{"title":"Philosophy of mathematics Books","description":"","products":[{"product_id":"quadrivium-the-four-classical-liberal-arts-of-number-geometry-music-and-cosmology-9781907155048","title":"Quadrivium: The Four Classical Liberal Arts of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe Quadrivium consists of the four Liberal Arts of Number, Geometry, Music, and Cosmology, studied from antiquity to the Renaissance as a way of glimpsing the nature of reality.  They synthesize number, space, and time. Geometry is number in space, music is number in time, and the cosmos expresses number in space and time. Number, music, and geometry are metaphysical truths, good and beautiful everywhere at all times. Life across the universe investigates them. They foreshadow the physical sciences. This is the first volume to bring together the Quadrivium for many hundreds of years.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Music to the eye\" - The New York Times. \"Fascinating\" - Financial Times. \"Excellent\" - New Scientist. \"Genuinely mind-expanding\" - Fortean Times. \"Engaging and accessible\" - Seattle Times. \"Beautiful\" - London Review of Books. \"Rich and artful\" - The Lancet.","brand":"Wooden Books","offers":[{"title":"Default Title","offer_id":47850606264663,"sku":"9781907155048","price":17.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781907155048.jpg?v=1710616237"},{"product_id":"weirdest-maths-at-the-frontiers-of-reason-9781786078056","title":"Weirdest Maths: At the Frontiers of Reason","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eMaths is everywhere, in everything.\u003c\/strong\u003e It’s in the finest margins of modern sport. It’s in the electrical pulses of our hearts and the flight of every bird. It is our key to secret messages, lost languages and perhaps even the shape of the universe of itself.\u003c\/p\u003e  \u003cp\u003eDavid Darling and Agnijo Banerjee reveal the mathematics at the farthest reaches of our world – from its role in the plots of novels to how animals employ numerical skills to survive. Along the way they explore what makes a genius, why a seemingly simple problem can confound the best and brightest for decades, and what might be the great discovery of the twenty-first century. As Bertrand Russell once said, ‘mathematics, rightly viewed, possesses not only truth, but supreme beauty’. Banerjee and Darling make sure we see it right again.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e‘The brilliant combination of an accomplished science writer and a young mathematical prodigy.’\u003c\/p\u003e -- Bobby Seagull, author of \u003ci\u003eThe Life-Changing Magic of Numbers\u003c\/i\u003e and co-presenter of \u003ci\u003eMonkman \u0026amp; Seagull’s Genius Guide to Britain\u003c\/i\u003e","brand":"Oneworld Publications","offers":[{"title":"Default Title","offer_id":47851258577239,"sku":"9781786078056","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781786078056.jpg?v=1710631346"},{"product_id":"how-numbers-work-discover-the-strange-and-beautiful-world-of-mathematics-9781529382044","title":"How Numbers Work: Discover the strange and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eThink of a number between one and ten.\u003c\/b\u003e\u003cbr\u003eNo, hang on, let's make this interesting. Between \u003ci\u003ezero\u003c\/i\u003e and \u003ci\u003einfinity\u003c\/i\u003e. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like \u003ci\u003epi\u003c\/i\u003e which never end. It literally never ends.\u003cbr\u003e\u003cbr\u003eThe world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - \u003ci\u003epi\u003c\/i\u003e, \u003ci\u003ee\u003c\/i\u003e, the \"imaginary\" number \u003ci\u003ei\u003c\/i\u003e and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?\u003cbr\u003e\u003cbr\u003e\u003ci\u003eHow Numbers Work \u003c\/i\u003etakes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eABOUT THE SERIES\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eNew Scientist Instant Expert\u003c\/i\u003e books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the \u003ci\u003eInstant Expert\u003c\/i\u003e series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.\u003c\/p\u003e","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":47851523637591,"sku":"9781529382044","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781529382044.jpg?v=1710638258"},{"product_id":"the-big-bang-of-numbers-how-to-build-the-universe-using-only-maths-9781526622938","title":"The Big Bang of Numbers: How to Build the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e'\u003cb\u003eWho knew numbers could be so charming? ... Suri takes us on a light-hearted journey all the way from nothing (zero) to infinity\u003c\/b\u003e' Karen Joy Fowler, New York Times bestselling author of \u003ci\u003eWe Are All Completely Beside Ourselves\u003c\/i\u003e  Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing – no matter, no cosmos, not even empty space – could we create a universe using only maths?  In this new mathematical origin story, mathematician and award-winning novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. With evocative and engaging examples ranging from multidimensional crochet to the Mona Lisa’s asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, \u003ci\u003eThe Big Bang of Numbers\u003c\/i\u003e charts a playful, inventive course to existence.  Distilled from almost four decades of teaching experience, and offering both striking new perspectives for maths aficionados and an accessible introduction for enthusiastic novices, \u003ci\u003eThe Big Bang of Numbers\u003c\/i\u003e proves that we can all fall in love with maths.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe fundamental[s] of maths presented like a delightful fairy-tale. Hugely enjoyed it * Dara O'Brien *\u003cbr\u003eA beautifully written meditation on mathematics: whimsical, thought-provoking and deep * Alex Bellos, author of Alex's Adventures in Numberland *\u003cbr\u003eWho knew numbers could be so charming? So industrious? Suri takes us on a light-hearted journey all the way from nothing (zero) to infinity. Math has rarely been so readable. * Karen Joy Fowler, New York Times bestselling author of We Are All Completely Beside Ourselves *\u003cbr\u003eIn \u003ci\u003eThe Big Bang of Numbers\u003c\/i\u003e, Manil Suri invites the reader to create a universe made of mathematical ideas, sparking a thrill that may catch you off guard—an exhilarating sensation of playfulness, power, and insight. * Steven Strogatz, New York Times bestselling author of Infinite Powers and The Joy of X *\u003cbr\u003eNumerophobic? This infinitely fascinating book will cure you ... Manil Suri’s march through maths is brimming with entertaining and yet discombobulating thoughts ... Suri has a knack for clarity and a welcome habit of grounding tricky concepts in the tangible * The Times *\u003cbr\u003eA most unusual, creative, and fascinating account of mathematics that relies not on equations or formulas, but on metaphors, paradoxes, and lovely vignettes. * John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper *\u003cbr\u003eA delightful ride of a book. Before I knew it, I was rooting for primes, doubting the wisdom of dividing by zero, and holding my breath as the universe starts to emerge from triangles and cones and planes. The book was so enjoyable and understandable, it almost made me want to take another stab at calculus. Almost. Proof that when a smart person who writes well and honestly explores their passion, that passion is contagious. * Ken Krimstein, author of When I Grow Up *\u003cbr\u003eAn excellent new book that could make anyone fall in love with math * Washingtonian *","brand":"Bloomsbury Publishing PLC","offers":[{"title":"Default Title","offer_id":47851935498583,"sku":"9781526622938","price":11.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781526622938.jpg?v=1710649402"},{"product_id":"the-ten-equations-that-rule-the-world-9780141991092","title":"The Ten Equations that Rule the World","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eTHE INTERNATIONAL BESTSELLER\u003cbr\u003e\u003cbr\u003e''An entertaining tour that will change how you see the world'' Sean Carroll, author of \u003ci\u003eSomething Deeply Hidden\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003eIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eThis book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.\u003cbr\u003e\u003cbr\u003eWith wit and clarity, mathematician David Sumpter shows that it isn''t the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone c\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eSometimes books about numbers come along and we're so ecstatic that we just pop with delight. One such book is \u003ci\u003eThe Ten Equations that Rule The World\u003c\/i\u003e\u003c\/b\u003e -- Tim Harford * More or Less BBC4 *\u003cbr\u003eHugely entertaining, erudite and at times genuinely witty . . . \u003cb\u003eit's nice to be spoken to in grown-up language by a genius\u003c\/b\u003e. You will come away from Sumpter's book with a much clearer idea of why the world is less messy than it appears * E\u0026amp;T Magazine *\u003cbr\u003eThese aren't the equations of Newton or Einstein -- crisp relations describing the evolution of a clockwork universe. These are the equations of randomness, expectation, and imperfect information. The equations, in other words, of the real world. David Sumpter provides \u003cb\u003ean entertaining tour that will change how you see the world \u003c\/b\u003e -- Sean Carroll author of Something Deeply Hidden\u003cbr\u003e\u003cb\u003eSumpter writes fascinatingly\u003c\/b\u003e about his experiences as a consulting mathematician. . .  I will encourage my mathematics undergraduates to read this book since it will inspire them by showing the relevance of mathematics to today's world and make them think about the moral issues they will face as mathematicians * Times Higher Education *\u003c\/p\u003e","brand":"Penguin Books Ltd","offers":[{"title":"Default Title","offer_id":48732512878935,"sku":"9780141991092","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780141991092.jpg?v=1719997210"},{"product_id":"godels-theorem-a-very-short-introduction-very-short-introductions-9780192847850","title":"Gödels Theorem A Very Short Introduction Very","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhen Kurt Gödel published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, it had a profound impact on mathematical ideas and philosophical thought. Adrian Moore places the theorem in its intellectual and historical context, explaining the key concepts and misunderstandings.","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732594798935,"sku":"9780192847850","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192847850.jpg?v=1719997578"},{"product_id":"fundamentals-of-bayesian-epistemology-2-arguments-challenges-alternatives-9780192863157","title":"Fundamentals of Bayesian Epistemology 2 Arguments","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBayesian ideas have recently been applied across such diverse fields as philosophy, statistics, economics, psychology, artificial intelligence, and legal theory. Fundamentals of Bayesian Epistemology examines epistemologists'' use of Bayesian probability mathematics to represent degrees of belief. Michael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implicationsVolume 1 begins by motivating the use of degrees of belief in epistemology. It then introduces, explains, and applies the five core Bayesian normative rules: Kolmogorov''s three probability axioms, the Ratio Formula for conditional degrees of belief, and Conditionalization for updating attitudes over time. Finally, it discusses further normative rules (such as the Principal Principle, or indifference principles) that have been proposed to supplement or replace the core five.Volume 2 gives arguments for the five core rules introduced in Volume 1, then considers challenges to Bayesian epistemology. It begins by detailing Bayesianism''s successful applications to confirmation and decision theory. Then it describes three types of arguments for Bayesian rules, based on representation theorems, Dutch Books, and accuracy measures. Finally, it takes on objections to the Bayesian approach and alternative formalisms, including the statistical approaches of frequentism and likelihoodism.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eMichael G. Titelbaum provides an accessible introduction to the key concepts and principles of the Bayesian formalism, enabling the reader both to follow epistemological debates and to see broader implications * MathSciNet *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIII Applications 6: Confirmation 7: Decision Theory IV Arguments for Bayesianism 8: Representation Theorems 9: Dutch Book Arguments 10: Accuracy Arguments Challenges and Objections 11: Memory Loss and Self-Location 12: Old Evidence, Logical Omniscience 13: Alternatives to Bayesianism 14: Comparisons, Ranges, Dempster-Shafer","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732603023703,"sku":"9780192863157","price":28.02,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192863157.jpg?v=1719997605"},{"product_id":"propositions-ontology-and-logic-rutgers-lectures-in-philosophy-series-9780197647035","title":"Propositions Ontology and Logic RUTGERS LECTURES","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eHis book adopts a self-consciously neo-Quinean methodology, and argues that the theory that is developed helps to motivate and clarify Quine's naturalistic metaphysical picture. * MathSciNet  *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction  Chapter I. The Quinean legacy  Chapter II. Propositions  Chapter III.  Predicates and predication   Chapter IV. First-order modal logic, and a first-order theory of propositions  Chapter V. Properties and relations  Chapter VI.  Possible worlds and possible individuals   References","brand":"Oxford University Press Inc","offers":[{"title":"Default Title","offer_id":48732667281751,"sku":"9780197647035","price":20.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780197647035.jpg?v=1719997866"},{"product_id":"leibniz-9780198718642","title":"Leibniz","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eGottfried Wilhelm Leibniz (1646-1716) was a man of extraordinary intellectual creativity who lived an exceptionally rich and varied intellectual life in troubled times. More than anything else, he was a man who wanted to improve the life of his fellow human beings through the advancement of all the sciences and the establishment of a stable and just political order. In this Very Short Introduction Maria Rosa Antognazza outlines the central features of Leibniz''s philosophy in the context of his overarching intellectual vision and aspirations. Against the backdrop of Leibniz''s encompassing scientific ambitions, she introduces the fundamental principles of Leibniz''s thought, as well as his theory of truth and theory of knowledge. Exploring Leibniz''s contributions to logic, mathematics, physics, and metaphysics, she considers how his theories sat alongside his concerns with politics, diplomacy, and a broad range of practical reforms: juridical, economic, administrative, technological, medical, and ecclesiastical. Discussing Leinbniz''s theories of possible worlds, she concludes by looking at what is ultimately real in this actual world that we experience, the good and evil there is in it, and Leibniz''s response to the problem of evil through his theodicy. