This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California's Stanford University, who has written lots of extra material including some on Interior Point Methods.

Probabilistic robotics is a new and growing area in robotics, concerned with perception and control in the face of uncertainty. 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.

Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction.<br />In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of <i>pure </i>mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.<br />By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

The Complexity of Robot Motion Planning makes original contributions both to robotics and to the analysis of algorithms. In this groundbreaking monograph John Canny resolves long-standing problems concerning the complexity of motion planning and, for the central problem of finding a collision free path for a jointed robot in the presence of obstacles, obtains exponential speedups over existing algorithms by applying high-powered new mathematical techniques.Canny's new algorithm for this "generalized movers' problem," the most-studied and basic robot motion planning problem, has a single exponential running time, and is polynomial for any given robot. The algorithm has an optimal running time exponent and is based on the notion of roadmaps - one-dimensional subsets of the robot's configuration space. In deriving the single exponential bound, Canny introduces and reveals the power of two tools that have not been previously used in geometric algorithms: the generalized (multivariable) resultant for a system of polynomials and Whitney's notion of stratified sets. He has also developed a novel representation of object orientation based on unnormalized quaternions which reduces the complexity of the algorithms and enhances their practical applicability.After dealing with the movers' problem, the book next attacks and derives several lower bounds on extensions of the problem: finding the shortest path among polyhedral obstacles, planning with velocity limits, and compliant motion planning with uncertainty. It introduces a clever technique, "path encoding," that allows a proof of NP-hardness for the first two problems and then shows that the general form of compliant motion planning, a problem that is the focus of a great deal of recent work in robotics, is non-deterministic exponential time hard. Canny proves this result using a highly original construction.John Canny received his doctorate from MIT And is an assistant professor in the Computer Science Division at the University of California, Berkeley. The Complexity of Robot Motion Planning is the winner of the 1987 ACM Doctoral Dissertation Award.

In 1942, Lt. Herman H. Goldstine, a former mathematics professor, was stationed at the Moore School of Electrical Engineering at the University of Pennsylvania. It was there that he assisted in the creation of the ENIAC, the first electronic digital computer. The ENIAC was operational in 1945, but plans for a new computer were already underway. The principal source of ideas for the new computer was John von Neumann, who became Goldstine's chief collaborator. Together they developed EDVAC, successor to ENIAC. After World War II, at the Institute for Advanced Study, they built what was to become the prototype of the present-day computer. Herman Goldstine writes as both historian and scientist in this first examination of the development of computing machinery, from the seventeenth century through the early 1950s. His personal involvement lends a special authenticity to his narrative, as he sprinkles anecdotes and stories liberally through his text.</p>

The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

This book covers Gaussian scale-space theory from its applications to its mathematical foundation. The reader not so familiar with scale-space will find it instructive to first consider some potential applications described in Part I. The next two parts both address fundamental aspects of scale-space. Whereas scale is treated as an essentially arbitrary constant in Part II, Part III emphasises the deep structure, i.e. the structure that is revealed by varying scale. Finally Part IV is devoted to non-linear extensions, notably non-linear diffusion techniques and morphological scale-spaces, and their relation to the linear case. Audience: This volume is addressed to researchers in the field of image analysis seeking mathematical foundation of algorithms.

We perceive objects in the world as having structures at both coarse and fine scales. A tree, for instance, may appear as having a roughly round or cylindrical shape when seen from a distance, even though it is built up from a large number of branches. At a closer look, individual leaves become visible, and we can observe that they in turn have texture at an even finer scale. The fact that objects in the world appear in different ways, depending upon the scale of observation, has important implications when analyzing measured data, such as images, with automatic methods. Scale-Space Theory in Computer Vision describes a formal framework, called scale-space representation, for handling the notion of scale in image data. It gives an introduction to the general foundations of the theory and shows how it applies to essential problems in computer vision such as computation of image features and cues to surface shape. The subjects range from mathematical underpinning to practical computational techniques. The power of the methodology is illustrated by a rich set of examples.

This excellent text provides a comprehensive treatment of the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbence terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. The book provides an excellent source for the development of practical courses on time series analysis.

Are all film stars linked to Kevin Bacon? Why do the stock markets rise and fall sharply on the strength of a vague rumour? How does gossip spread so quickly? Are we all related through six degrees of separation? There is a growing awareness of the complex networks that pervade modern society. We see them in the rapid growth of the Internet, the ease of global communication, the swift spread of news and information, and in the way epidemics and financial crises develop with startling speed and intensity. This introductory book on the new science of networks takes an interdisciplinary approach, using economics, sociology, computing, information science and applied mathematics to address fundamental questions about the links that connect us, and the ways that our decisions can have consequences for others.

Tool-making or culture, language or religious belief: ever since Darwin, thinkers have struggled to identify what fundamentally differentiates human beings from other animals. In this much-anticipated book, Michael Tomasello weaves his twenty years of comparative studies of humans and great apes into a compelling argument that cooperative social interaction is the key to our cognitive uniqueness. Once our ancestors learned to put their heads together with others to pursue shared goals, humankind was on an evolutionary path all its own.

Tomasello argues that our prehuman ancestors, like today's great apes, were social beings who could solve problems by thinking. But they were almost entirely competitive, aiming only at their individual goals. As ecological changes forced them into more cooperative living arrangements, early humans had to coordinate their actions and communicate their thoughts with collaborative partners. Tomasello's "shared intentionality hypothesis" captures how these more socially complex forms of life led to more conceptually complex forms of thinking. In order to survive, humans had to learn to see the world from multiple social perspectives, to draw socially recursive inferences, and to monitor their own thinking via the normative standards of the group. Even language and culture arose from the preexisting need to work together. What differentiates us most from other great apes, Tomasello proposes, are the new forms of thinking engendered by our new forms of collaborative and communicative interaction.

A Natural History of Human Thinking is the most detailed scientific analysis to date of the connection between human sociality and cognition.

From the Reviews: "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." - "Philosophy and Phenomenological Research".

Think Python is an introduction to Python programming for students with no programming experience. It starts with the most basic concepts of programming, and is carefully designed to define all terms when they are first used and to develop each new concept in a logical progression. Larger pieces, like recursion and object-oriented programming are divided into a sequence of smaller steps and introduced over the course of several chapters.

Provides a comprehensive treatment of semiconductor device physics and technology, with emphasis on modern planar silicon devices. Physical principles are explained by the use of simple physical models and illustrated by experimental measurements.