The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

    Their applications range from network routing and computational genomics to public-key cryptography and database system implementation. Studying algorithms can make you a better programmer, a clearer thinker, and a master of technical interviews. Algorithms Illuminated is an accessible introduction to the subject---a transcript of what an expert algorithms tutor would say over a series of one-on-one lessons. The exposition is rigorous but emphasizes the big picture and conceptual understanding over low-level implementation and mathematical details. Part 1 of the book series covers asymptotic analysis and big-O notation, divide-and-conquer algorithms and the master method, randomized algorithms, and several famous algorithms for sorting and selection.

    We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

    Ware's updated review of empirical research and interface design examples will do much to accelerate innovation and adoption of information visualization." —Ben Shneiderman, University of Maryland"Colin Ware is the perfect person to write this book, with a long history of prominent contributions to the visual interaction with machines and to information visualization directly. It goes a long way towards joining science to the practical design of information visualization systems." —from the foreword by Stuart Card, PARCMost designers know that yellow text presented against a blue background reads clearly and easily, but how many can explain why, and what really are the best ways to help others and ourselves clearly see key patterns in a bunch of data? When we use software, access a web site, or view graphics, our understanding is greatly enhanced or impeded by the way information is presented. By explaining in detail how we think visually, this book provides guidance on how to construct effective interactive information displays.This book combines a strictly scientific approach to human perception with a practical concern for the rules governing the effective visual presentation of information. Surveying the research of leading psychologists and neurophysiologists, author Colin Ware isolates key principles at work in vision and perception, and from them derives specific and effective visualization techniques suitable for a wide range of scenarios. Information Visualization offers practical guidelines that can be applied by anyone, and covers all facets of visual perception: color, organization, space perception, motion, and texture.* Major revision of this classic work, with a new chapter on visual thinking, new sections on face perception and flow visualization, an appendix on how to evaluate visualizations,and a greatly expanded chapter on color and color sequences. *New to this edition is the full-color treatment throughout, to better display over 400 illustrations.*From a leading researcher in the field of human perception who has brought together, in a single resource, all current scientific insight into the question of data visualization.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

     Douglas Montgomery arms readers with the most effective approach for learning how to design, conduct, and analyze experiments that optimize performance in products and processes. He shows how to use statistically designed experiments to obtain information for characterization and optimization of systems, improve manufacturing processes, and design and develop new processes and products. You will also learn how to evaluate material alternatives in product design, improve the field performance, reliability, and manufacturing aspects of products, and conduct experiments effectively and efficiently. Discover how to improve the quality and efficiency of working systems with this highly-acclaimed book. This 6th Edition: Places a strong focus on the use of the computer, providing output from two software products: Minitab and DesignExpert. Presents timely, new examples as well as expanded coverage on adding runs to a fractional factorial to de-alias effects. Includes detailed discussions on how computers are currently used in the analysis and design of experiments. Offers new material on a number of important topics, including follow-up experimentation and split-plot design. Focuses even more sharply on factorial and fractional factorial design.

    The text is non-threatening and presents concepts clearly and succinctly with a conversational writing style. All statistical concepts are illustrated with solved applied examples immediately upon introduction. Self reviews and exercises for each section, and review sections for groups of chapters also support the student learning steps. Modern computing applications (Excel, Minitab, and MegaStat) are introduced, but the text maintains a focus on presenting statistics concepts as applied in business as opposed to technology or programming methods. The thirteenth edition continues as a students' text with increased emphasis on interpretation of data and results.

    This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory.The book is divided into three parts. Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of neurons. Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics. Part III analyzes the role of plasticity in development and learning. An appendix covers the mathematical methods used, and exercises are available on the book's Web site.

    In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, the new edition remains the most practical, comprehensive handbook of scientific computing available today.

    Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required. 0201157675B07092001

    Beginning with the background and very nature of probability theory, the book then proceeds through sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, stochastic processes, and more. The book's comprehensive approach provides a complete view of theory along with enlightening examples along the way.

    With this practical book, you’ll learn techniques for extracting and transforming features—the numeric representations of raw data—into formats for machine-learning models. Each chapter guides you through a single data problem, such as how to represent text or image data. Together, these examples illustrate the main principles of feature engineering.Rather than simply teach these principles, authors Alice Zheng and Amanda Casari focus on practical application with exercises throughout the book. The closing chapter brings everything together by tackling a real-world, structured dataset with several feature-engineering techniques. Python packages including numpy, Pandas, Scikit-learn, and Matplotlib are used in code examples.

    Fully revised to meet the needs of the wide range of students beginning engineering courses, this edition has an extended Foundation section including new chapters on graphs, trigonometry, binomial series and functions and a CD-ROM

    That's what Ben Lindbergh and Sam Miller got to do when the Sonoma Stompers, an independent minor-league team in California, offered them the chance to run the team's baseball operations according to the most advanced statistics. The Only Rule Is It Has to Work is unlike any other baseball tale you've ever read.We tag along as Lindbergh and Miller apply their number-crunching insights to all aspects of assembling and running a team. We meet colorful figures like general manager Theo Fightmaster and boundary-breakers like the first openly gay professional player and the first Japanese manager in American professional baseball. Even José Canseco makes a cameo appearance.Will sabermetrics bring the Stompers a championship, or will they fall on their face? Will the team have a competitive advantage or is the old folk wisdom really true after all? Will the players be able to maximize their talents and attract the attention of big-league scouts, or will this be a fast track to oblivion?It's a wild ride, as the authors' infectious enthusiasm and feel for the absurd make the Stompers' story one that will speak to numbers geeks and traditionalists alike. And it proves that you don't need a bat or a glove to make a genuine contribution to the game.

    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.