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCONCLUSION; REFERENCES; FURTHER READING; INDEX","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732769845591,"sku":"9780198718642","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"journey-to-the-edge-of-reason-9780198866435","title":"Journey to the Edge of Reason","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e A remarkable account of Kurt Gödel, weaving together creative genius, mental illness, political corruption, and idealism in the face of the turmoil of war and upheaval. \u003c\/b\u003eAt age 24, a brilliant Austrian-born mathematician published a mathematical result that shook the world. Nearly a hundred years after Kurt Gödel''s famous 1931 paper On Formally Undecidable Propositions appeared, his proof that every mathematical system must contain propositions that are true - yet never provable within that system - continues to pose profound questions for mathematics, philosophy, computer science, and artificial intelligence. His close friend Albert Einstein, with whom he would walk home every day from Princeton''s famous Institute for Advanced Study, called him the greatest logician since Aristotle. He was also a man who felt profoundly out of place in his time, rejecting the entire current of 20th century philosophical thought in his belief that mathematical truths existed independent of the\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eBudiansky opens up the history of a time where great progress was achieved in foundations of mathematics against the backdrop of the Second World War. This is an easily accessible account for those who did not have the chance to meet Kurt Gödel in person...For the generations that possibly enjoy the t-shirt version of Gödel's work, I would hope that the variety of his work would spark more diversified Gödel merchandise * Annika Kanckos, Metascience *\u003cbr\u003eIt would be easy to fall into the trap of repeating somewhat exaggerated anecdotes and to ridicule the leading character of this biography. Therefore, it is a pleasure to read a book on the life of Gödel that does all but that. The book offers a serious and unapologetic account of Gödel's life ... The new take on the topics is refreshing and brings the past to life through a coherent narrative. * Annika Kanckos, Metascience *\u003cbr\u003eSelected as a 2021 Book of the Year in the Times Literary Supplement\u003cbr\u003ewonderfully engrossing * Adam Gopnik, The New Yorker *\u003cbr\u003eBudiansky, for all his tremendous efforts and exhaustive interrogations of Gödel's times and places, acquaintances and offices, can only leave us, at the end, with an immeasurably enriched version of Gödel the wise child. It's an undeniably distracting and reductive picture. But - and this is the trouble - it's not wrong. * Simon Ings, Spectator *\u003cbr\u003eJourney to the Edge of Reason covers [Gödel's life and work] engagingly and clearly, which is quite a feat given the difficulty of the material. The author... also manages successfully to convey Gödel's naivety, eccentricity and paranoia as well as his genius. * Nick Spencer, Financial Times *\u003cbr\u003eIn this excellent new biography, Stephen Budiansky introduces the reader to Gödel's stunning achievements in logic, illuminates his devastating mental illness and considers how the two might be related. * Cheryl Misak, Times Literary Supplement *\u003cbr\u003eAn engaging read, both on a personal and professional level. * David Lorimer, Paradigm Explorer *\u003cbr\u003eOne of the great geniuses of the 20th century, barely known outside the academy today, receives a much-needed expert biographical treatment ... An outstanding biography of a man of incomprehensible brilliance. * Kirkus reviews *\u003cbr\u003eJourney to the Edge of Reason is an intimate and haunting portrait of one of the most elusive gods on Princeton's Mt. Olympus. A triumph of research and a wonderful read. * Sylvia Nasar, author of A Beautiful Mind *\u003cbr\u003eKurt Gödel's mathematical results on incompleteness and undecidable propositions leave it up to us, as individuals, to choose whether to mourn these limits to the power of formal systems, or celebrate his proof that even the most rigid numerical bureaucracy contains the tools by which higher truth will always be able to effect an escape. Stephen Budianksy's Journey to the Edge of Reason expertly and humanely frames these results between Gödel's childhood under the dark shadow of the Austrian and Nazi bureaucracies, his escape to America, his descent into physical and mental illness, and his achievement of a reconciliation between spiritual faith and scientific proof. * George Dyson, author of Analogia and Turing's Cathedral *\u003cbr\u003eA painstakingly researched and lucidly presented biography—a close-up of one of the most influential and enigmatic thinkers of the twentieth century—full of vivid detail and sharp historical insight. * Karl Sigmund, professor of mathematics, University of Vienna, and author of Exact Thinking in Demented Times *\u003cbr\u003eA brilliant biography of one of the most original thinkers of all time, Journey to the Edge of Reason is as deep and precise as the genius it describes. In a paradox befitting Gödel himself, it takes a tale of logic and its limits and finds, at its heart, something strangely soulful and sympathetic. * Steven Strogatz, professor of mathematics, Cornell University, and author ofInfinite Powers *\u003cbr\u003ePrepare yourself for a great adventure and fascinating book that can be picked up at ease and read at pace..Budiansky provides a gripping and interesting dialogue fitting the great story of this fascinating figure...an excellent book. * Kenny Green, Mathematics Today *","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732821651799,"sku":"9780198866435","price":19.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198866435.jpg?v=1719998544"},{"product_id":"morality-and-mathematics-9780198898863","title":"Morality and Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTo what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they ar\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eReview from previous edition Morality and Mathematics is an outstanding achievement and will be a standard point of reference for future work on the topics of which it treats. * Hallvard Lillehammer, International Journal for the Study of Skepticism *\u003cbr\u003eClarke-Doane ... brings remarkable expertise and ... research to [this project]. The main argument [is] copiously defended in this lucid but highly technical treatise. ... Underlying [the argument] is the important distinction between realism and objectivity. * Sheila Mason, CHOICE *\u003cbr\u003eClarke-Doane's book offers a coherent and plausible set of answers to the notorious epistemological questions provoked by morality, and to the analogous questions that are provoked by mathematics. It is striking for its creativity, its rigorous arguments, its many subtle but important distinctions, its unusual breadth of expertise (covering the philosophy of language, metaphysics, epistemology, philosophy of mathematics, and meta-ethics), and its rational control of a daunting battery of interacting considerations from these various branches of the subject. Exceptionally impressive philosophical talent and maturity are on display here. Needless to say, we probably haven't yet been given the final truth about these matters. But it's certain that anyone aiming to do better will have to grapple with Clarke-Doane's formidable arguments and conclusions. * Paul Horwich, New York University *\u003cbr\u003eJustin Clarke-Doane raises fascinating and important issues about evolutionary debunking arguments. He argues that insofar as our knowledge of the evolutionary origins of morality poses a challenge for moral realism, exactly similar difficulties will arise for mathematical realism. * Matthew Braddock, Andreas Mogensen, and Walter Sinnott-Armstrong, PEASoup *\u003cbr\u003eClarke-Doane's overarching metaphilosophical conclusion ... is ... that across a large range of philosophical debates ... the real philosophical questions are not metaphysical ... but practical, about which concepts to use. ... [W]e are left with a purely practical question of which framework to pick, which cannot itself be justified by appeal to more normativity. ...[P]erhaps a monist response can be afforded via an adaptation of Quine's response to Carnap. ... But whether or not this response ... can be made to fly, Clarke-Doane's achievement ... is substantial. ... [I]ncreased specialization makes serious engagement across subfields of philosophy a challenge. Morality and Mathematics rises to this challenge, and will serve as a springboard to further serious engagement across the subdisciplines * Mary Leng, Mind *\u003cbr\u003eThis excellent book ... compares morality and mathematics. Their similarities and differences are not what one might naively supposee, as the author demonstrates. The book is highly recommended to philosophers interested in both subjects, and to anyone who seeks a global understanding of how morality and mathematics fit into our belief system. ... The idea that practical questions alone resist deflation in the face of pluralist ... realism ... facilitated by the tension between realism and objectivity ... mak[es] ... for a rather striking metaphilosophical vision. * Michael Bevan \u0026amp; Alexander Paseau, Philosophia Mathematica *\u003cbr\u003eIn this brilliantly original book, Justin Clarke-Doane ... has upended many long-held views on morality and mathematics. ... Accept it or reject it, it manifests Clarke-Doane's extraordinary combination of philosophical imagination and logical skill, and what I have discussed in this review is only a small sample of the philosophical gold to be found in his book. * David Gordon, Philosophical Quarterly *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction 1: Realism, Ontology, and Objectivity 2: Self-Evidence, Proof, and Disagreement 3: Observation and Indispensability 4: Genealogical Debunking Arguments 5: Explaining our Reliability 6: Realism, Objectivity, and Evaluation Conclusion","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732829417815,"sku":"9780198898863","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"category-theory-9780199237180","title":"Category Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCategory theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda''s lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe book is well organised and very well written. The presentation of the material is from the concrete to the abstract, proofs are worked out in detail and the examples and the exercises spread throughout the text mark a pleasant rhythm for its reading. In all, Awodey's Category Theory is a very nice and recommendable introduction to the subject. * Pere Pascual, EMS Newsletter *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ; 1. Categories ; 2. Abstract Structures ; 3. Duality ; 4. Groups and Categories ; 5. Limits and Colimits ; 6. Exponentials ; 7. Naturality ; 8. Categories of Diagrams ; 9. Adjoints ; 10. Monads and Algrebras ; References ; Solutions to Selected Exercises ; Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732837577047,"sku":"9780199237180","price":61.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199237180.jpg?v=1719998611"},{"product_id":"reactionary-mathematics-9780226826721","title":"Reactionary Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The complex relationship between tradition and modernization is the pulsing heart of this engaging book. Beside a valuable historical analysis, \u003ci\u003eReactionary Mathematics\u003c\/i\u003e offers an interesting and useful synthesis vision to help us understand, in these times of rapid and convulsive transformation, the mathematics of the present and, most importantly, the reasons for the mathematics that will come.” * Nature *\u003cbr\u003e“\u003ci\u003eReactionary Mathematics\u003c\/i\u003e is an ambitious book that is more than just a history of mathematics but an episode in the history of reason, furnished with a delightful display of different kinds of evidence, from archival documents to political satires to theological treatises to paintings to mathematics textbooks. . . . [It] is a deftly written and timely book brimming with empirical, conceptual and historiographical insights.” * British Journal for the History of Science *\u003cbr\u003e\"For anyone interested in the \"politics of mathematical modernity,\" this book shows how allegiances to particular types or styles of mathematics may indeed be related to Neapolitan academicians' personal responses to the urgent political pressures of their day.\" * Choice *\u003cbr\u003e“One notable strength of Mazzotti’s book is its ability to transition seamlessly between different levels of analysis. It connects an in-depth historical exploration of a specific local context, such as Naples, with the social and political constraints unique to that site. Simultaneously, it addresses major upheavals and broad conceptual changes such as the evolution of purity, rigor, and abstraction and the very definition of 'modernity' in mathematics. In doing so, the book tackles a critical methodological challenge in the social history of mathematics, bridging the gap between the claim of universality associated with mathematical knowledge and the intricate study of the local contexts and social practices that underpin the production of such knowledge. Mazzotti’s thought-provoking narrative not only demonstrates . . . that mathematics is intimately connected to its cultural, social and political context, but it also prompts readers to consider new avenues of research.” * Historia Mathematica *\u003cbr\u003e“Mazzotti offers us a superbly crafted historical study of the interweaving of mathematics, politics, religion, social order, and even olive oil presses in the Kingdom of Naples around 1800. This gives him a distinctive, striking platform from which to address big questions: the relationship between science and politics, the connections between mathematics and modernity, and how we should understand mathematics’ past.” -- Donald MacKenzie, University of Edinburgh\u003cbr\u003e“Mazzotti has written a fascinating case study of ‘mathematical resistance’ in late eighteenth- and nineteenth-century Naples. On the most fundamental level, the book’s exploration of ‘mathematics as politics’ observes the reciprocal interactions between the mathematical imagination of historical actors and their sociopolitical circumstances. Mazzotti’s keen attention to the political actors themselves tells a very human story of mathematics, and of the events and changes that led to the development of this seemingly quixotic Neapolitan resistance to mathematical modernity.” -- Sean Cocco, Trinity College\u003cbr\u003e“A landmark account of Neapolitan reactionary mathematics in context that contributes insightfully to the histories of Naples, reaction, and mathematics in their separate and interacting respects.” -- Michael Barany, University of Edinburgh\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction: Mathematics as Social Order\u003cbr\u003e 1 Adventures of the Analytic Reason\u003cbr\u003e 2 Mathematics at the Barricades\u003cbr\u003e 3 Empire of Analysis\u003cbr\u003e 4 The Shape of the Kingdom\u003cbr\u003e Intermezzo: Algorithm or Intuition?