Before this explosive growth into the modern age took place, an all-but-forgotten genius strove for forty years to win acceptance for the atomic theory of matter and an altogether new way of doing physics. Ludwig Boltz-mann battled with philosophers, the scientific establishment, and his own potent demons. His victory led the way to the greatest scientific achievements of the twentieth century. Now acclaimed science writer David Lindley portrays the dramatic story of Boltzmann and his embrace of the atom, while providing a window on the civilized world that gave birth to our scientific era. Boltzmann emerges as an endearingly quixotic character, passionately inspired by Beethoven, who muddled through the practical matters of life in a European gilded age. Boltzmann's story reaches from fin de siecle Vienna, across Germany and Britain, to America. As the Habsburg Empire was crumbling, Germany's intellectual might was growing; Edinburgh in Scotland was one of the most intellectually fertile places on earth; and, in America, brilliant independent minds were beginning to draw on the best ideas of the bureaucratized old world.Boltzmann's nemesis in the field of theoretical physics at home in Austria was Ernst Mach, noted today in the term Mach I, the speed of sound. Mach believed physics should address only that which could be directly observed. How could we know that frisky atoms jiggling about corresponded to heat if we couldn't see them? Why should we bother with theories that only told us what would probably happen, rather than making an absolute prediction? Mach and Boltzmann both believed in the power of science, but their approaches to physics could not have been more opposed. Boltzmann sought to explain the real world, and cast aside any philosophical criteria. Mach, along with many nineteenth-century scientists, wanted to construct an empirical edifice of absolute truths that obeyed strict philosophical rules. Boltzmann did not get on well with authority in any form, and he did his best work at arm's length from it. When at the end of his career he engaged with the philosophical authorities in the Viennese academy, the results were personally disastrous and tragic. Yet Boltzmann's enduring legacy lives on in the new physics and technology of our wired world.Lindley's elegant telling of this tale combines the detailed breadth of the best history, the beauty of theoretical physics, and the psychological insight belonging to the finest of novels.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    From the Knights Templars to the freemasons, an intimate look at the inner workings of secret societies.

    Using the data they are constantly collecting about where we travel, where we shop, what we buy, and what interests us, they can begin to predict our daily habits, and increasingly we are relinquishing our decision-making to algorithms. Are we giving this up too easily?Without understanding what mathematics can and can't do it is impossible to get a handle on how it is changing our lives. Outnumbered is a journey to the dark side of mathematics, from how it dictates our social media activities to our travel routes. David Sumpter investigates whether mathematics is crossing dangerous lines when it comes to what we can make decisions about.This book will show how math impacts all parts of our lives: from the algorithms that decide whom we interact with to the statistical methods that categorize us as potential criminals. It tests financial algorithms that purport to generate money from nothing, and reveals that we are constantly manipulated by the math used by others, from algorithms choosing the news we hear to automated hospital waiting lists deciding whether we receive treatment.Using interviews with those people working at the cutting edge of mathematical and data research, Outnumbered will explain how math and stats work in the real world, and what we should and shouldn't worry about.

    Lohr maps out the unique seductions of programming, and gives us an intimate portrait of the peculiar kind of genius that is drawn to this blend of art, science, and engineering, introducing us to the movers and shakers of the 1950s and the open-source movement of today. With original reporting and deft storytelling, Steve Lohr shows us how software transformed the world, and what it holds in store for our future.

    It resurrects from the vaults of neglect the polymath Jerome Cardano, a Milanese of the sixteenth century. Who is he? A gambler and blasphemer, inventor and chancer, plagued by demons and anxieties, astrologer to kings, emperors and popes. This stubborn and unworldly man was the son of a lawyer and a brothel keeper, but also a gifted physician and the unacknowledged discoverer of the mathematical foundations of quantum physics. That is the argument of this charming and intoxicatingly clever book, which is truly original in its style, and in the manner of the modernists embodies in its very form its theories about the world.'The Quantum Astrologer’s Handbook' is a science book with the panache of a novel, for readers of Carlo Rovelli or Umberto Eco. It is a work of and about genius.

