was the first book exclusively on the theory of NP-completeness and computational intractability. The book features an appendix providing a thorough compendium of NP-complete problems (which was updated in later printings of the book). The book is now outdated in some respects as it does not cover more recent development such as the PCP theorem. It is nevertheless still in print and is regarded as a classic: in a 2006 study, the CiteSeer search engine listed the book as the most cited reference in computer science literature.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    

     Neural networks are a key element of deep learning and artificial intelligence, which today is capable of some truly impressive feats. Yet too few really understand how neural networks actually work. This guide will take you on a fun and unhurried journey, starting from very simple ideas, and gradually building up an understanding of how neural networks work. You won't need any mathematics beyond secondary school, and an accessible introduction to calculus is also included. The ambition of this guide is to make neural networks as accessible as possible to as many readers as possible - there are enough texts for advanced readers already! You'll learn to code in Python and make your own neural network, teaching it to recognise human handwritten numbers, and performing as well as professionally developed networks. Part 1 is about ideas. We introduce the mathematical ideas underlying the neural networks, gently with lots of illustrations and examples. Part 2 is practical. We introduce the popular and easy to learn Python programming language, and gradually builds up a neural network which can learn to recognise human handwritten numbers, easily getting it to perform as well as networks made by professionals. Part 3 extends these ideas further. We push the performance of our neural network to an industry leading 98% using only simple ideas and code, test the network on your own handwriting, take a privileged peek inside the mysterious mind of a neural network, and even get it all working on a Raspberry Pi. All the code in this has been tested to work on a Raspberry Pi Zero.

    In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    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 aboutHow to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiencyAncient paradoxes, beautiful theorems, and the productive tension between continuous and discreteA simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on itPowerful mathematical approaches to abstractionHow abstract algebra provides the idea at the heart of generic programmingAxioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structuresSurprising subtleties of simple programming tasks and what you can learn from themHow practical implementations can exploit theoretical knowledge

    For anyone who has ever wondered how computers solve problems, an engagingly written guide for nonexperts to the basics of computer algorithms.

    It provides students with skills that will enable them to make productive use of computational techniques, including some of the tools and techniques of "data science" for using computation to model and interpret data. The book is based on an MIT course (which became the most popular course offered through MIT's OpenCourseWare) and was developed for use not only in a conventional classroom but in in a massive open online course (or MOOC) offered by the pioneering MIT--Harvard collaboration edX.Students are introduced to Python and the basics of programming in the context of such computational concepts and techniques as exhaustive enumeration, bisection search, and efficient approximation algorithms. The book does not require knowledge of mathematics beyond high school algebra, but does assume that readers are comfortable with rigorous thinking and not intimidated by mathematical concepts. Although it covers such traditional topics as computational complexity and simple algorithms, the book focuses on a wide range of topics not found in most introductory texts, including information visualization, simulations to model randomness, computational techniques to understand data, and statistical techniques that inform (and misinform) as well as two related but relatively advanced topics: optimization problems and dynamic programming.Introduction to Computation and Programming Using Python can serve as a stepping-stone to more advanced computer science courses, or as a basic grounding in computational problem solving for students in other disciplines.

    

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    Python is easy to learn, and it's perfect for exploring topics like statistics, geometry, probability, and calculus. You’ll learn to write programs to find derivatives, solve equations graphically, manipulate algebraic expressions, even examine projectile motion.Rather than crank through tedious calculations by hand, you'll learn how to use Python functions and modules to handle the number crunching while you focus on the principles behind the math. Exercises throughout teach fundamental programming concepts, like using functions, handling user input, and reading and manipulating data. As you learn to think computationally, you'll discover new ways to explore and think about math, and gain valuable programming skills that you can use to continue your study of math and computer science.If you’re interested in math but have yet to dip into programming, you’ll find that Python makes it easy to go deeper into the subject—let Python handle the tedious work while you spend more time on the math.