The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    But how it gets from the ground to the glass is far more convoluted than we might think.In this revised edition of Drinking Water, UCLA professor and environmental policy expert James Salzman shows how drinking water highlights the most pressing issues of our time. He adds eye-opening, contemporary examples about our relationship to and consumption of water, and a new chapter about the tragedies that occurred in Flint, Michigan. Provocative, insightful, and engaging, Drinking Water shows just how complex a simple glass of water can be.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    This important new book offers an engaging and challenging introduction to the thorny paths of the globalization debate.

    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

    He then jets forward to the nineteenth century, where systems we can easily recognize as modern bureaucracies come into being. In some areas of life—like with the modern postal systems of Germany and France—these bureaucracies have brought tremendous efficiencies to modern life. But Graeber argues that there is a much darker side to modern bureaucracy that is rarely ever discussed. Indeed, in our own “utopia of rules,” freedom and technological innovation are often the casualties of systems that we only faintly understand.Provocative and timely, the book is a powerful look and history of bureaucracy over the ages and its power in shaping the world of ideas.

    Were the futurists and SF writers of the day just wrong? Or has something more interesting and important happened? Will we ever get flying cars? This book offers a compelling analysis of the past and a surprising view of the future.

    The Truth Machine is the best book so far on what has happened and what may come along. It demands the attention of anyone concerned with our economic future." --Lawrence H. Summers, Charles W. Eliot University Professor and President Emeritus at Harvard, Former Treasury SecretaryFrom Michael J. Casey and Paul Vigna, the authors of The Age of Cryptocurrency, comes the definitive work on the Internet's Next Big Thing: The Blockchain.Big banks have grown bigger and more entrenched. Privacy exists only until the next hack. Credit card fraud is a fact of life. Many of the "legacy systems" once designed to make our lives easier and our economy more efficient are no longer up to the task. Yet there is a way past all this--a new kind of operating system with the potential to revolutionize vast swaths of our economy: the blockchain.In The Truth Machine, Michael J. Casey and Paul Vigna demystify the blockchain and explain why it can restore personal control over our data, assets, and identities; grant billions of excluded people access to the global economy; and shift the balance of power to revive society's faith in itself. They reveal the disruption it promises for industries including finance, tech, legal, and shipping.Casey and Vigna expose the challenge of replacing trusted (and not-so-trusted) institutions on which we've relied for centuries with a radical model that bypasses them. The Truth Machine reveals the empowerment possible when self-interested middlemen give way to the transparency of the blockchain, while highlighting the job losses, assertion of special interests, and threat to social cohesion that will accompany this shift. With the same balanced perspective they brought to The Age of Cryptocurrency, Casey and Vigna show why we all must care about the path that blockchain technology takes--moving humanity forward, not backward.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    Ramachandra Guha takes as his point of departure the dominant environmental philosophies in these two countries—identified as "agrarianism" in India and "wilderness thinking" in the U.S. Proposing an inclusive "social ecology" framework that goes beyond these partisan ideologies, Guha arrives at a richer understanding of controversies over large dams, state forests, wildlife reserves, and more. He offers trenchant critiques of privileged and isolationist proponents of conservation, persuasively arguing for biospheres that care as much for humans as for other species. He also provides profiles of three remarkable environmental thinkers and activists—Lewis Mumford, Chandi Prasad Bhatt, and Madhav Gadgil. Finally, the author asks the fundamental environmental question—how much should a person or country consume?—and explores a range of answers.Copub: Permanent Black

    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.

    Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column?These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves – or discover for the first time – that maths is relevant to almost everything we do.Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    However, rather than resting on that reputation, the new edition of this text marks a significant advance in the already excellent quality of the book. While preserving concise language, state of the art educational pedagogy, and top-notch worked examples, the Eighth Edition features a unified art design as well as streamlined and carefully reorganized problem sets that enhance the thoughtful instruction for which Raymond A. Serway and John W. Jewett, Jr. earned their reputations. Likewise, PHYSICS FOR SCIENTISTS AND ENGINEERS, will continue to accompany Enhanced WebAssign in the most integrated text-technology offering available today. In an environment where new Physics texts have appeared with challenging and novel means to teach students, this book exceeds all modern standards of education from the most solid foundation in the Physics market today.