But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide.With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity—his eccentricities, his brilliance, his fatal candor—and elegantly explains his work and its implications.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is “probably approximately correct” algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant’s theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence.Offering a powerful and elegant model that encompasses life’s complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.

    Feynman (1918–1988)—physicist, teacher, author, and cultural icon. His autobiographies and biographies have been read and enjoyed by millions of readers around the world, while his wit and eccentricities have made him the subject of TV specials and even a theatrical film. The spectacular reception of the book and audio versions of Feynman’s Six Easy Pieces (published in 1995) resulted in a worldwide clamor for “More Feynman! More Feynman!” The outcome is these six additional lectures, drawn from the celebrated three-volume Lectures on Physics. Though slightly more challenging than the first six, these lectures are more focused, delving into the most revolutionary discovery in twentieth-century physics: Einstein’s Theory of Relativity. No single breakthrough in twentieth-century physics (with the possible exception of quantum mechanics) changed our view of the world more than that of Einstein’s discovery of relativity. The notions that the flow of time is not a constant, that the mass of an object depends on its velocity, and that the speed of light is a constant no matter what the motion of the observer, at first seemed shocking to scientists and laymen alike. But, as Feynman shows so clearly and so entertainingly in the lectures chosen for this volume, these crazy notions are no mere dry principles of physics, but are things of beauty and elegance. No one—not even Einstein himself—explained these difficult, anti-intuitive concepts more clearly, or with more verve and gusto, than Richard Feynman.

    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.

    It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena. In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology.

    However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice-freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You'll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you've mastered these techniques, you'll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes - Learning the Bayesian "state of mind" and its practical implications - Understanding how computers perform Bayesian inference - Using the PyMC Python library to program Bayesian analyses - Building and debugging models with PyMC - Testing your model's "goodness of fit" - Opening the "black box" of the Markov Chain Monte Carlo algorithm to see how and why it works - Leveraging the power of the "Law of Large Numbers" - Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning - Using loss functions to measure an estimate's weaknesses based on your goals and desired outcomes - Selecting appropriate priors and understanding how their influence changes with dataset size - Overcoming the "exploration versus exploitation" dilemma: deciding when "pretty good" is good enough - Using Bayesian inference to improve A/B testing - Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    On Lisp explains the reasons behind Lisp's growing popularity as a mainstream programming language. On Lisp is a comprehensive study of advanced Lisp techniques, with bottom-up programming as the unifying theme. It gives the first complete description of macros and macro applications. The book also covers important subjects related to bottom-up programming, including functional programming, rapid prototyping, interactive development, and embedded languages. The final chapter takes a deeper look at object-oriented programming than previous Lisp books, showing the step-by-step construction of a working model of the Common Lisp Object System (CLOS). As well as an indispensable reference, On Lisp is a source of software. Its examples form a library of functions and macros that readers will be able to use in their own Lisp programs.

    In this book, a wealth of exercises are provided throughout each section, designed to reinforce learning and the logical comprehension of topics. The use of real data is incorporated much more extensively than in any other book on the market. Consist of strong coverage of computer-based methods, especially in the coverage of analysis of variance and regression. This text stresses mastery of methods most often used in medical research, with specific reference to actual medical literature and actual medical research. The approach minimizes mathematical formulation, yet gives complete explanations of all important concepts. Every new concept is systematically developed through completely worked-out examples from current medical research problems. Computer output is used to illustrate concepts when appropriate.

    Its big-picture, calculus-based approach makes it an especially authoriatative reference for engineering and science majors. Now thoroughly update, this second edition includes vital new coverage of order statistics, best critical regions, likelihood ratio tests, and other key topics.

    Inside: Logic Resource CD-ROM

    By combining ArcGIS tutorials with self-study exercises intended to gradually build upon basic skills, the GIS Tutorial 1 is fully adaptable to individual needs, as well as the classroom setting. The tutorial demonstrates a range of GIS functionality, from creating maps and collecting data to using geoprocessing tools and models as well as ArcGIS 3D Analyst and ArcGIS Spatial Analyst extensions for further analysis. GIS Tutorial 1 includes a data CD for working through the exercises and fully functioning 180-day trial DVD of ArcGIS Desktop10 software, making it the smart choice for GIS beginners.

    This book teaches you how to conduct examinations by explaining what digital forensics is, the methodologies used, key technical concepts and the tools needed to perform examinations. Details on digital forensics for computers, networks, cell phones, GPS, the cloud, and Internet are discussed. Readers will also learn how to collect evidence, document the scene, and recover deleted data. This is the only resource your students need to get a jump-start into digital forensics investigations.This book is organized into 11 chapters. After an introduction to the basics of digital forensics, the book proceeds with a discussion of key technical concepts. Succeeding chapters cover labs and tools; collecting evidence; Windows system artifacts; anti-forensics; Internet and email; network forensics; and mobile device forensics. The book concludes by outlining challenges and concerns associated with digital forensics. PowerPoint lecture slides are also available.This book will be a valuable resource for entry-level digital forensics professionals as well as those in complimentary fields including law enforcement, legal, and general information security.