\u003cbr\u003e 5 The Geometry of Reaction\u003cbr\u003e 6 A Scientific Counterrevolution\u003cbr\u003e 7 A Reactionary Reason\u003cbr\u003e 8 Mathematical Purity as Return to Order\u003cbr\u003e Notes\u003cbr\u003e Bibliography\u003cbr\u003e Index","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":48732930965847,"sku":"9780226826721","price":85.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226826721.jpg?v=1719998998"},{"product_id":"reactionary-mathematics-a-genealogy-of-purity-9780226826745","title":"Reactionary Mathematics A Genealogy of Purity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The complex relationship between tradition and modernization is the pulsing heart of this engaging book. Beside a valuable historical analysis, \u003ci\u003eReactionary Mathematics\u003c\/i\u003e offers an interesting and useful synthesis vision to help us understand, in these times of rapid and convulsive transformation, the mathematics of the present and, most importantly, the reasons for the mathematics that will come.” * Nature *\u003cbr\u003e“\u003ci\u003eReactionary Mathematics\u003c\/i\u003e is an ambitious book that is more than just a history of mathematics but an episode in the history of reason, furnished with a delightful display of different kinds of evidence, from archival documents to political satires to theological treatises to paintings to mathematics textbooks. . . . [It] is a deftly written and timely book brimming with empirical, conceptual and historiographical insights.” * British Journal for the History of Science *\u003cbr\u003e\"For anyone interested in the \"politics of mathematical modernity,\" this book shows how allegiances to particular types or styles of mathematics may indeed be related to Neapolitan academicians' personal responses to the urgent political pressures of their day.\" * Choice *\u003cbr\u003e“One notable strength of Mazzotti’s book is its ability to transition seamlessly between different levels of analysis. It connects an in-depth historical exploration of a specific local context, such as Naples, with the social and political constraints unique to that site. Simultaneously, it addresses major upheavals and broad conceptual changes such as the evolution of purity, rigor, and abstraction and the very definition of 'modernity' in mathematics. In doing so, the book tackles a critical methodological challenge in the social history of mathematics, bridging the gap between the claim of universality associated with mathematical knowledge and the intricate study of the local contexts and social practices that underpin the production of such knowledge. Mazzotti’s thought-provoking narrative not only demonstrates . . . that mathematics is intimately connected to its cultural, social and political context, but it also prompts readers to consider new avenues of research.” * Historia Mathematica *\u003cbr\u003e“Mazzotti offers us a superbly crafted historical study of the interweaving of mathematics, politics, religion, social order, and even olive oil presses in the Kingdom of Naples around 1800. This gives him a distinctive, striking platform from which to address big questions: the relationship between science and politics, the connections between mathematics and modernity, and how we should understand mathematics’ past.” -- Donald MacKenzie, University of Edinburgh\u003cbr\u003e“Mazzotti has written a fascinating case study of ‘mathematical resistance’ in late eighteenth- and nineteenth-century Naples. On the most fundamental level, the book’s exploration of ‘mathematics as politics’ observes the reciprocal interactions between the mathematical imagination of historical actors and their sociopolitical circumstances. Mazzotti’s keen attention to the political actors themselves tells a very human story of mathematics, and of the events and changes that led to the development of this seemingly quixotic Neapolitan resistance to mathematical modernity.” -- Sean Cocco, Trinity College\u003cbr\u003e“A landmark account of Neapolitan reactionary mathematics in context that contributes insightfully to the histories of Naples, reaction, and mathematics in their separate and interacting respects.” -- Michael Barany, University of Edinburgh\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction: Mathematics as Social Order\u003cbr\u003e 1 Adventures of the Analytic Reason\u003cbr\u003e 2 Mathematics at the Barricades\u003cbr\u003e 3 Empire of Analysis\u003cbr\u003e 4 The Shape of the Kingdom\u003cbr\u003e Intermezzo: Algorithm or Intuition?\u003cbr\u003e 5 The Geometry of Reaction\u003cbr\u003e 6 A Scientific Counterrevolution\u003cbr\u003e 7 A Reactionary Reason\u003cbr\u003e 8 Mathematical Purity as Return to Order\u003cbr\u003e Notes\u003cbr\u003e Bibliography\u003cbr\u003e Index","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":48732931064151,"sku":"9780226826745","price":30.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226826745.jpg?v=1719998999"},{"product_id":"science-and-an-african-logic-9780226853918","title":"Science and an African Logic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDoes two and two equal four? Ask someone and they should answer yes. An equation such as this seems the very definition of certainty, but is it? Helen Verran describes how she went from the conclusion that logic and maths are culturally relative, to a new understanding of all generalizing logic.","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":48732935127383,"sku":"9780226853918","price":26.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226853918.jpg?v=1719999013"},{"product_id":"in-pursuit-of-zeta3-9780691247649","title":"In Pursuit of Zeta3","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Nahin’s style is entertaining, directly addressing his readers. . . . Highly recommended.\"\u003cb\u003e---Adhemar Bultheel, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This book will be both enjoyable and a rich source of useful as well as intriguing information to a wide range of readers.\"\u003cb\u003e---Michael Th. Rassias, \u003ci\u003ezbMATH Open\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"I thoroughly enjoyed this book!\"\u003cb\u003e---Jonathan Shock, \u003ci\u003eMathemafrica.org\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"N\/A\"\u003cb\u003e---Andrew Simoson, \u003ci\u003eThe Mathematical Intelligencer\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48735991300439,"sku":"9780691247649","price":16.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691247649.jpg?v=1723810433"},{"product_id":"inside-mathforum-org-9781107138858","title":"Inside Mathforum.Org","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe internet has dramatically transformed social space and time for many people in many different contexts. This dramatic warping of the social fabric has happened slowly over time as digital technologies have evolved and internet speeds have increased. While we are all aware of these changes, the impact is often little understood. There are few monographs about social groups made possible by the internet, and even fewer about educational communities made possible through digital technologies. Inside Mathforum.org details the ways that digital media are used to enhance the practices that teachers and students of mathematics engage in. The book also shows how different kinds of mathematical conversations and interactions become possible through the digital media. Unlike many other educational uses of digital media, the Math Forum''s community has provided online resources and sustained support for teachers and students, and it leads the way in showing the power of digital media for educ\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This case study of The Math Forum highlights the contributions to mathematics education made by this online math resource center, making clear the essential components of the technology, invisible elements of the social structure its design invites and supports, and the cultural elements (e.g., values, ethos) that affected its original design and that have sustained its life over two decades. Shumar's analysis suggests lessons about building and sustaining communities of practice that have implications for teacher learning, online education more generally, and design of a wide range of other spaces for transformation.' Janet L. Kolodner, Chief Learning Scientist, Concord Consortium\u003cbr\u003e'One of the pleasures of reading Shumar's ethnography, Inside Mathforum.org, is the care he takes in portraying how larger neoliberal structures, digital technologies, and the affordances of the Math forum community unfold over the long term, almost twenty years. This portrait shows different strategic moments in the existence of Tthe Math Forum whose creative staff and online participants facilitate the emergence of community spaces both in spite of and because of the increasing commodification of the university. Rather than situate himself against some literature, his more intellectually generous approach is to use that literature to generate a sense of a broad interdisciplinary field where both structure, agency, and indeterminacy allow us to understand the potential for learning and pitfalls for organization faced by the Math Forum. Brilliant ideas and exegesis emerge on every page.' Jonathan Church, Arcadia University, Pennsylvania\u003cbr\u003e'Many years before Khan Academy, a distributed network of math educators were conducting Problems of the Week and inspiring learners. In my online learning communities courses, I've always enjoyed teaching with Wesley Shumar's ethnographic research writings on the pioneering Math Forum. This book now provides the ultimate resource on this seminal effort for spawning and sustaining community discourse about mathematics.' Roy Pea, Stanford University, California\u003cbr\u003e'Shumar presents a well-researched analysis of the political and cultural impacts to and the contributions of MathForum.org, as well as the broader scope of the internet in education. An ethnography in method and style, the book is organized in concise, yet dense, sections, offering a discussion that spans ethnography to neoliberalism. The inclusion of figures from the Forum, including the grading rubric and mentoring example, assist in transforming the community from an abstract idea to a tangible place of learning.' C. R. Hebert, Choice\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction; 2. Ethnography with a leading internet-based educational center; 3. History of the Math Forum; 4. Possibilities and their foreclosure in the digital educational economy; 5. Mathematical conversations and mathematical thinking; 6. Mentoring students and faculty with digital technology; 7. Noticing and wondering in a mediated environment; 8. Space, affinity, and consciousness; 9. Identity and online interaction; 10. Conclusion; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738247311703,"sku":"9781107138858","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"mathematics-all-that-matters-9781473601734","title":"Mathematics All That Matters","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eMathematics often gets a bad press. \u003c\/b\u003eDescribing someone as ''calculating'' or ''rational'' is hardly as flattering as being labelled ''artistic'' or ''creative'' and mathematicians in movies or novels are often portrayed as social misfits who rarely get the guy or girl. No wonder some folks say ''oh I don''t care for mathematics, I was never any good at it'' with a wistful sense of pride.\u003cbr\u003e\u003cbr\u003eYet professional mathematicians talk of the subject differently. They look for elegant solutions to problems, revel in playing around with mathematical ideas and talk of the creative nature of mathematics. As the Russian mathematician Sophia Kovalevskaya said It is impossible to be a mathematician without being a poet in soul.\u003cbr\u003e\u003cbr\u003eBy looking at some of the history of mathematics, psychological studies into how we come to know mathematics and key ideas in mathematics itself, this book will, if not make you fall in love with mathematics, then at least come to understand its nature a l\u003c\/p\u003e","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":48739499802967,"sku":"9781473601734","price":11.07,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781473601734.jpg?v=1720052413"},{"product_id":"i-am-a-number-9781603094191","title":"I Am A Number","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis wordless collection of strips by renowned artist\/designer Rian Hughes reveals the lighter side of our obsession with social rankings.\u003cbr\u003e\u003cbr\u003eWhen everyone has a number, everyone knows their place. Lower numbers are better, higher numbers are less important, and that''s just the way it is. But what if that number could change? You might try to buck the system and assert your individuality... or you might end up with a big fat zero.\u003cbr\u003e\u003cbr\u003eBig questions are explored and unexpected answers found in the first solo comics collection from award-winning designer \u0026amp; illustrator Rian Hughes. His whimsical, witty, and insightful strips will make you both smile and consider. Where do you stand in the pecking order? Is your number up? \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e2018 Pubwest Design Awards - Gold Winner for Graphic Album, New Material","brand":"Top Shelf Productions","offers":[{"title":"Default Title","offer_id":48740591468887,"sku":"9781603094191","price":17.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781603094191.jpg?v=1720055099"},{"product_id":"numbers-10-things-you-should-know-9781841885636","title":"Numbers: 10 Things You Should Know","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eUncover the language of our universe - numbers - in this wide-ranging whistle-stop tour of the history and majesty of mathematics.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eOur world simply wouldn't function if we didn't have numbers. But where do they come from? Why do we cut cake the wrong way? How can there be different sizes of infinity?\u003cbr\u003e\u003cbr\u003eAll these questions and more are answered in this engaging romp through the history of numbers by acclaimed science writer, Colin Stuart. From the mathematicians who have (and haven't) shouted 'Eureka!' to the theories that affect and inform our everyday lives; \u003ci\u003eNumbers\u003c\/i\u003e shows us that maths was never boring - we were just being taught it in the wrong way.\u003cbr\u003e\u003cbr\u003eConsisting of ten bite-sized essays, there's no better guide to this fundamental science.\u003c\/p\u003e","brand":"Orion Publishing Co","offers":[{"title":"Default Title","offer_id":48742074909015,"sku":"9781841885636","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781841885636.jpg?v=1720059926"},{"product_id":"metamaths-9781843545255","title":"Metamaths","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eOne of the world's greatest mathematicians explains his revolutionary hypothesis about the enigma at the heart of maths: omega. \u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e'Chaitin comes across as a kind of mathematical Richard Feynman, intuitive and high-spirited, irreverent and plain-spoken.' -- Peter Pesic, \u003ci\u003eTLS\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003ci\u003eMeta Maths\u003c\/i\u003e is Gregory Chaitin's exuberant account of his discovery of 'omega': the infinitely long, exquisitely complex and utterly incalculable representation of randomness and unknowability in mathematics. From Euclid to Gödel to Turing, Chaitin's infectious narrative guides us on a spellbinding journey through the historical advances in maths and science that led to his breakthrough discovery. Once there he takes us further, to the very frontiers of scientific thinking. \u003ci\u003eMeta Maths\u003c\/i\u003e shows that mathematics is as much art form as logic, as much science as pure reasoning, and sheds light on what we can ultimately hope to know about the universe and the very nature of life.