    In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

    

    Channelling our twin urges to explore and understand, geographers uncover the hidden connections of human existence, from infant mortality in inner cities to the decision-makers who fly overhead in executive jets, from natural disasters to over-use of fossil fuels.In this incisive introduction to the subject, Danny Dorling and Carl Lee reveal geography as a science which tackles all of the biggest issues that face us today, from globalisation to equality, from sustainability to population growth, from climate change to changing technology - and the complex interactions between them all.Illustrated by a series of award-winning maps created by Benjamin D. Hennig, this is a book for anyone who wants to know more about why our world is the way it is today, and where it might be heading next.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    For each volume, a series editor reads pieces from hundreds of periodicals, then selects between fifty and a hundred outstanding works. That selection is pared down to the twenty or so very best pieces by a guest editor who is widely recognized as a leading writer in his or her field. This unique system has helped make the Best American series the most respected -- and most popular -- of its kind. Here you will find another "splendid array of unpredictable and delectable essays" (Booklist), chosen by the Pulitzer Prize-winning writer Louis Menand, another collection with "delights on every page" (Dallas Morning News). The Best American Essays once again earns its place as the liveliest and leading annual of its kind.

    But what sort of person was the young Albert Einstein, before he became universally acclaimed as the archetypal genius? And how did his genius unfold? In this brilliant new Kindle Single, scientist Robyn Arianrhod blends biography with popular science to tell the story of how young Albert developed a theory that – unknown to him at first – contained the seeds of his extraordinary equation E = mc2. Arianrhod, who wrote her PhD on Einstein’s general theory of relativity, makes the ideas behind the equation accessible to the lay reader, and sets young Einstein’s exploration of these ideas against the backdrop of his first loves, his family and marriage, and, above all, his childlike wonder at the nature of the universe. She introduces his heroes and scientific inspirations, and the friends who believed in him when no one else did. In personalising Einstein, she brings to life both the man and his science, in a short, easy-to-read narrative. In showing how he discovered his famous equation, and what it means, she draws a compelling portrait of this prodigious intellect whose unfathomable grasp of the building blocks of physics would change our world forever. About the Author: Dr Robyn Arianrhod is the author of two critically acclaimed works of popular science and scientific history: Einstein’s Heroes: Imagining the World Through the Language of Mathematics, and Seduced by Logic: Émilie du Châtelet, Mary Somerville and the Newtonian Revolution. Both were shortlisted for major book awards and are published in the USA. Einstein’s Heroes was translated into several languages. Robyn was awarded her PhD for research on Einstein’s general theory of relativity and has lectured in applied mathematics (including special relativity) for many years. She is currently an Adjunct Research Fellow in the School of Mathematical Sciences at Monash University in Melbourne, where she is undertaking research on the structure of relativistic space-times. She is also a technical reviewer for the American Mathematical Society. Praise for Robyn Arianrhod's books: Einstein’s Heroes ‘Arianrhod’s achievement is to so masterfully combine history, biography, and mathematics as to absorb and enlighten even the mathematically maladroit’ – Booklist ‘An intriguing blend of science, history, and biography . . . Arianrhod’s well-written, fascinating discussion of intertwined topics is highly recommended’ – Library Journal (starred review) ‘A thrilling story . . . Arianrhod brings out the human side of the scientists’ – Bloombergnews ‘Offers readers an engaging intellectual exercise combining physics, language, mathematics, and biography’ – Science News Seduced by Logic ‘Seduced by Logic offers the lay reader an easy and agreeable introduction to the evolution of some crucial scientific debates . . . One cannot help be captivated by her intellectual honesty and enthusiasm’ – Times Higher Education ‘An elegant and inspiring history of how scientific revolutions make their way’ – Edward Dolnick, The Clockwork Universe ‘Here is a skillfully written tapestry of the science, history and portrayal of two of the most charismatic women of mathematical science. Robyn Arianrhod has produced a captivating masterpiece’ – Joseph Mazur, author of Euclid in the Rainforest and What’s Luck Got to Do with It?

    Keeping an open mind, looking for unusual number combinations, using multiple skills (like subtracting to add) and looking for patterns will guarantee any child success in math. In MATH APPEAL, Tang continues to challenge kids with his innovative approach to math.

    The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

    The book takes the reader on a fascinating journey around the Tube network to reveal the history behind the names of all 268 stations. Packed full of lively stories about the colourful characters and remarkable events connected to the places that bear these names, the book delves deep into London’s rich history to recall tales of terrible fires, profligate playboys, ancient relics, devious criminals, squalid slums, lost rivers, grisly executions and unsolved mysteries. This is a book for anyone who has ever taken a trip on the Tube – the perfect gift for visitors, commuters and Londoners alike. It is a Tube guide to the city’s past. So sit back and enjoy the ride and discover something new about London and its historic Underground.