Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)"No matter how gently one introduces students to the concept of Dirac's bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)Reviews of the Second Edition:"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. ... It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:- Clear, accessible treatment of underlying mathematics- A review of Newtonian, Lagrangian, and Hamiltonian mechanics- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates- Unsurpassed coverage of path integrals and their relevance in contemporary physicsThe requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book's self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

    Presents essential ideas on critical phenomena developed over the last decade in simple, qualitative terms. This new edition maintains the simple structure of the first and puts new emphasis on pedagogical considerations. Thermostatistics is incorporated into the text without eclipsing macroscopic thermodynamics, and is integrated into the conceptual framework of physical theory.

    Features exceptionally clear explanations and descriptions, step-by-step examples, more than 50 practical applications, over 2000 easy-to-challenging practice problems, and comprehensive coverage of essentials. PSpice, OrCAd version 9.2 Lite Edition, Multisims 2001 version of Electronics Workbench, and MathCad software references and examples are used throughout. Computer programs (C++, BASIC and PSpice) are printed in color, as they run, at the point in the book where they are discussed. Current and Voltage. Resistance. Ohm's Law, Power, and Energy. Series Circuits. Parallel Circuits. Series-Parallel Networks. Methods of Analysis & Selected Topics. Network Theorems. Capacitors. Magnetic Circuits. Inductors. Sinusodial Alternating Waveforms. The Basic Elements and Phasors. Series and Parallel ac Circuits. Series-Parallel ac Networks. Methods of Analysis and Related Topics. Network Theorems (ac). Power (ac). Resonance. Transformers. Polyphase Systems. Decibels, Filters, and Bode Points. Pulse Waveforms and the R-C Response. Nonsinusodial Circuits. System Analysis: An Introduction. For those working in electronic technology.

    The impressive result is this fascinating story--the first comprehensive account--of the space age. Here are the strategists and war planners; engineers and scientists; politicians and industrialists; astronauts and cosmonauts; science fiction writers and journalists; and plain, ordinary, unabashed dreamers who wanted to transcend gravity's shackles for the ultimate ride. The story is written from the perspective of a witness who was present at the beginning and who has seen the conclusion of the first space age and the start of the second.From the Hardcover edition.

    Building on the field of mathematical statistics, probabilistic robotics endows robots with a new level of robustness in real-world situations. This book introduces the reader to a wealth of techniques and algorithms in the field. All algorithms are based on a single overarching mathematical foundation. Each chapter provides example implementations in pseudo code, detailed mathematical derivations, discussions from a practitioner's perspective, and extensive lists of exercises and class projects. The book's Web site, www.probabilistic-robotics.org, has additional material. The book is relevant for anyone involved in robotic software development and scientific research. It will also be of interest to applied statisticians and engineers dealing with real-world sensor data.

    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.

    This book gives you a solid understanding of statistics without being too simple, yet without the numbing complexity of most college texts. You get a firm grasp of the fundamentals and a hands-on understanding of how to apply them before moving on to the more advanced material that follows. Each chapter presents you with easy-to-follow descriptions illustrated by graphics, formulas, and plenty of solved examples. Before you know it, you'll learn to apply statistical reasoning and statistical techniques, from basic concepts of probability and hypothesis testing to multivariate analysis. Organized into four distinct sections, Statistics in a Nutshell offers you:Introductory material: Different ways to think about statistics Basic concepts of measurement and probability theoryData management for statistical analysis Research design and experimental design How to critique statistics presented by others Basic inferential statistics: Basic concepts of inferential statistics The concept of correlation, when it is and is not an appropriate measure of association Dichotomous and categorical data The distinction between parametric and nonparametric statistics Advanced inferential techniques: The General Linear Model Analysis of Variance (ANOVA) and MANOVA Multiple linear regression Specialized techniques: Business and quality improvement statistics Medical and public health statistics Educational and psychological statistics Unlike many introductory books on the subject, Statistics in a Nutshell doesn't omit important material in an effort to dumb it down. And this book is far more practical than most college texts, which tend to over-emphasize calculation without teaching you when and how to apply different statistical tests. With Statistics in a Nutshell, you learn how to perform most common statistical analyses, and understand statistical techniques presented in research articles. If you need to know how to use a wide range of statistical techniques without getting in over your head, this is the book you want.

    However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist niche to become mainstream, while graphical models have emerged as a general framework for describing and applying probabilistic models. Also, the practical applicability of Bayesian methods has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation. Similarly, new models based on kernels have had a significant impact on both algorithms and applications. This new textbook reflects these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners, and assumes no previous knowledge of pattern recognition or machine learning concepts. Knowledge of multivariate calculus and basic linear algebra is required, and some familiarity with probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.

    KEY TOPICS: The major changes of the revision are reorganization of chapter material and the addition of a much wider range of difficulties.

    “The result is a veritable pi

    

    The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

    Each