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eMeta Maths\u003c\/i\u003e is truly idiosyncratic. Informal, chatty and cerebral... it mixes mathematics with Chaitin's outlook on life and philosophy... Great fun. -- Alan Cane * Financial Times *","brand":"Atlantic Books","offers":[{"title":"Default Title","offer_id":48742085460311,"sku":"9781843545255","price":16.19,"currency_code":"GBP","in_stock":false}]},{"product_id":"sequents-and-trees-an-introduction-to-the-theory-and-applications-of-propositional-sequent-calculi-9783030571443","title":"Sequents and Trees: An Introduction to the Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results.  The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained.  Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation.  Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.\u003cbr\u003eAfter a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications.  The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.\u003cbr\u003e\u003ci\u003eSequents and Trees\u003c\/i\u003e is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics.  It will also be of interest to researchers in computer science and philosophers.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Each chapter of the book is structured in a similar way and contains the basic definitions, facts and necessary discussion regarding the key notions, accompanied with new ideas and a wide reference list, followed by the author's clear and approachable style. This book is self-contained, presenting an extensive survey of the applications and usefulness of cut elimination, and seems to be an extremely interesting source not only for logicians and philosophers, but also for researchers in computer science.” (Branislav Boričić, Mathematical Reviews, May, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Analytic Sequent Calculus for CPL.- Gentzen's Sequent Calculus LK.- Purely Logical Sequent Calculus.- Sequent Calculi for Modal Logics.- Alternatives to CPL.- Appendix.\u003cbr\u003e\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743040811351,"sku":"9783030571443","price":41.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030571443.jpg?v=1720063851"},{"product_id":"plato-diagrammatic-reasoning-and-mental-models-9783031276576","title":"Plato, Diagrammatic Reasoning and Mental Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book analyses the role of diagrammatic reasoning in Plato’s philosophy: the readers will realize that Plato, describing the stages of human cognitive development using a diagram, poses a logic problem to stimulate the general reasoning abilities of his readers. Following the examination of mental models in this book, the readers will reflect on what inferences can be useful to approach this kind of logic problem. Plato calls for a collaboration between writer and readers. In this book the readers will examine the connection between diagrams and discovery, realizing the important epistemic role of visualization. They will recognize the crucial role that diagrams play in problem solving. The logic problem elaborated by Plato is addressed considering the epistemic function of mental models. These models introduce to an advanced stage of cognitive development, in which reasoning uses in its investigations a higher-level of mathematical complexity, represented by structuralism.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCHAPTER ONE: \u003cb\u003eIntroduction,\u003c\/b\u003e- CHAPTER TWO: \u003cb\u003eThe \u003ci\u003eCollaboration \u003c\/i\u003ebetween Writer and Reader,\u003c\/b\u003e- CHAPTER THREE: \u003cb\u003eVisual Thinking,\u003c\/b\u003e- CHAPTER FOUR: \u003cb\u003eDiagrammatic Reasoning,\u003c\/b\u003e- CHAPTER FIVE: \u003cb\u003eMental Models,-Chapter 6. \u003c\/b\u003e\u003cb\u003eTheoretical Adulthood and Structuralism\u003c\/b\u003e\u003cp\u003e\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e.\u003cbr\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743078527319,"sku":"9783031276576","price":29.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031276576.jpg?v=1720064016"},{"product_id":"mathematics-for-human-flourishing-9780300258516","title":"Mathematics for Human Flourishing","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Beautifully written, contains well-chosen and interesting mathematical puzzles, and offers an important viewpoint for mathematicians to consider. . . . The book is aimed at a broader audience and is also a call to being more inclusive, to recognising that there are many paths to success.”—Pamela Gorkin, \u003ci\u003eMathematical Intelligencer\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003eAwarded Book of the Year by Aleo Review\u003cbr\u003e\u003cbr\u003eWinner of the Euler Book Prize, sponsored by the Mathematical Association of America\u003cbr\u003e\u003cbr\u003eSelected for the 2021 Phi Beta Kappa Award for Science Short List\u003cbr\u003e\u003cbr\u003e“The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.”—Kevin Hartnett, \u003ci\u003eQuanta Magazine\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “Please read this beautiful, compelling, galvanizing book if you care about mathematics, social justice, or humanity, which I hope is everyone.”—Eugenia Cheng, author of \u003ci\u003eThe Art of Logic in an Illogical World\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “The world desperately needs this all‑embracing and deeply human perspective on what mathematics is and why it matters. The key qualities developed by mathematical thinking are characteristics that we should all value and long for.”—Eddie Woo, author of \u003ci\u003eIt’s a Numberful World\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “I was mesmerized by this unusual, sublime book. Original insights and engaging puzzles made me feel young again, discovering a way to Zen and the Art of Mathematics.”—Nalini Joshi, University of Sydney\u003cbr\u003e  \u003cbr\u003e “Francis Su believes that math can make us better humans—and he leads by example. Every page is a work of generosity and compassion. Plus, the puzzles will haunt you for weeks.”—Ben Orlin, author of \u003ci\u003eMath with Bad Drawings\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “A celebration of mathematics and the human spirit. Learning mathematics enriches our lives, and Su wants everyone to have a seat at the banquet.”—Edward Scheinerman, author ofv\u003ci\u003eThe Mathematics Lover’s Companion\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “A delightful mixture of philosophy, mathematical illustrations, and compassion.”—John Cook, Singular Value Consulting\u003cbr\u003e  \u003cbr\u003e “Francis Su has written a lyrical meditation on the beauty of mathematics and how it connects to our common humanity.”—John Urschel, author of \u003ci\u003eMind and Matter: A Life in Math and Football\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “Su elegantly uncovers the beauty and power of mathematics as they relate to our desires to be loved, trusted, and accepted. A powerful narrative of mathematical beauty, this book is the antidote for a mathematically fixed mindset.”—Talithia Williams, author of \u003ci\u003ePower in Numbers: The Rebel Women of Mathematics\u003c\/i\u003e\u003cbr\u003e  \u003cbr\u003e “This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math Project\u003cbr\u003e\u003cbr\u003e“The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.”—Kevin Hartnett, \u003ci\u003eQuanta Magazine\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e","brand":"Yale University Press","offers":[{"title":"Default Title","offer_id":48864349880663,"sku":"9780300258516","price":12.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780300258516.jpg?v=1722271535"},{"product_id":"i-is-a-strange-loop-9780571360734","title":"I is a Strange Loop","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAlone in a cube that's glowing in the darkness, X is content within its little universe of infinite thought. This solitude is disturbed by the appearance of Y, who insists on exposing X to the richness of the physical world. Each begins to long for what the other has, luring them into a strange loop.\u003cbr\u003e\u003cbr\u003eIn this play for two variables, Marcus du Sautoy and Victoria Gould use mathematics and theatre to navigate the furthest reaches of our world. Through a series of surreal episodes, X and Y tackle some of life's greatest questions: where did the universe come from, does time have an end, do we have free will?\u003cbr\u003e\u003cbr\u003e\u003ci\u003eI is a Strange Loop\u003c\/i\u003e was first performed by the authors at the Barbican Pit, London, in March 2019.\u003cbr\u003e\u003cbr\u003e''\u003ci\u003eI is a Strange Loop\u003c\/i\u003e is a play that plays with ideas, concepts, abstractions and relationships that are, usually, hidden from the sight of ordinary mortals, articulating the ineffable, incarnating the incorporeal, revealing the inconceivable. It make\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'\u003ci\u003eI is a Strange Loop\u003c\/i\u003e is a play that plays with ideas, concepts, abstractions andrelationships that are, usually, hidden from the sight of ordinary mortals, articulatingthe ineffable, incarnating the incorporeal, revealing the inconceivable.It makes us feel we know a great deal more than we do. It is also very funny,utterly compelling and marvellously human.' - Simon McBurney\u003cbr\u003e\u003cbr\u003e'[An] ambitious and stimulating piece.' - \u003ci\u003eFinancial Times\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e'Tackles what it means to be human at a time when advances in technologyand scientific research are hurtling forward with unprecedented speed.' - British Theatre Guide\u003c\/p\u003e","brand":"Faber \u0026 Faber","offers":[{"title":"Default Title","offer_id":48865126121815,"sku":"9780571360734","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780571360734.jpg?v=1722273654"},{"product_id":"humble-pi-9780593084694","title":"Humble Pi","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Penguin Putnam Inc","offers":[{"title":"Default Title","offer_id":48865145094487,"sku":"9780593084694","price":16.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780593084694.jpg?v=1722273748"},{"product_id":"mathematics-in-ancient-iraq-a-social-history-9780691091822","title":"Mathematics in Ancient Iraq  A Social History","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTraces the origins and development of mathematics in the ancient Middle East, from its earliest beginnings in the fourth millennium BCE to the end of indigenous intellectual culture in the second century BCE when cuneiform writing was gradually abandoned.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eWinner of the 2011 Pfizer Award for Best Scholarly Book, History of Science Society One of Choice's Outstanding Academic Titles for 2009 Honourable Mention in the British-Kuwait Friendship Society Prize in Middle Eastern Studies 2009, British Society for Middle Eastern Studies \"[F]ascinating.\"--Edward Rothstein, New York Times \"Robson brings both a profound erudition in cuneiform and a nondogmatic constructionist view of mathematics to tell the history of Mesopotamian mathematics over the three millennia before the Common Era, connecting as she does the mathematical accomplishments to the cultural and societal norms of the day... A magisterial work, lucidly written, certain to endure.\"--M. Schiff, Choice \"Author Robson deals admirably with an enormous scope (more than 3,000 years, with roughly equal space devoted to each 500-year epoch); numerous sources (950 published clay tablets, all of which are available at a simple Website); and the cultural context (social history, an ethnomathematical approach).\"--Mathematics Magazine \"Robson's book is a wonderful summary of what we know so far, and will be the standard for this generation, but the potential is there for far more research to teach us even more about mathematics in ancient Iraq.\"--Victor J. Katz, Mathematical Reviews \"For archaeologists and archaeologically-minded historians ... Robson provide[s] significant new insights into the mathematics of ancient civilisations, while challenging us to consider how language, material culture, and socio-technical practices are integrated, not only in mathematics, but in many domains.\"--Stephen Chrisomalis, Antiquity \"The wealth of detail and breadth of scope make this an excellent resource for a wide variety of readership. It can be read as one great narrative sweep, or one can bear down on a particular facet. The work is a huge advance in the presentation of modern scholarship on ancient mathematics to interested readers, specialist and non-specialist alike.\"--Duncan J. Melville, Historia Mathematica \"Nothing comparable has been done before, and it has been a great pleasure to read the book, from which I have learned much.\"--Jens Hoyrup, Mathematical Intelligencer \"Eleanor Robson's book Mathematics in Ancient Iraq is presently unique and will surely become a classic in the history of early mathematics. Despite the meticulous and detailed presentation of a representative selection of available sources, the book is very readable and captures the attention of the interested reader from the first to the last page. I recommend it to anyone who would like to learn something about the fascinating story of the development of mathematical activities in Mesopotamia.\"--Peter Damerow, Notices of the AMS \"[Mathematics in Ancient Iraq] is argued passionately, persuasively and, I am pleased to add, enjoyably.\"--Bob Berghout, Australian Mathematical Society Gazette \"Mathematics in Ancient Iraq fills a gap that has existed for a very long time.\"--Annette Imhausen, British Society for the History of Maths \"Robson displays a confidence, familiarity, and breadth of scholarship that is impressive and inspiring. She epitomizes a new wave of research in the history of mathematics. She provides context, setting, and interpretative themes for generations of scholars to come, whether they will embrace them or resist them. Indeed, Robson's work is more than just a social history--it is emblematic of a new approach to this discipline. The details will excite specialists, the generalities will delight the uninitiated. 'Sparkling' indeed, this work is guaranteed to be an influential and foundational reference book, indispensable to the collections of the many disciplines it draws from.\"--Clemency Montelle, Journal of the American Oriental Society \"Robson, as a professional assyriologist, is preeminently well positioned to write a history that situates Mesopotamian mathematics in its ancient social and intellectual context; and whether or not one always agrees with her interpretations of the mathematics, her competence in these aspects is nowhere in doubt.