Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

    These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

    It features a visual presentation, designed to encourage learning; revised exercises to ensure clarity, balance and relevance; and clear commentary on the difficult subject of critical multivariable calculus topics.

    Each chapter is bursting with creative and classic ideas to make the day as meaningful as it is beautiful: Stationery: Save-the-date cards do double duty when printed on coasters or delicate handkerchiefs.Ceremonies: An auspicious bird’s nest adds a beautiful and rustic touch for carrying rings at a farm wedding.Dressing Up: A retro bride goes glam with a feathered veil and pearl button–accented gloves. A casual groom and his mates add a personality pop with chocolate-brown Keds to match their wedding chinos.Cocktail Hour: For a low-key affair, mini grilled cheeses dipped in shot glasses of tomato soup satisfy.Centerpieces: Fruit slices suspended in crystal vases overflowing with Crayola-bright poppies and orchids offer a cheery setting.Cakes: White lace frosting details that match the bride’s dress and the couple’s monogram turn a pale green cake into a chic masterpiece.From classic white-on-white palettes to floral themes to fun fantasy ideas, the choices are limitless. Purple, pink, red, robin’s egg blue—find inspiration at every turn in all the colors a bride can dream of! And The Knot Ultimate Wedding Lookbook is loaded with money-saving ideas that don’t sacrifice style. Expert advice and rich images add up to a delicious visual feast and essential resource to help you create an event as special as you are as a couple.

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    Provides a review of introductory noncalculus-based physics for those who do not have a strong background in mathematics.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    In this richly illustrated book, accessible examples are used to show how information theory can be understood in terms of everyday games like '20 Questions', and the simple MatLab programs provided give hands-on experience of information theory in action. Written in a tutorial style, with a comprehensive glossary, this text represents an ideal primer for novices who wish to become familiar with the basic principles of information theory.Download chapter 1 from http://jim-stone.staff.shef.ac.uk/Boo...

    How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

    Included in this edition is a new chapter on the revolutionary topic of quantum computing.

    Relevant psychological principles will help you predict your viewer's emotional reaction to your photographic images, giving you more power, control, and tools for communicating your desired message. Knowing how our minds work helps photographers, graphic designers, videographers, animators, and visual communicators both create and critique sophisticated works of visual art. Benefit from this insight in your work. Topics covered in this book: gestalt grouping, memory and association, space, time, color, contours, illusion and ambiguity, morphics, personality, subliminals, critiquing photographs, and rhetoric.

    These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.

    Packed with plenty of sample programs, it explains how to work with range objects, control program flow, develop custom dialog boxes, create custom toolbars and menus, and much more.Discover how toGrasp essential programming concepts Use the Visual Basic Editor Navigate the new Excel user interface Communicate with your users Deal with errors and bugs