Albert-László Barabási, the nation’s foremost expert in the new science of networks and author of Bursts, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information. Just as James Gleick and the Erdos–Rényi model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barabási–Albert model.

    Whether they bind computers, economies, or terrorist organizations, networks are everywhere in the real world, yet only recently have scientists attempted to explain their mysterious workings.From epidemics of disease to outbreaks of market madness, from people searching for information to firms surviving crisis and change, from the structure of personal relationships to the technological and social choices of entire societies, Watts weaves together a network of discoveries across an array of disciplines to tell the story of an explosive new field of knowledge, the people who are building it, and his own peculiar path in forging this new science.

    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.

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    Love is.Currently in its eighteenth printing in Japan, this best-selling novel is available in English at last. Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks. Math Girls has something for everyone, from advanced high school students to math majors and educators.

    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.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

    Written by one of the foremost experts on mathematical magic, it employs considerable historical data to summarize all previous work in this field. It is also a creative examination of laws and their exemplification, with scores of new tricks, insights, and demonstrations. Dozens of topological tricks are explained, and dozens of manipulation tricks are aligned with mathematical law.Nontechnical, detailed, and clear, this volume contains 115 sections discussing tricks with cards, dice, coins, etc.; topological tricks with handkerchiefs, cards, etc.; geometrical vanishing effects; demonstrations with pure numbers; and dozens of other topics. You will learn how a Moebius strip works and how a Curry square can "prove" that the whole is not equal to the sum of its parts.No skill at sleight of hand is needed to perform the more than 500 tricks described because mathematics guarantees their success. Detailed examination of laws and their application permits you to create your own problems and effects.

    While such visualizations can better inform us, they can also deceive by displaying incomplete or inaccurate data, suggesting misleading patterns—or simply misinform us by being poorly designed, such as the confusing “eye of the storm” maps shown on TV every hurricane season.Many of us are ill equipped to interpret the visuals that politicians, journalists, advertisers, and even employers present each day, enabling bad actors to easily manipulate visuals to promote their own agendas. Public conversations are increasingly driven by numbers, and to make sense of them we must be able to decode and use visual information. By examining contemporary examples ranging from election-result infographics to global GDP maps and box-office record charts, How Charts Lie teaches us how to do just that.

    Your guide to a higher math score on standardized tests*SATACT(R)ASVABGMAT(R)GRE(R)CBEST(R)PRAXIS I(R)GED(R) And More!Why CliffsNotes?Go with the name you know and trustGet the information you need-fast!About the Contents:IntroductionHow to use this bookOverview of the examsPart I: Basic Skills ReviewArithmetic and Data AnalysisAlgebraPart II: Strategies and PracticeMathematical AbilityQuantitative ComparisonData SufficiencyEach section includes a diagnostic test, explanations of rules, concepts withexamples, practice problems with complete explanations, a review test, and aglossary!Test-Prep Essentials from the Experts at CliffsNotes(R)For more test-prep help, visit CliffsNotes.com(R)*SAT is a registered trademark of the College Board, which was not involved inthe production of, and does not endorse, this product.

    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.

    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.

    Each clever equation is a tiny, perfect poem that prompts readers to look at the ordinary and see the miraculous. Can you look at an egg in a nest and see a jewelry box? How are sunlight and heat like an alarm clock? Engaging sidebars reveal the science behind the signs of spring.

    But its myriad occurrences in art, nature, and science have been a source of speculation and wonder for thousands of years. Divine Proportion draws upon both religion and science to tell the story of Phi and to explore its manifestations in such diverse places as the structure of the inner ear, the spiral of a hurricane, the majesty of the Parthenon, and the elusive perfection of the Mona Lisa. A universal key to harmony, regeneration, and balance, Phi is at the heart of a tantalizing story begun on clay tablets in ancient Babylon, and which will continue to be written for centuries to come.