\"--Alexander Jones, British Journal for the History of Science \"[T]he book is a very significant contribution to the history of mathematics. It is well written, solidly founded and argued, and easy to understand. It is a fine and important addition to the literature on Babylonian mathematics, and it will be very useful to readers from both inside and outside the field. The book is warmly recommended to everyone who is interested in mathematics and its history, in ancient cultures, or in science seen as an integrated part of culture, and to the broader public of historians of early science or Mesopotamian culture.\"--Lis Brack-Bernsen, Journal of World History \"The book contains numerous charts, tables, images and databases that help us understand the issues addressed. It is excellently documented and it contains a comprehensive and up to date bibliography. Eleanor Robson is a scholar who commands the field that she investigates.\"--Piedad Yuste, Metascience \"[T]he publication of a book of this kind is very welcome. Nothing like it has been published before, and it is going to be immensely helpful to both writers and readers of future articles and books about the subject.\"--Joran Friberg, Archive Fur Orientforschung\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Figures xi  List of Tables xvii  Preface xxi  Acknowledgments xxv      Chapter One: Scope, Methods, Sources 1  1.1 The Subject: Ancient Iraq and Its Mathematics 1  1.2 The Artefacts: Assyriological and Mathematical Analysis 8  1.3 The Contexts: Textuality, Materiality, and Social History 17      Chapter Two: Before the Mid-Third Millennium 27  2.1 Background and Evidence 28  2.2 Quantitative Management and Emerging Statehood 33  2.3 Enumeration and Abstraction 40  2.4 Symmetry, Geometry, and Visual Culture 45  2.5 Conclusions 51      Chapter Three: The Later Third Millennium 54  3.1 Background and Evidence 55  3.2 Maps, Plans, and Itineraries: Visual and Textual Representations of Spatial Relationships 60  3.3 Accounting for Time and Labour: Approximation, Standardisation, Prediction 67  3.4 The Development of the Sexagesimal Place Value System (SPVS) 75  3.5 Conclusions 83      Chapter Four: The Early Second Millennium 85  4.1 Background and Evidence 86  4.2 Metrology, Multiplication, Memorisation: Elementary Mathematics Education 97  4.3 Words and Pictures, Reciprocals and Squares 106  4.4 Measurement, Justice, and the Ideology of Kingship 115  4.5 Conclusions 123      Chapter Five: Assyria 125  5.1 Background and Evidence 126  5.2 Palatial and Mercantile Numeracy in Early Assyria 129  5.3 Counting Heads, Marking Time: Quantifi cations in Royal Inscriptions and Records 136  5.4 Aru: Number Manipulation in Neo-Assyrian Scholarship 143  5.5 Conclusions 149      Chapter Six: The Later Second Millennium 151  6.1 Background and Evidence 151  6.2 Tabular Accounting in Southern Babylonia 157  6.3 Land Surveyors and Their Records in Northern Babylonia 166  6.4 Quantifi cation as Literary Device in the Epic of Gilgames 177  6.5 Conclusions 181      Chapter Seven: The Early First Millennium 183  7.1 Background and Evidence 184  7.2 Libraries and Schools: The Formalisation of the First-Millennium Scribal Curriculum 192  7.3 Home Economics: Numeracy in a Mid-First-Millennium Urban Household 198  7.4 Measuring Houses, Maintaining Professionalism 206  7.5 Conclusions 212      Chapter Eight: The Later First Millennium 214  8.1 Background and Evidence 215  8.2 Babylon: Mathematics in the Service of Astronomy? 220  8.3 Achaemenid Uruk: The Sangu-Ninurta and Ekur-z?kir Families 227  8.4 Seleucid Uruk: The Hunzu and Sin-leqi-unninni Families 240  8.5 Conclusions 260      Chapter Nine: Epilogue 263  9.1 The Big Picture: Three Millennia of Mathematics in Ancient Iraq 263  9.2 Ancient Mathematics in the Modern World 268  9.3 Inside Ancient Mathematics: Translation, Representation, Interpretation 274  9.4 The Worlds of Ancient Mathematics: History, Society, Community 284  9.5 Conclusions 288      Appendix A: Metrological Systems 291  Appendix B: Published Mathematical Tablets 299  Notes 345  Bibliography 373  Index of Tablets 409  Subject Index 425","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865517470039,"sku":"9780691091822","price":59.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691091822.jpg?v=1722274352"},{"product_id":"the-mathematics-of-egypt-mesopotamia-china-india-and-islam-9780691114859","title":"The Mathematics of Egypt Mesopotamia China India","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides a collection of English translations of mathematical texts from five important ancient and medieval non-Western mathematical cultures, and puts them into historical and mathematical context. This book is intended for mathematics teachers who want to use non-Western mathematical ideas in the classroom.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eJoseph Warren Dauben, Winner of the 2012 Albert Leon Whiteman Memorial Prize, American Mathematical Society \"This pioneering work provides English translations of mathematical texts from each of these regions and cultures, and a better understanding of their contributions to mathematics. There are nuggets of information difficult to find elsewhere. The use of non-mathematical sources, particularly letters and administrative documents from Egypt and Mesopotamia, reveals the practical applications of mathematics and the scribes who composed and used the documents...An essential resource for anyone wishing to know more about how the mathematics of the different regions influenced and shaped the development of world mathematics.\"--George Gheverghese Joseph, Nature \"We're aware that the ancient cultures were mathematically advanced. Now translations of early texts from five key regions are available together for the first time, and put into context by experts.\"--Nature Physics \"The corrections to the Eurocentrism that understandably characterized Western assays of the intellectual history of the planet early on must inevitably be applied to the history of mathematics. Editor Katz and his scholarly coauthors have greatly advanced the process with this one-volume sourcebook...The introductory essays that precede each section are lucidly written, well within the reach of an undergraduate math major. Katz asks more or less rhetorically 'how much effect the mathematics of these civilizations had on what is now world mathematics of the twenty-first century.' This invaluable book will help significantly in formulating an answer.\"--M. Schiff, Choice \"This book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.\"--L'Enseignement Mathematique \"The Mathematics of Egypt, Mesopotamia, China, India, and Islam is a wonderful collection, for which Victor Katz is to be commended. This book is a one-stop source for numerous original mathematical texts in translation. I cannot overemphasize how wonderful it is to have this large, exquisite selection of ... mathematical texts together in one volume... Every history of mathematics teacher will want a copy of this book in their personal library as well as in the library of their college or university.\"--James V. Rauff, Mathematics and Computer Education \"What we have here is a useful selection, one that should be of interest to specialists in world history or in the history of the sciences in any of these culture areas and, in particular, to scholars who are engaged with the history of mathematics as specialists or because of its role as a tool.\"--Tom Archibald, Isis \"[This] is the biggest sourcebook containing the newest fruit of historical research and that is why the book can replace older sources for the history of mathematics.\"--EMS Newsletter\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix Permissions xi Introduction 1   Chapter 1: Egyptian Mathematics Annette Imhausen Preliminary Remarks 7 I. Introduction 9 a. Invention of writing and number systems 13 b. Arithmetic 14 c.Metrology 17 II. Hieratic Mathematical Texts 17 a. Table texts 18 b. Problem texts 24 III. Mathematics in Administrative Texts 40 a. Middle Kingdom texts: The Reisner papyri 40 b. New Kingdom texts: Ostraca from Deir el Medina 44 IV. Mathematics in the Graeco-Roman Period 46 a. Context 46 b. Table texts 47 c. Problem texts 48 V. Appendices 52 a. Glossary of Egyptian terms 52 b. Sources 52 c. References 54   Chapter 2: Mesopotamian Mathematics Eleanor Robson I. Introduction 58 a. Mesopotamian mathematics through Western eyes 58 b.Mathematics and scribal culture in ancient Iraq 62 c. From tablet to translation 65 d. Explananda 68 II. The Long Third Millennium, c. 3200-2000 BCE 73 a. Uruk in the late fourth millennium 73 b. Shuruppag in the mid-third millennium 74 c. Nippur and Girsu in the twenty-fourth century BCE 76 d. Umma and Girsu in the twenty-first century BCE 78 III. The Old Babylonian Period, c. 2000-1600 BCE 82 a. Arithmetical and metrological tables 82 b. Mathematical problems 92 c. Rough work and reference lists 142 IV. Later Mesopotamia, c. 1400-150 BCE 154 V. Appendices 180 a. Sources 180 b. References 181   Chapter 3: Chinese Mathematics Joseph W. Dauben Preliminary Remarks 187 I. China: The Historical and Social Context 187 II. Methods and Procedures: Counting Rods, The \"Out-In\" Principle 194 III. Recent Archaeological Discoveries: The Earliest Yet-Known Bamboo Text 201 IV. Mathematics and Astronomy: The Zhou bi suan jing and Right Triangles (The Gou-gu or \"Pythagorean\" Theorem) 213 V. The Chinese \"Euclid\", Liu Hui 226 a. The Nine Chapters 227 b. The Sea Island Mathematical Classic 288 VI. The \"Ten Classics\" of Ancient Chinese Mathematics 293 a. Numbers and arithmetic: The Mathematical Classic of Master Sun 295 b. The Mathematical Classic of Zhang Qiujian 302 VII. Outstanding Achievements of the Song and Yuan Dynasties (960-1368 CE) 308 a. Qin Jiushao 309 b. Li Zhi (Li Ye) 323 c. Yang Hui 329 d. Zhu Shijie 343 VIII. Matteo Ricci and Xu Guangxi, \"Prefaces\" to the First Chinese Edition of Euclid's Elements (1607) 366 IX. Conclusion 375 X. Appendices 379 a. Sources 379 b. Bibliographic guides 379 c. References 380   Chapter 4: Mathematics in India Kim Plofker I. Introduction: Origins of Indian Mathematics 385 II. Mathematical Texts in Ancient India 386 a. The Vedas 386 b. The S'ulbasutras 387 c. Mathematics in other ancient texts 393 d. Number systems and numerals 395 III. Evolution of Mathematics in Medieval India 398 a.Mathematics chapters in Siddhanta texts 398 b. Transmission of mathematical ideas to the Islamic world 434 c. Textbooks on mathematics as a separate subject 435 d. The audience for mathematics education 477 e. Specialized mathematics: Astronomical and cosmological problems 478 IV. The Kerala School 480 a. Madhava, his work, and his school 480 b. Infinite series and the role of demonstrations 481 c. Other mathematical interests in the Kerala school 493 V. Continuity and Transition in the Second Millennium 498 a. The ongoing development of Sanskrit mathematics 498 b. Scientific exchanges at the courts of Delhi and Jaipur 504 c. Assimilation of ideas from Islam; mathematical table texts 506 VI. Encounters with Modern Western Mathematics 507 a. Early exchanges with European mathematics 507 b. European versus \"native\" mathematics education in British India 508 c. Assimilation into modern global mathematics 510 VII. Appendices 511 a. Sources 511 b. References 512   Chapter 5: Mathematics in Medieval Islam J. Lennart Berggren I. Introduction 515 II. Appropriation of the Ancient Heritage 520 III. Arithmetic 525 IV. Algebra 542 V. Number Theory 560 VI. Geometry 564 a. Theoretical geometry 564 b. Practical geometry 610 VII. Trigonometry 621 VIII. Combinatorics 658 IX. On mathematics 666 X. Appendices 671 a. Sources 671 b. References 674   Contributors 677 Index 681","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865517863255,"sku":"9780691114859","price":100.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691114859.jpg?v=1722274352"},{"product_id":"the-mathematics-of-the-heavens-and-the-earth-9780691129730","title":"The Mathematics of the Heavens and the Earth","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents the history in English of the origins and early development of trigonometry. This book identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and examines the revolutionary discoveries of Hipparchus. It traces trigonometry's development into a full-fledged mathematical discipline in India and Islam.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Fans of the history of mathematics will be richly rewarded by this exhaustively researched book, which focuses on the early development of trigonometry... Finally, the generous and lucid explanations provided throughout the text make Van Brummelen's history a rewarding one for the mathematical tourist.\"--Mathematics Teacher \"[T]his new and comprehensive history of trigonometry is more than welcome--even more so because it is the first in English... [T]his book will be appreciated by many with an interest--general or more specific--in the history of mathematics.\"--Steven Wepster, Centaurus \"[T]his book will have wide appeal, for students, researchers, and teachers of history and\/or trigonometry. The excerpts selected are balanced and their significances well articulated... It is a book written by an expert after many years of exposure to individual sources and in this way Van Brummelen uniquely advances the field. The book will no doubt become a necessary addition to the libraries of mathematicians and historians alike.\"--Clemency Montelle and Kathleen M. Clark, Aestimatio \"Van Brummelen's history does far more than simply fill a vacant spot in the historical literature of mathematics. He recounts the history of trigonometry in a way that is both captivating and yet more than satisfying to the crankiest and most demanding of scholars... The Mathematics of the Heavens and the Earth should be a part of every university library's mathematics collection. It's also a book that most mathematicians with an interest in the history of the subject will want to own.\"--Rob Bradley, MAA Reviews \"I highly recommend the book to all those interested in the way in which the ancient people solve their practical problems and hope that the next volume of this interesting history of spherical and plane trigonometry will appear soon.\"--Cristina Blaga, Studia Mathematica\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi The Ancient Heavens 1   Chapter 1: Precursors 9 What Is Trigonometry? 9 The Seqed in Ancient Egypt 10 * Text 1.1 Finding the Slope of a Pyramid 11 Babylonian Astronomy, Arc Measurement, and the 360  Circle 12 The Geometric Heavens: Spherics in Ancient Greece 18 A Trigonometry of Small Angles? Aristarchus and Archimedes on Astronomical Dimensions 20 * Text 1.2 Aristarchus, the Ratio of the Distances of the Sun and Moon 24   Chapter 2: Alexandrian Greece 33 Convergence 33 Hipparchus 34 A Model for the Motion of the Sun 37 * Text 2.1 Deriving the Eccentricity of the Sun's Orbit 39 Hipparchus's Chord Table 41 The Emergence of Spherical Trigonometry 46 Theodosius of Bithynia 49 Menelaus of Alexandria 53 The Foundations of Spherical Trigonometry: Book III of Menelaus's Spherics 56 * Text 2.2 Menelaus, Demonstrating Menelaus's Theorem 57 Spherical Trigonometry before Menelaus? 