Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    Algorithms in a Nutshell describes a large number of existing algorithms for solving a variety of problems, and helps you select and implement the right algorithm for your needs -- with just enough math to let you understand and analyze algorithm performance. With its focus on application, rather than theory, this book provides efficient code solutions in several programming languages that you can easily adapt to a specific project. Each major algorithm is presented in the style of a design pattern that includes information to help you understand why and when the algorithm is appropriate. With this book, you will:Solve a particular coding problem or improve on the performance of an existing solutionQuickly locate algorithms that relate to the problems you want to solve, and determine why a particular algorithm is the right one to useGet algorithmic solutions in C, C++, Java, and Ruby with implementation tipsLearn the expected performance of an algorithm, and the conditions it needs to perform at its bestDiscover the impact that similar design decisions have on different algorithmsLearn advanced data structures to improve the efficiency of algorithmsWith Algorithms in a Nutshell, you'll learn how to improve the performance of key algorithms essential for the success of your software applications.

    Algorithms have made our lives more efficient, more entertaining, and, sometimes, better informed. At the same time, complex algorithms are increasingly violating the basic rights of individual citizens. Allegedly anonymized datasets routinely leak our most sensitive personal information; statistical models for everything from mortgages to college admissions reflect racial and gender bias. Meanwhile, users manipulate algorithms to "game" search engines, spam filters, online reviewing services, and navigation apps.Understanding and improving the science behind the algorithms that run our lives is rapidly becoming one of the most pressing issues of this century. Traditional fixes, such as laws, regulations and watchdog groups, have proven woefully inadequate. Reporting from the cutting edge of scientific research, The Ethical Algorithm offers a new approach: a set of principled solutions based on the emerging and exciting science of socially aware algorithm design. Michael Kearns and Aaron Roth explain how we can better embed human principles into machine code - without halting the advance of data-driven scientific exploration. Weaving together innovative research with stories of citizens, scientists, and activists on the front lines, The Ethical Algorithm offers a compelling vision for a future, one in which we can better protect humans from the unintended impacts of algorithms while continuing to inspire wondrous advances in technology.

    Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

    This guide provides explanations of eigenvalues, eigenvectors, linear transformations, linear equations, vectors, and matrices.

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    Marketers want to change their customers’ minds and leaders want to change organizations. Start-ups want to change industries and nonprofits want to change the world. But change is hard. Often, we persuade and pressure and push, but nothing moves. Could there be a better way?This book takes a different approach. Successful change agents know it’s not about pushing harder, or providing more information, it’s about being a catalyst. Catalysts remove roadblocks and reduce the barriers to change. Instead of asking, “How could I change someone’s mind?” they ask a different question: “Why haven’t they changed already? What’s stopping them?”The Catalyst identifies the key barriers to change and how to mitigate them. You’ll learn how catalysts change minds in the toughest of situations: how hostage negotiators get people to come out with their hands up and how marketers get new products to catch on, how leaders transform organizational culture and how activists ignite social movements, how substance abuse counselors get addicts to realize they have a problem, and how political canvassers change deeply rooted political beliefs.This book is designed for anyone who wants to catalyze change. It provides a powerful way of thinking and a range of techniques that can lead to extraordinary results. Whether you’re trying to change one person, transform an organization, or shift the way an entire industry does business, this book will teach you how to become a catalyst.

    Featuring all the important advice and suggestions in the original edition of What’s Math Got to Do with It?, this revised edition is now updated with new research on the brain and mathematics that is revolutionizing scientists’ understanding of learning and potential.As always Jo Boaler presents research findings through practical ideas that can be used in classrooms and homes. The new What’s Math Got to Do with It? prepares teachers and parents for the Common Core, shares Boaler’s work on ways to teach mathematics for a “growth mindset,” and includes a range of advice to inspire teachers and parents to give their students the best mathematical experience possible.

    Always timely, topical, and distinctively “useful, with a pleasant degree of humor,” the Almanac is consulted daily by users from all walks of life, throughout the year.   The 2021 edition contains the fun facts, predictions, and feature items that have made it a cultural icon: traditionally 80 percent–accurate weather forecasts; notable astronomical events and time-honored astrological dates; horticultural, culinary, fashion, and other trends; historical hallmarks; best fishing days; time- and money-saving garden advice; recipes for refreshment; facts on folklore, farmers, home remedies, and husbandry; amusements and contests, plus too much more to mention—all in the inimitable way that the Almanac has done since 1792.   • Beloved by generations for being “useful, with a pleasant degree of humor,” The Old Farmer’s Almanac features everything under the Sun, including its much-in-demand long-range weather predictions, essential astronomical timetables, 2021 holidays, fascinating trends, best fishing days, valuable gardening information, tantalizing recipes, fun folklore, amusements, contests, and much more! • Exclusive: 32 reference pages, covering such popular topics as full Moon names, hurricane names, flowers that attract birds and butterflies, U.S./metric measurement conversions, and many more! • Easy-to-read edition, with crisp, white paper and larger type than the regular paperback version • Includes 112 full-color pages • Hard cover with dust jacket helps to protect the pages—a plus for those who collect the Almanac each year!

    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Contains 640 problems including solutions; additional practice problems with answers; explanations of complex variable theory; coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    It’s time we stand face-to-digital-face with the true powers and limitations of the algorithms that already automate important decisions in healthcare, transportation, crime, and commerce. Hello World is indispensable preparation for the moral quandaries of a world run by code, and with the unfailingly entertaining Hannah Fry as our guide, we’ll be discussing these issues long after the last page is turned.

    It can urge the reader to explore new methodologies to have maximum fun with numbers, and opt for a higher course in mathematics. The book was specifically designed to help the student community, and develop a strong affinity towards problem solving.the book offers many complicated, and interesting challenges for the user, keeping them engaged throughout. A large number of solved problems are also included in challenge and thrill of pre-college mathematics, to give readers an insight into the subject. The book can be an eye-opener for school students of class 7 and above. The materials given in the book are powerful enough to help them develop a strong interest for the subject. The concepts are explained in a simple and comprehensive manner, providing them with a good understanding of mathematical fundamentals.what makes the book distinct is its detailed sections on geometry, that can improve the reasoning skills of students. There are also detailed accounts on algebra and trigonometry, enhancing the competitive ability of the users. The topics such as combinatorics, number theory, and probability are also explained in detail, in the book. Each chapter was designed with the intention of motivating students to appreciate the excitement that mathematical problems can provide. Published in 2003 by new age international publishers, the book is available in paperback. Key features: the book includes a collection of more than 300 solved numerical problems, compiled from various national, as well as international mathematical olympiads.it is widely recommended by students and teachers, alike as an essential preparatory book for those writing competitive examinations.