Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, alwayschoosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum ofmathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issuesand has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    Cases, datasets, and examples allow for a more real-world perspective and explore relevant uses of regression techniques in business today.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    The author defines all terms, points out potential pitfalls in algebraic calculation, and makes problem solving a fun activity. New in this edition are painless approaches to understanding and graphing linear equations, solving systems of linear inequalities, and graphing quadratic equations. Barron’s popular Painless Series of study guides for middle school and high school students offer a lighthearted, often humorous approach to their subjects, transforming details that might once have seemed boring or difficult into a series of interesting and mentally challenging ideas. Most titles in the series feature many fun-to-solve “Brain Tickler” problems with answers at the end of each chapter.

    Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    He would return in September. For the next ten weeks my survival would depend on foraging, hunting and fishing on an island I would share with 1,600 brown bears. This is my story of hunger and solitude, salmon fishing and stormy seas, torrential rains and mountain sunsets, giant halibut and deer hunting, campfires and killer whales. Illustrated with nearly fifty photos and a map.

    Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces basic counting systems; significant numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; how numbers affect architecture. Lundy explains why the ideas of Pythagoras still resonate, and she profiles each number from one to ten to show its distinct qualities: why, for example, the golden section is associated with five, and seven with the Virgin Mary.

    Winning the 2008 national championship was certainly the highlight, but the most dominant era in school history also includes a national-best 300 wins, three Final Fours and nine Big 12 titles since 2001.The consistency was unmatched.As a sportswriter covering the Jayhawks, first for The Kansas City Star and then for Yahoo! Sports, Jason King was there to chronicle it all. From Roy Williams' stunning departure to Mario's Miracle against Memphis to Kansas' 69-game winning streak at Allen Fieldhouse, King witnessed all the highlights - and lowlights - from 2000 and beyond. In short, he was the ultimate insider.Now you will be, too.With "Beyond the Phog," King provides Kansas fans with an unprecedented glimpse into one of the most memorable eras in the program's rich history. Extensive interviews with nearly 40 players from the last decade, as well as both head coaches, reveal fascinating details about the inner-workings of a true college basketball dynasty.You'll laugh, you'll cry, you'll be riveted - and, at times, shocked. Whatever the case, even the most ardent Kansas supporters will be exposed to candid, behind the scenes stories and anecdotes that, until now, had been confined to the Jayhawks' locker room.Here's a sample of what's inside:• Did Drew Gooden's shoes cost Kansas the 2002 NCAA title?• Nick Collison and Kirk Hinrich lament their final game against Syracuse• Roy Williams provides details about his final few weeks at Kansas and his relationship with Al Bohl• Why did Wayne Simien almost quit basketball?• Jeff Graves comes clean about violating a sacred locker room rule• Russell Robinson describes why he tried to fight his own coach• J.R. Giddens gives his version of the Moon Bar stabbing• Darrell Arthur explains why he's been hesitant to return to campus since winning the 2008 title• Mario Chalmers provides a step-by-step account of his heroic shot against Memphis• Tyshawn Taylor discusses the aftermath of the Jayhawks' 2011 loss to VCU• Josh Selby talks about his decision to enter the NBA draft• And hundreds of other stories from favorites such as Sherron Collins, Keith Langford, Jeff Boschee, Aaron Miles, Michael Lee, Eric Chenowith, Xavier Henry, Luke Axtell, Sasha Kaun, Tyrel Reed, Jeff Hawkins, Brady Morningstar, Darnell Jackson and others.Time has clearly loosened lips in Lawrence. "Beyond the Phog" is an honest, candid look at what really happened during a magical - and often controversial - period in Kansas basketball history.

    Practical illustrations of how these techniques can be applied to the most common mental health problems ensure that theory translates into real-life practice. New to this edition, the authors examine:o cultural diversity in greater deptho the current topicality of CBT, especially within the NHSo latest Roth/Pilling CBT competencieso the impact of third wave CBT in more detail.As well as exploring depression, panic and agoraphobia, OCD and anxiety disorders, the book covers other less common disorders. Discussion of different methods of delivery includes work with individuals, groups, couples and families. This edition also includes extra case study material, student exercises and discussion points.This fully updated Introduction remains the key textbook for those coming to CBT for the first time, whether on training courses or as part of their everyday work. It is also useful for more experienced therapists wanting to refresh their core skills.

    Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. More information concerning licenses is available at: www.nr.com/licenses New key features: 2 new chapters, 25 new sections, 25% longer than Second Edition Thorough upgrades throughout the text Over 100 completely new routines and upgrades of many more. New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector MachinesNew Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions An expanded treatment of ODEs with completely new routines Plus comprehensive coverage of linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory

    It covers all relevant areas, including molecular spectroscopy, electronic structure computations, molecular beam methods and time-resolved measurements of chemical systems.

    It moves beyond a mere study of algorithms without sacrificing the rigor that faculty desire. As in every edition, Winston reinforces the book's successful features and coverage with the most recent developments in the field. The Student Suite CD-ROM, which now accompanies every new copy of the text, contains the latest versions of commercial software for optimization, simulation, and decision analysis.

    The material is reinforced with numerous examples to illustrate principles and imaginative, well-illustrated problems of varying degrees of difficulty. The book is committed to developing users' problem-solving skills. Features new "Photorealistc" figures (approximately 400) that have been rendered in often 3D photo quality detail to appeal to visual learners. Presents a thorough combination of both static and dynamic engineering mechanics theory and applications. Features a large variety of problem types from a broad range of engineering disciplines, stressing practical, realistic situations encountered in professional practice, varying levels of difficulty, and problems that involve solution by computer. For professionals in mechanical engineering, civil engineering, aeronautical engineering, and engineering mechanics careers.