63 Claudius Ptolemy 68 Ptolemy's Chord Table 70 Ptolemy's Theorem and the Chord Subtraction\/Addition Formulas 74 The Chord of 1  76 The Interpolation Table 77 Chords in Geography: Gnomon Shadow Length Tables 77 * Text 2.3 Ptolemy, Finding Gnomon Shadow Lengths 78 Spherical Astronomy in the Almagest 80 Ptolemy on the Motion of the Sun 82 * Text 2.4 Ptolemy, Determining the Solar Equation 84 The Motions of the Planets 86 Tabulating Astronomical Functions and the Science of Logistics 88 Trigonometry in Ptolemy's Other Works 90 * Text 2.5 Ptolemy, Constructing Latitude Arcs on a Map 91 After Ptolemy 93   Chapter 3: India 94 Transmission from Babylon and Greece 94 The First Sine Tables 95 Aryabhata's Difference Method of Calculating Sines 99 * Text 3.1 Aryabhata, Computing Sines 100 Bhaskara I's Rational Approximation to the Sine 102 Improving Sine Tables 105 Other Trigonometric Identities 107 * Text 3.2 Varahamihira, a Half-angle Formula 108 * Text 3.3 Brahmagupta, the Law of Sines in Planetary Theory? 109 Brahmagupta's Second-order Interpolation Scheme for Approximating Sines 111 * Text 3.4 Brahmagupta, Interpolating Sines 111 Taylor Series for Trigonometric Functions in Madhava's Kerala School 113 Applying Sines and Cosines to Planetary Equations 121 Spherical Astronomy 124 * Text 3.5 Varahamihira, Finding the Right Ascension of a Point on the Ecliptic 125 Using Iterative Schemes to Solve Astronomical Problems 129 * Text 3.6 Paramesvara, Using Fixed-point Iteration to Compute Sines 131 Conclusion 133   Chapter 4: Islam 135 Foreign Junkets: The Arrival of Astronomy from India 135 Basic Plane Trigonometry 137 Building a Better Sine Table 140 * Text 4.1 Al-Samaw'al ibn Yahya al-Maghribi, Why the Circle Should Have 480 Degrees 146 Introducing the Tangent and Other Trigonometric Functions 149 * Text 4.2 Abu'l-Rayhan al-Biruni, Finding the Cardinal Points of the Compass 152 Streamlining Astronomical Calculation 156 * Text 4.3 Kushyar ibn Labban, Finding the Solar Equation 156 Numerical Techniques: Approximation, Iteration, Interpolation 158 * Text .4 Ibn Yunus, Interpolating Sine Values 164 Early Spherical Astronomy: Graphical Methods and Analemmas 166 * Text 4.5 Al-Khwarizmi, Determining the Ortive Amplitude Geometrically 168 Menelaus in Islam 173 * Text 4.6 Al-Kuhi, Finding Rising Times Using the Transversal Theorem 175 Menelaus's Replacements 179 Systematizing Spherical Trigonometry: Ibn Mucadh's Determination of the Magnitudes and Nasir al-Din al-Tusi's Transversal Figure 186 Applications to Religious Practice: The Qibla and Other Ritual Needs 192 * Text 4.7 Al-Battani, a Simple Approximation to the Qibla 195 Astronomical Timekeeping: Approximating the Time of Day Using the Height of the Sun 201 New Functions from Old: Auxiliary Tables 205 * Text 4.8 Al-Khalili, Using Auxiliary Tables to Find the Hour-angle 207 Trigonometric and Astronomical Instruments 209 * Text 4.9 Al-Sijzi (?), On an Application of the Sine Quadrant 213 Trigonometry in Geography 215 Trigonometry in al-Andalus 217   Chapter 5: The West to 1550 223 Transmission from the Arab World 223 An Example of Transmission: Practical Geometry 224 * Text 5.1 Hugh of St. Victor, Using an Astrolabe to Find the Height of an Object 225 * Text 5.2 Finding the Time of Day from the Altitude of the Sun 227 Consolidation and the Beginnings of Innovation: The Trigonometry of Levi ben Gerson, Richard of Wallingford, and John of Murs 230 * Text 5.3 Levi ben Gerson, The Best Step Size for a Sine Table 233 * Text 5.4 Richard of Wallingford, Finding Sin(1 ) with Arbitrary Accuracy 237 Interlude: The Marteloio in Navigation 242 * Text 5.5 Michael of Rhodes, a Navigational Problem from His Manual 244 From Ptolemy to Triangles: John of Gmunden, Peurbach, Regiomontanus 247 * Text 5.6 Regiomontanus, Finding the Side of a Rectangle from Its Area and Another Side 254 * Text 5.7 Regiomontanus, the Angle-angle-angle Case of Solving Right Triangles 255 Successors to Regiomontanus: Werner and Copernicus 264 * Text 5.8 Copernicus, the Angle-angle-angle Case of Solving Triangles 267 * Text 5.9 Copernicus, Determining the Solar Eccentricity 270 Breaking the Circle: Rheticus, Otho, Pitiscus and the Opus Palatinum 273   Concluding Remarks 284 Bibliography 287 Index 323","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865519501655,"sku":"9780691129730","price":51.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691129730.jpg?v=1722274361"},{"product_id":"how-mathematicians-think-using-ambiguity-contradiction-and-paradox-to-create-mathematics-9780691145990","title":"How Mathematicians Think  Using Ambiguity","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTo many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically - even algorithmically - from one black-and-white deduction to another. This book reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eWinner of the 2007 Best Sci-Tech Books in Mathematics, Library Journal One of Choice's Outstanding Academic Titles for 2007 \"Ambitious, accessible and provocative...[In] How Mathematicians Think, William Byers argues that the core ingredients of mathematics are not numbers, structure, patterns or proofs, but ideas...Byers' view springs from the various facets of his career as a researcher and administrator (and, he says, his interest in Zen Buddhism). But it is his experience as a teacher that gives the book some of its extraordinary salience and authority...Good mathematics teaching should not banish ambiguity, but enable students to master it...Everyone should read Byers...His lively and important book establishes a framework and vocabulary to discuss doing, learning, and teaching mathematics, and why it matters.\"--Donal O'Shea, Nature \"From Byers's book, if you work at it, you will learn some mathematics and, more important, you may begin to see how mathematicians think.\"--Peter Cameron, Times Higher Education Supplement \"As William Byers points out in this courageous book, mathematics today is obsessed with rigor, and this actually suppresses creativity... Perfectly formalized ideas are dead, while ambiguous, paradoxical ideas are pregnant with possibilities and lead us in new directions: they guide us to new viewpoints, new truths... Bravo, Professor Byers, and my compliments to Princeton University Press for publishing this book.\"--Gregory Chaitin, New Scientist \"Many people assume that mathematicians' thinking processes are strictly methodical and algorithmic. Integrating his experience as a mathematician and as a Buddhist, Byers examines the validity of this assumption. Much of mathematical thought is based on intuition and is in fact outside the realm of black-and-white logic, he asserts. Byers introduces and defines terms such as mathematical ambiguity, contradiction, and paradox and demonstrates how creative ideas emerge out of them. He gives as examples some of the seminal ideas that arose in this manner, such as the resolution of the most famous mathematical problem of all time, the Fermat conjecture. Next, he takes a philosophical look at mathematics, pondering the ambiguity that he believes lies at its heart. Finally, he asks whether the computer accurately models how math is performed. The author provides a concept-laden look at the human face of mathematics.\"--Science News \"This book is a radically new account of mathematical discourse and mathematical thinking...What Byers's book reveals is that ambiguity is always present...You can't quite say that nobody has said this before. But nobody has said it before in this all-encompassing, coherent way, and in this readable, crystal clear style...This book strikes me as profound, unpretentious, and courageous.\"--Reuben Hersh, Notices of the AMS \"This is a truly exceptional work. In an almost gripping tour de force, Byers examines the creative impulse of mathematics, which to him is the notion of ambiguity, understood to 'involve a single idea that is perceived in two self-consistent but mutually incompatible frames of reference'...[I]t is a sorely needed complement to often-formulaic textbooks... An incredible book.\"--J. Mayer, Choice \"William Byers...has written a passionate defense of the uniquely human aspect of mathematics...Byers [demonstrates] that the insights of mathematicians come about through a discipline that...has something in common with Zen practice. First, there is a positive use of difficulty: 'the paradox has the enormous value of highlighting a fertile area of thought.' Then the breakthrough: 'An idea emerges in response to the tension that results from the conflict inherent in ambiguity.' These sentences from Byers's book apply equally to scientific and spiritual work.\"--Eliot Fintushel, Tricycle \"After a lifetime of research and teaching, [Byers argues] that mathematical breakthroughs do not come from simply manipulating symbols according to strict rules. Byers writes with verve and clarity about deep and difficult mathematical and philosophical issues such as the relationship between great mathematical ideas and cultural crises. Byers discusses in depth some examples of great ideas and crises...and explains why he is dead against seeing the mind as a computer.\"--Andrew Robinson, Physics World \"It is a pleasure to read [Byers'] well written, carefully referenced, and clearly illustrated arguments. Byers describes what 'doing math is: a process characterized by the complementary poles of proof and idea, of ambiguity and logic.' Byers' book has given me a greater appreciation for mathematics. I recommend it to anyone interested in, and open-minded about, the attempt to define mathematics.\"--Lee Kennard, Math Horizons \"Byers subverts the widely held notion that mathematicians are a form of computer, or robotic followers of unbending rules. In his view, thinking about math requires creativity and the use of non-logical forms of thought. Thus the ambiguity, paradox and contradiction of the subtitle.\"--The Globe and Mail \"Well-organized and carefully written the present book is very useful to all who are interested in How Mathematicians Think!\"--Ioan A. Rus, Mathematica \"[A] brilliant and easily accessible book on the creative foundations of math and psychology.\"--Ernest Rossi, Psychological Perspectives \"What does one like to learn when one reads a book? Because the reading of a book is a union between its text and the reader's consciousness, one answer is the wedding custom of 'something old, something new, something borrowed, something blue'. All are there in this book... It is a useful book for the apprentice mathematician by clarifying the importance of boldness in making mistakes and declaring that one does not fully understand some technical details which at first sight appear to be more complex than they really are.\"--Bob Anderssen, Australian Mathematical Society Gazette \"Excellent discussions are presented.\"--EMS Newsletter \"[Byers'] book helps us not to eliminate the myths surrounding mathematics and mathematicians, but to master them.\"--David Cohen, European Legacy \"The author is a mathematician, and he plainly knows what he is talking about. In my opinion he has done a good job of getting it across... The book has a lot of worthwhile material to recommend.\"--Robert Thomas, Philosophia Mathematica \"Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.\"--World Book Industry\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments vii  INTRODUCTION: Turning on the Light 1  SECTION I: THE LIGHT OF AMBIGUITY 21  CHAPTER 1: Ambiguity in Mathematics 25  CHAPTER 2: The Contradictory in Mathematics 80  CHAPTER 3: Paradoxes and Mathematics: Infinity and the Real Numbers 110  CHAPTER 4: More Paradoxes of Infinity: Geometry, Cardinality, and Beyond 146  SECTION II: THE LIGHT AS IDEA 189  CHAPTER 5: The Idea as an Organizing Principle 193  CHAPTER 6: Ideas, Logic, and Paradox 253  CHAPTER 7: Great Ideas 284  SECTION III: THE LIGHT AND THE EYE OF THE BEHOLDER 323  CHAPTER 8: The Truth of Mathematics 327  CHAPTER 9: Conclusion: Is Mathematics Algorithmic or Creative? 368  Notes 389  Bibliography 399  Index 407","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865523269975,"sku":"9780691145990","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"heavenly-mathematics-9780691148922","title":"Heavenly Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSpherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. This title traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Choice's Outstanding Academic Titles for 2013 Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics \"Once a mainstay of mathematics, spherical trigonometry no longer appears on school curricula. Here, Glen Van Brummelen reasserts the field's importance, sharing in illuminating detail how it figured in astronomy, cartography and our understanding of Earth's rotation.\"--Rosalind Metcalfe, Nature \"The present book is very well written; it leaves a clear impression that the author intended to endear--not merely present and teach--spherical trigonometry to the reader. Although not a history book, there are separate chapters shedding light on the approaches to the subject in the ancient, medieval, and modern times. There are also chapters on spherical geometry, polyhedra, stereographic projection and the art of navigation. The book is thoroughly illustrated and is a pleasant read. Chapters end with exercises; the appendices contain a long list of available and not so available textbooks and recommendations for further reading organized by individual chapters. The book made a valuable addition to my library. I freely recommend it to math teachers and curious high schoolers.\"--Alexander Bogomolny, CTK Insights \"A no-nonsense introduction to spherical trigonometry.\"--Book News, Inc. \"A beautiful popular book.\"--ThatsMaths.com \"Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun.\"--R. Balashankar, Organiser \"Heavenly Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry... As readers discover this discipline, they will also appreciate the beauty inherent in the topic.\"--Choice \"Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader.\"--Florin Diacu, Literary Review of Canada \"Van Brummelen has written a wonderful introduction ... that draws on the history of [spherical trigonometry] to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about.\"--Metascience \"[Heavenly Mathematics] is an excellent survey of spherical trigonometry... Simply an appreciation of a beautiful lost subject, with historical overtones... [D]istinguishable for its appealingly fresh style.\"--Mathematical Reviews \"[Heavenly Mathematics] is a lovely book to read... [A] wonderful introduction for anyone who wishes to learn more about this subject... I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it.\"--Mathematics Today \"Engaging, clear and not overly technical; you can safely lend this book to your friends in the history department... [Heavenly Mathematics] is excellent.\"--Zentralblatt MATH \"Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject.\"--Jan P. Hogendijk, Isis \"This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students.\"--Teresa Floyd, Mathematics Teacher \"Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins... Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative.\"--P.N. Ruane, Mathematical Gazette \"An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics.\"--Elizabeth Hamm, Aestimatio Critical Reviews in the History of Science\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii  1 Heavenly Mathematics 1  2 Exploring the Sphere 23  3 The Ancient Approach 42  4 The Medieval Approach 59  5 The Modern Approach: Right- Angled Triangles 73  6 The Modern Approach: Oblique Triangles 94  7 Areas, Angles, and Polyhedra 110  8 Stereographic Projection 129  9 Navigating by the Stars 151  Appendix A. Ptolemy's Determination of the Sun's Position 173  Appendix B. Textbooks 179  Appendix C. Further Reading 182  Index 189","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865524416855,"sku":"9780691148922","price":36.