Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Explaining how, why, and when the techniques can be expected to work, the Seventh Edition places an even greater emphasis on building readers' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. Applied problems from diverse areas, such as engineering and physical, computer, and biological sciences, are provided so readers can understand how numerical methods are used in real-life situations. The Seventh Edition has been updated and now addresses the evolving use of technology, incorporating it whenever appropriate.

    Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

    Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

    Following on the success of the first six editions of the series, this work introduces theoretical and pedagogical innovations in statics, dynamics, and mechanics of materials education.

    Each chapter includes many illustrative examples to assist the reader. The book emphasizes methods for finding solutions to differential equations. It provides many abundant exercises, applications, and solved examples with careful attention given to readability. Elementary Differential Equations includes a thorough treatment of power series techniques. In addition, the book presents a classical treatment of several physical problems to show how Fourier series become involved in the solution of those problems. The eighth edition of Elementary Differential Equations has been revised to include a new supplement in many chapters that provides suggestions and exercises for using a computer to assist in the understanding of the material in the chapter. It also now provides an introduction to the phase plane and to different types of phase portraits. A valuable reference book for readers interested in exploring the technological and other applications of differential equations.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    The book teaches a range of design and analysis techniques for problems that arise in computing applications. The text encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    Highly recommended for graduate-level libraries.' ChoiceThis highly successful text, which first appeared in the year 1972 and has continued to be popular ever since, has now been brought up-to-date by incorporating the remarkable developments in the field of 'phase transitions and critical phenomena' that took place over the intervening years. This has been done by adding three new chapters (comprising over 150 pages and containing over 60 homework problems) which should enhance the usefulness of the book for both students and instructors. We trust that this classic text, which has been widely acclaimed for its clean derivations and clear explanations, will continue to provide further generations of students a sound training in the methods of statistical physics.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.

    A wealth of accompanying figures and exercises illustrate and develop the material in more depth. They describe what a quantum computer is, how it can be used to solve problems faster than familiar "classical" computers, and the real-world implementation of quantum computers. Their book concludes with an explanation of how quantum states can be used to perform remarkable feats of communication, and of how it is possible to protect quantum states against the effects of noise.

    Learn You a Haskell for Great Good! introduces programmers familiar with imperative languages (such as C++, Java, or Python) to the unique aspects of functional programming. Packed with jokes, pop culture references, and the author's own hilarious artwork, Learn You a Haskell for Great Good! eases the learning curve of this complex language, and is a perfect starting point for any programmer looking to expand his or her horizons. The well-known web tutorial on which this book is based is widely regarded as the best way for beginners to learn Haskell, and receives over 30,000 unique visitors monthly.

    Bellow. Strauss. Friedman. The University of Chicago has been the home of some of the most important thinkers of the modern age. But perhaps no name has been spoken with more respect than Turabian. The dissertation secretary at Chicago for decades, Kate Turabian literally wrote the book on the successful completion and submission of the student paper. Her Manual for Writers of Research Papers, Theses, and Dissertations, created from her years of experience with research projects across all fields, has sold more than seven million copies since it was first published in 1937.Now, with this seventh edition, Turabian’s Manual has undergone its most extensive revision, ensuring that it will remain the most valuable handbook for writers at every level—from first-year undergraduates, to dissertation writers apprehensively submitting final manuscripts, to senior scholars who may be old hands at research and writing but less familiar with new media citation styles. Gregory G. Colomb, Joseph M. Williams, and the late Wayne C. Booth—the gifted team behind The Craft of Research—and the University of Chicago Press Editorial Staff combined their wide-ranging expertise to remake this classic resource. They preserve Turabian’s clear and practical advice while fully embracing the new modes of research, writing, and source citation brought about by the age of the Internet.Booth, Colomb, and Williams significantly expand the scope of previous editions by creating a guide, generous in length and tone, to the art of research and writing. Growing out of the authors’ best-selling Craft of Research, this new section provides students with an overview of every step of the research and writing process, from formulating the right questions to reading critically to building arguments and revising drafts. This leads naturally to the second part of the Manual for Writers, which offers an authoritative overview of citation practices in scholarly writing, as well as detailed information on the two main citation styles (“notes-bibliography” and “author-date”). This section has been fully revised to reflect the recommendations of the fifteenth edition of The Chicago Manual of Style and to present an expanded array of source types and updated examples, including guidance on citing electronic sources.The final section of the book treats issues of style—the details that go into making a strong paper. Here writers will find advice on a wide range of topics, including punctuation, table formatting, and use of quotations. The appendix draws together everything writers need to know about formatting research papers, theses, and dissertations and preparing them for submission. This material has been thoroughly vetted by dissertation officials at colleges and universities across the country.This seventh edition of Turabian’s Manual for Writers of Research Papers, Theses, and Dissertations is a classic reference revised for a new age. It is tailored to a new generation of writers using tools its original author could not have imagined—while retaining the clarity and authority that generations of scholars have come to associate with the name Turabian.

    Designed for the junior- level astrophysics course, each topic is approached in the context of the major unresolved questions in astrophysics. The core chapters have been designed for a course in stellar structure and evolution, while the extended chapters provide additional coverage of the solar system, galactic structure, dynamics, evolution, and cosmology. * Two versions of this text are available: An Introduction to Modern Stellar Astrophysics, (Chapters 1-17), and An Introduction to Modern Astrophysics, (Chapters 1-28). * Computer programs included with the text allow students to explore the physics of stars and galaxies. * In designing a curriculum, instructors can combine core and extended chapters with the optional advanced sections so as to meet their individual goals. * Up-to-date coverage of current astrophysical discoveries are included. * This text emphasizes computational physics, including computer problems and on-line programs. * This text also includes a selection of over 500 problems. For additional information and computer codes to be used