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691148922.jpg?v=1722274383"},{"product_id":"pythagoras-revenge-9780691150192","title":"Pythagoras Revenge","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSet in 1998 with flashbacks to classical Greece, this title investigates the confrontation between opposing views of mathematics and reality, and explores ideas from both early and cutting-edge mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Who would have guessed that a murder-treasure mystery lay hidden behind a geometric formula familiar to every high-schooler? Weaving a wealth of mathematical scholarship into a compellingly plotted novel, Sangalli recounts a fascinating tale of ancient arson and modern sleuthing, as Pythagoras of Samos (forever linked to the triangular theorem bearing his name) perishes amid brutal intrigues sweeping an early Greek colony, yet leaves behind a tantalizing legacy of numerical reasoning and paranormal mysticism... To be sure, it is the author's own fertile imagination that generates the characters who form this resolute band and then scripts the adventures they encounter in their unlikely international quest... [R]eaders will learn a great deal about real mathematics and its history as they join Pythagoras' modern epigones in pondering the meaning of geometrical patterns, the surprising randomness in numbers, and the logic of mathematical proofs... [T]his engaging narrative will persuade many readers that mathematics offers far more excitement than they had previously supposed.\"--Bryce Christensen, Booklist \"[The book] comes together [around] the tantalizing possibility that Pythagoras, who forbade his followers to write down any of his sayings, may just have left something tangible after all. Sangalli builds his story on this, using clues from ancient texts, bits of mathematical lore and interesting arcana, like the puzzle that couldn't be patented because it had no solution. For a total escape, this novel is perfect.\"--Margaret Cannon, Globe and Mail \"Pythagoras' Revenge: A Mathematical Mystery is more than just a novel. It is also an introduction to several big ideas in mathematics, from infinite series to unsolvable puzzles... [T]his romp through ancient and modern mathematics is entertaining in patches, and certainly a cut above standard holiday reading. Despite occasional plot hiccups, its gripping story will likely hold readers to the end.\"--Physics World \"Initially Pythagoras' Revenge was intended to discuss the tyranny of numbers in modern societies in the same style as Sangalli's previous book. But, as if by magic, it became instead a work of fiction... What remains after the end of this page-turner is Sangalli's impressive capacity to communicate mathematics. Let us take this book as a reminder to capitalize on the full potential of scientific storytelling.\"--Javier Fresan, Notices of the AMS \"This is an entertaining read, and although the plot is implausible at times it succeeds in conveying a variety of mathematical and philosophical ideas in a simple and light-hearted way... Pythagoras' Revenge is a gripping novel that offers a refreshing way to learn about mathematics.\"--Sarah Shepherd, iSquared \"Human beings are story making animals, and this book shows that there is an opportunity to make use of this approach in the field. A fascinating attempt.\"--Brian Clegg, Popular Science \"Read this book if you like mathematics and spend some time ruminating over the larger philosophical questions that are implicit in modern math. Such questions go directly to the heart of modern scientific culture.\"--William Byers, European Legacy \"If you like conspiracy adventure, and can dismiss the shallow characters and clunky sub-plots, it's a fun read as you get the history, philosophy, and theories on randomness and math, and of a figure who famously said, 'All is Number.'\"--Phil Semler, San Francisco Book Review\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix List of Main Characters xi Prologue xiii   PART I: A TIME CAPSULE? Chapter 1. The Fifteen Puzzle 3 Chapter 2. The Impossible Manuscript 10 Chapter 3. Game Over 19 Chapter 4. A Trip to London 25 Chapter 5. A Letter from the Past 32 Chapter 6. Found and Lost 38 Chapter 7. A Death in the Family 46   PART II: AN EXTRAORDINARILY GIFTED MAN Chapter 8. The Mission 53 Chapter 9. Norton Thorp 63 Chapter 10. Random Numbers 69 Chapter 11. Randomness Everywhere 76 Chapter 12. Vanished 82   PART III: A SECT OF NEO-PYTHAGOREANS Chapter 13. The Mandate 85 Chapter 14. The Beacon 87 Chapter 15. The Team 98 Chapter 16. The Hunt 106 Chapter 17. The Symbol of the Serpent 115 Chapter 18. A Professional Job 122 Chapter 19. With a Little Help from Your Sister 126   PART IV: PYTHAGORAS' MISSION Chapter 20. All Roads Lead to Rome 139 Chapter 21. Kidnapped 152 Chapter 22. The Last Piece of the Puzzle 158 Epilogue 169 Appendix 1: Jule's Solution 171 Appendix 2: Infi nitely Many Primes 173 Appendix 3: Random Sequences 175 Appendix 4: A Simple Visual Proof of the Pythagorean Theorem 177 Appendix 5: Perfect and Figured Numbers 178 Notes, Credits, and Bibliographical Sources 181","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865524777303,"sku":"9780691150192","price":16.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691150192.jpg?v=1722274384"},{"product_id":"henri-poincare-9780691152714","title":"Henri Poincaré","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHenri Poincar (1854-1912) was not just one of the most inventive, versatile, and productive mathematicians of all time - he was also a leading physicist who almost won a Nobel Prize for physics. This book explores all the fields that Poincar touched, the debates sparked by his investigations, and how his discoveries still contribute to society.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Choice's Outstanding Academic Titles for 2013 \"[M]asterly ... Gray encapsulates Poincare's multiple dimensions; his intellectual biography is both a tour de force and a triumph of readability.\"--George Szpiro, Nature \"Gray shows us the full dazzling sweep of what Poincare accomplished, including the work on dynamical systems and chaos that only came into its own in recent years. A tour de force, Gray's masterful treatment will long remain an invaluable resource for all who want to understand Poincare, so embedded within his times and yet so far ahead of them.\"--Peter Pesic, Science \"[A] comprehensive but uncluttered guide to Poincare's extensive oeuvres.\"--Madeline Muntersbjorn, Times Higher Education \"Full of the mathematical, physical and metaphysical ideas of a man who was not only a dispassionate observer of the world around us, but of our way of understanding it.\"--Mark Ronan, Standpoint Magazine (U.K.) \"[A] comprehensive assessment of Poincare's work and its importance, essential for anyone interested in Poincare's scholarship or the history of mathematics.\"--Laura Tarwater Scharp, Sacramento Book Review \"Comprehensive.\"--Science News \"A fundamental study of the scientific work of one of the greatest mathematicians and mathematical physicists of the three decades straddling the 19th and 20th centuries... Chapters are organized topically, not chronologically. Each illuminates in depth one or other of Poincare's works but all are set in context both historical and temathic such that each can serve as an introduction into the many subjects to which Poincare made a contribution.\"--Alexander Bogomolny, CTK Insights \"Poincare's work is fully alive in science today. This biography is one of the first thorough introductions to his work, it should get the attention of mathematicians, natural scientists and philosophers.\"--Ferdinand Verhulst, European Legacy \"Gray, a mathematics historian and scholar on the life and work of Henry Poincare, has, with the support of a Leverhulme Research Fellowship, produced this comprehensive and definitive 'scientific biography.' Gray offers abundant rich information on Poincare's ideas and scientific process, the evolution and maturity of his mathematics including missteps, the dexterity of his reasoning, and the influences that shaped his thought.\"--Choice \"I recommend [this] book highly.\"--Robert E. O'Malley, Jr., SIAM Review \"Jeremy Gray's book on Poincare's mathematics, physics, and philosophy is an important contribution to the literature and a huge step towards a full biography of this pioneer of modern science.\"--Reinhard Siegmund-Schultze, Zentralblatt MATH \"Gray's book is a comprehensive scientific biography of Poincare. It embraces the broad scope of Poincare's work, from his philosophical speculations to his popular writing, and gives a thorough overview of his extensive mathematical researches.\"--Peter Lynch, Irish Mathematical Society Bulletin \"[T]he author does not simply give platitudes when writing about Poincare's ideas: mathematicians will enjoy reading about his discoveries concerning the three-body problem, the theory of functions, topology, number theory, Lie theory, algebraic geometry, and probability. This scientific biography is the first to comprehensively cover all of Poincare's main contributions to mathematics, philosophy, and physics.\"--Alan S. McRae, Mathemematical Reviews Clippings \"Jeremy Gray has done a marvelous job of exposition and of binding together the many different cognitive, social and biographical strands into the coherent whole of a challenging, but highly rewarding, 'scientific biography'.\"--Klaus Hentschel, British Journal for the History of Science \"A good intellectual biography of an artist should help the reader see how a particular worldview shapes the pursuit of art. Gray's book does that most admirably.\"--Daniel S. Alexander, H-France Review \"Henry Poincare is likely to remain the standard by which scientific biographies, at least those that concern physicists and mathematicians, are judged for some time.\"--Christopher Cumo, Canadian Journal of History \"I warmly recommend the book to anyone with an interest in the development of modern mathematics. It will surely be the definitive scientific biography of Poincare for the foreseeable future.\"--John Stillwell, Notices of the AMS \"Gray describes Poincare's scientific epoch in a beautiful way. Due attention is paid to the mathematical and further scientific aspects of his life, and the intellectual complexity of his achievements, both in their range and their depth, are amply discussed. Gray displays a mastery of his material that is rare even among historians of mathematics and science, and his biography is richly rewarding, engrossing, and informative. He deserves our congratulations.\"--H. W. Broer, Journal of the British Society for the History of Mathematics \"Gray succeeds admirably in presenting both the conceptual and the historical context necessary to appreciate Poincare's contributions. Gray's masterful biography may well serve as a standard example for future endeavors of this kind.\"--Tilman Sauer, Isis \"The obvious virtue of this book is its comprehensiveness. The deeper virtue is to connect Poincare's views of all the parts of his work and to encourage more of that. Gray gives us Poincare's view of Science as a whole.\"--Colin McLarty, Mathematical Intelligencer \"The book is an endless source of interesting insights by Poincare... I would recommend the book for mathematicians, mathematics educators, and philosophers in higher education who want a rich understanding of Poincare, his work, and his times.\"--Mary L. Garner, Mathematics Teacher\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Figures ix   Preface xi   Introduction 1  * Views of Poincare 3  * Poincare's Way of Thinking 6 1 The Essayist 27  * Poincare and the Three Body Problem 27  * Poincare's Popular Essays 34  * Paris Celebrates the New Century 59  * Science, Hypothesis, Value 67  * Poincare and Projective Geometry 76  * Poincare's Popular Writings on Physics 100  * The Future of Mathematics 112  * Poincare among the Logicians 123  * Poincare's Defenses of Science 144 2 Poincare's Career 153  * Childhood, Schooling 153  * The Ecole Polytechnique 157  * The Ecole des Mines 158  * Academic Life 160  * The Dreyfus Affair 165  * National Spokesman 169  * Contemporary Technology 177  * International Representative 187  * The Nobel Prize 192  *\"1911\", \"1912\" 200  * Remembering Poincare 202 3 The Prize Competition of 1880 207  * The Competition 207  * Fuchs, Schwarz, Klein, and Automorphic Functions 224  * Uniformization, 1882 to 1907 247 4 The Three Body Problem 253  * Flows on Surfaces 253  * Stability Questions 265  * Poincare's Essay and Its Supplements 266  *Les Methodes Nouvelles de la Mecanique Celeste 281  * Poincare Returns 291 5 Cosmogony 300  * Rotating Fluid Masses 300 6 Physics 318  * Theories of Electricity before Poincare: Maxwell 318  * Poincare's Electricite et Optique, 1890 329  * Larmor and Lorentz: The Electron and the Ether 338  * Poincare on Hertz and Lorentz 346  * St. Louis, 1904 356  * The Dynamics of the Electron 361  * Poincare and Einstein 367  * Early Quantum Theory 378 7 Theory of Functions and Mathematical Physics 382  * Function Theory of a Single Variable 382  * Function Theory of Several Variables 391  * Poincare's Approach to Potential Theory 402  * The Six Lectures in Gottingen, 1909 416   8 Topology 427  * Topology before Poincare 427  * Poincare's Work, 1895 to 1905 432 9 Interventions in Pure Mathematics 467  * Number Theory 467  * Lie Theory 489  * Algebraic Geometry 498 10 Poincare as a Professional Physicist 509  * Thermodynamics 513  * Probability 518 11 Poincare and the Philosophy of Science 525  * Poincare: Idealist, Skeptic, or Structural Realist? 525 12 Appendixes 543  * Elliptic and Abelian Functions 543  * Maxwell's Equations 545  * Glossary 548 References 553  * Articles and Books by Poincare 554  * Other Authors 564 Name Index 585    Subject Index 589","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865526251863,"sku":"9780691152714","price":36.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691152714.jpg?v=1722274393"},{"product_id":"john-napier-9780691155708","title":"John Napier","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eJohn Napier (1550-1617) is celebrated today as the man who invented logarithms--an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier's pioneering efforts, his life and\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"John Napier fills a gap concerning an important, and often ignored, chapter of mathematical history.\"--George Szpiro, Nature \"In this engaging book, we learn more about Napier the mathematician, the religious zealot, the person.\"--Devorah Bennu, The Guardian, Grrl Scientist \"Edinburgh born John Napier, the inventor of logarithms, is in danger of fading into the shadows of the scientific landscape. In the new book John Napier: Life, Logarithms, and Legacy, Julian Havil does a marvelous job of bringing Napier back into the spotlight.\"--Stephanie Blanda, American Mathematical Society blog \"I'm sure after reading this entertaining and enjoyable book, Napier will climb some rungs on your ladder of famous mathematicians.\"--A. Bultheel, European Mathematical Society \"Havil ... gives a rich history of Napier's involvement in the Protestant reformation, his introduction of logarithms, and his legacy.\"--Choice \"With this book, the author continues his impressive series of illuminating, accessible monographs on the history of mathematics.\"--Bart J. I. Van Kerkhove, Mathematical Review \"This book fills a clear gap in published work on Napier and is likely to be the standard point of departure for those interested in his life and work for some years to come.\"--Mark McCartney, London Mathematical Society Newsletter \"It is clearly a very interesting book.\"--Ernesto Nungesser, Irish Math Society Bulletin \"Havil's attention to detail is without equal in the opinion of this reviewer.\"--John A. Adam, Scotia\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments xv  Introduction 1  Chapter One Life and Lineage 8  Chapter Two Revelation and Recognition 35  Chapter Three A New Tool for Calculation 62  Chapter Four Constructing the Canon 96  Chapter Five Analogue and Digital Computers 131  Chapter Six Logistics: The Art of Computing Well 155  Chapter Seven Legacy 179  Epilogue 207  Appendix A Napier's Works 209  Appendix B The Scottish Science Hall of Fame 210  Appendix C Scotland and Conflict 211  Appendix D Scotland and Reformation 216  Appendix E A Stroll Down Memory Lane 220  Appendix F Methods of Multiplying 229  Appendix G Amending Napier's Kinematic Model 232  Appendix H Napier's Inequalities 233  Appendix I Hos Ego Versiculos Feci 236  Appendix J The Rule of Three 238  Appendix K Mercator's Map 250  Appendix L The Swiss Claimant 264  References 270  Index 275","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865527497047,"sku":"9780691155708","price":31.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691155708.jpg?v=1722274398"},{"product_id":"four-colors-suffice-9780691158228","title":"Four Colors Suffice","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOn October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history - one that would confound thousands of puzzlers for more than a century. This book tells the amazing story of how the \"map problem\" was solved.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The simplicity of the four-color conjecture is deceptive. Just how deceptive is made clear by Robin Wilson's delightful history of the quest to resolve it... Four Colors Suffice is strewn with good anecdotes, and the author ... proves himself skillful at making the mathematics accessible.\"--Jim Holt, New York Review of Books \"Wilson's lucid history weaves together lively anecdotes, biographical sketches, and a non-technical account of the mathematics.\"--Science \"Earlier books ... relate some of the relevant history in their introductions, but they are primarily technical. In contrast, Four Colors Suffice is a blend of history anecdotes and mathematics. Mathematical arguments are presented in a clear, colloquial style, which flows gracefully.\"--Daniel S. Silver, American Scientist \"Robin Wilson appeals to the mathematical novice with an unassuming lucidity. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride.\"--Jascha Hoffman, The Boston Globe \"A thoroughly accessible history of attempts to prove the four-color theorem. Wilson defines the problem and explains some of the methods used by those trying to solve it. His descriptions of the contributions made by dozens of dedicated, and often eccentric, mathematicians give a fascinating insight into how mathematics moves forward, and how approaches have changed over the past 50 years... It's comforting to know that however indispensable computers become, there will always be a place for the delightfully eccentric mathematical mind. Let's hope that Robin Wilson continues to write about them.\"--Elizabeth Sourbut, New Scientist \"An attractive and well-written account of the solution of the Four Color Problem... It tells in simple terms an exciting story. It ... give[s] the reader a view into the world of mathematicians, their ideas and methods, discussions, competitions, and ways of collaboration. As such it is warmly recommended.\"--Bjarne Toft, Notices of the American Mathematical Society \"Recreational mathematicians will find Wilson's history of the conjecture an approachable mix of its technical and human aspects... Wilson explains all with exemplary clarity and an accent on the eccentricities of the characters.\"--Booklist \"Wilson gives a clear account of the proof ... enlivened by historical tales.\"--Alastair Rae, Physics World \"Wilson provides a lively narrative and good, easy-to-read arguments showing not only some of the victories but the defeats as well... Even those with only a mild interest in coloring problems or graphs or topology will have fun reading this book... [It is] entertaining, erudite and loaded with anecdotes.\"--G.L. Alexanderson, MAA Online\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword by Ian Stewart xi Preface to the Revised Color Edition xiii Preface to the Original Edition xv 1The Four-Color Problem 1 What Is the Four-Color Problem? | Why Is It Interesting? | Is It Important? | What Is Meant by \"Solving\" It? | Who Posed It, and How Was It Solved? | Painting by Numbers | Two Examples 2The Problem Is Posed 12 De Morgan Writes a Letter | Hotspur and the Athenaeum | Mobius and the Five Princes | Confusion Reigns 3Euler's Famous Formula 28 Euler Writes a Letter | From Polyhedra to Maps | Only Five Neighbors | A Counting Formula 4Cayley Revives the Problem ... 45 Cayley's Query | Knocking Down Dominoes | Minimal Criminals | The Six-Color Theorem 5... and Kempe Solves It 55 Sylvester's New Journal | Kempe's Paper | Kempe Chains | Some Variations | Back to Baltimore 6A Chapter of Accidents 71 A Challenge for the Bishop | A Visit to Scotland | Cycling around Polyhedra | A Voyage around the World | Wee Planetoids 7A Bombshell from Durham 86 Heawood's Map | A Salvage Operation | Coloring Empires | Maps on Bagels | Picking Up the Pieces 8Crossing the Atlantic 105 Two Fundamental Ideas | Finding Unavoidable Sets | Finding Reducible Configurations | Coloring Diamonds | How Many Ways? 9A New Dawn Breaks 124 Bagels and Traffic Cops | Heinrich Heesch | Wolfgang Haken | Enter the Computer | Coloring Horseshoes 10Success! 139 A Heesch-Haken Partnership? | Kenneth Appel | Getting Down to Business | The Final Onslaught | A Race against Time | Aftermath 11Is It a Proof? 157 Cool Reaction | What Is a Proof Today? | Meanwhile ... | A New Proof | Into the Next Millennium | The Future Chronology of Events 171 Notes and References 175 Glossary 187 Picture Credits 193 Index 195","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865529004375,"sku":"9780691158228","price":20.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691158228.jpg?v=1722274406"},{"product_id":"philosophy-of-mathematics-9780691161402","title":"Philosophy of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Excellent. . . . [A]n exceptionally well-informed, very readable and clear introduction to the subject. If you are looking for an entry point into the extensive philosophical literature on the nature of mathematics, look no further.\"\u003cb\u003e---A. C. Paseau, \u003ci\u003eMathematical Gazette\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Linnebo's slender volume is an admirable addition to the many existing books on the philosophy of mathematics. It is clear, concise, and well written. . . . All in all, this is an excellent introduction to the philosophy of mathematics and should be seriously considered by any individual interested in the subject.\" * Choice *\u003cbr\u003e\"This is a thought-provoking book, and is a useful addition to the textbook literature on this subject.\" * MAA Reviews *\u003cbr\u003e\"This book provides a nice \u003ci\u003elay of the land \u003c\/i\u003efor anyone interested in contemporary philosophy of mathematics.\"\u003cb\u003e---Gregory Lavers, \u003ci\u003ePhilosophia Mathematica\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[This book] is very, very good. Superbly clear, concise, well organised, it gives not only a very accessible introduction but also takes the reader all the way to the cutting edge of what philosophers are doing in the philosophy of mathematics. Above all, Linnebo writes as a fully engaged philosopher and makes his preferred choice of philosophical position clear. But this is no mere polemic: I felt he clearly and forcefully presents the strengths and weaknesses of all the philosophical positions he discusses.\"\u003cb\u003e---Henri Laurie, \u003ci\u003eMathemafrica\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"[A] very readable and . . . superb introduction to the philosophy of mathematics.\"\u003cb\u003e---Jason Wakefield, \u003ci\u003eAvello Publishing Journal\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments vii  Introduction 1  1 Mathematics as a Philosophical Challenge 4  2 Frege's Logicism 21  3 Formalism and Deductivism 38  4 Hilbert's Program 56  5 Intuitionism 73  6 Empiricism about Mathematics 88  7 Nominalism 101  8 Mathematical Intuition 116  9 Abstraction Reconsidered 126  10 The Iterative Conception of Sets 139  11 Structuralism 154  12 The Quest for New Axioms 170  Concluding Remarks 183  Bibliography 189  Index 199","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865530380631,"sku":"9780691161402","price":27.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691161402.jpg?v=1722274413"},{"product_id":"elliptic-tales-9780691163505","title":"Elliptic Tales","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The authors present their discussion in an informal, sometimes playful manner and with detail that will appeal to an audience with a basic understanding of calculus. This book will captivate math enthusiasts as well as readers curious about an intriguing and still unanswered question.\"--Margaret Dominy, Library Journal \"Minimal prerequisites and its clear writing make this book (which even has a few exercises) a great choice for a seminar for mathematics majors, who at some point should have such an excursion to one of the frontiers of mathematics.\"--Mathematics Magazine \"The authors of Elliptic Tales do a superb job in demonstrating the approach that mathematicians take when they confront unsolved problems involving elliptic curves.\"--Sungkon Chang, Times Higher Education \"One cannot help being impressed, in reading the book and pursuing a few of the references, by the magnitude of the enterprise it chronicles.\"--James Case, SIAM News \"Ash and Gross thoroughly explain the statement and significance of the linchpin Birch and Swinnerton-Dyer conjection... [A]sh and Gross deliver ample and current intellectual and technical substance.\"--Choice \"I would envision this book as an excellent text for an undergraduate 'capstone' course in mathematics; the book lends itself to independent reading, but topics may be explored in much greater depth and rigor in the classroom. Additionally, the book indeed brings together ideas from calculus, complex variables and algebra, showing how a single mathematical research question may require an integrated understanding of the various branches of mathematics. Thus, it encourages students to reinforce their understanding of these various fields, while simultaneously introducing them to an open question in mathematics and a vibrant field of study.\"--Lisa A. Berger, Mathematical Reviews Clippings \"The book is very pleasantly written, and in my opinion, the authors have done an admirable job in giving an idea to non-experts what the Birch-Swinnerton Dyer conjecture is about.\"--Jan-Hendrik Evertse, Zentralblatt MATH \"The book's most important contributions ... are the sense of discovery, invention, and insight into the habits of mind used by mathematicians on this journey. I would recommend this book to anyone who wants to be challenged mathematically or who wants to experience mathematics as creative and exciting.\"--Jacqueline Coomes, Mathematics Teacher \"[T]his book is a wonderful introduction to what is arguably one of the most important mathematical problems of our time and for that reason alone it deserves to be widely read. Another reason to recommend this book is the opportunity to share in the readily apparent joy the authors have for their subject and the beauty they see in it, not least because ... joy and beauty are the most important reasons for doing mathematics, irrespective of its dollar value.\"--Rob Ashmore, Mathematics Today \"This book has many nice aspects. Ash and Gross give a truly stimulating introduction to elliptic curves and the BSD conjecture for undergraduate students. The main achievement is to make a relative easy exposition of these so technical topics.\"--Jonathan Sanchez-Hernandez, Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xiii Acknowledgments xix Prologue 1   PART I. DEGREE   Chapter 1. Degree of a Curve 13 1.Greek Mathematics 13 2.Degree 14 3.Parametric Equations 20 4.Our Two Definitions of Degree Clash 23   Chapter 2. Algebraic Closures 26 1.Square Roots of Minus One 26 2.Complex Arithmetic 28 3.Rings and Fields 30 4.Complex Numbers and Solving Equations 32 5.Congruences 34 6.Arithmetic Modulo a Prime 38 7.Algebraic Closure 38   Chapter 3. The Projective Plane 42 1.Points at Infinity 42 2.Projective Coordinates on a Line 46 3.Projective Coordinates on a Plane 50 4.Algebraic Curves and Points at Infinity 54 5.Homogenization of Projective Curves 56 6.Coordinate Patches 61   Chapter 4. Multiplicities and Degree 67 1.Curves as Varieties 67 2.Multiplicities 69 3.Intersection Multiplicities 72 4.Calculus for Dummies 76   Chapter 5. B'ezout's Theorem 82 1.A Sketch of the Proof 82 2.An Illuminating Example 88   PART II. ELLIPTIC CURVES AND ALGEBRA   Chapter 6. Transition to Elliptic Curves 95   Chapter 7. Abelian Groups 100 1.How Big Is Infinity? 100 2.What Is an Abelian Group? 101 3.Generations 103 4.Torsion 106 5.Pulling Rank 108 Appendix: An Interesting Example of Rank and Torsion 110   Chapter 8. Nonsingular Cubic Equations 116 1.The Group Law 116 2.Transformations 119 3.The Discriminant 121 4.Algebraic Details of the Group Law 122 5.Numerical Examples 125 6.Topology 127 7.Other Important Facts about Elliptic Curves 131 5.Two Numerical Examples 133   Chapter 9. Singular Cubics 135 1.The Singular Point and the Group Law 135 2.The Coordinates of the Singular Point 136 3.Additive Reduction 137 4.Split Multiplicative Reduction 139 5.Nonsplit Multiplicative Reduction 141 6.Counting Points 145 7.Conclusion 146 Appendix A: Changing the Coordinates of the Singular Point 146 Appendix B: Additive Reduction in Detail 147 Appendix C: Split Multiplicative Reduction in Detail 149 Appendix D: Nonsplit Multiplicative Reduction in Detail 150   Chapter 10. Elliptic Curves over Q 152 1.The Basic Structure of the Group 152 2.Torsion Points 153 3.Points of Infinite Order 155 4.Examples 156   PART III. ELLIPTIC CURVES AND ANALYSIS   Chapter 11. Building Functions 161 1.Generating Functions 161 2.Dirichlet Series 167 3.The Riemann Zeta-Function 169 4.Functional Equations 171 5.Euler Products 174 6.Build Your Own Zeta-Function 176   Chapter 12. Analytic Continuation 181 1.A Difference that Makes a Difference 181 2.Taylor Made 185 3.Analytic Functions 187 4.Analytic Continuation 192 5.Zeroes, Poles, and the Leading Coefficient 196   Chapter 13. L-functions 199 1.A Fertile Idea 199 2.The Hasse-Weil Zeta-Function 200 3.The L-Function of a Curve 205 4.The L-Function of an Elliptic Curve 207 5.Other L-Functions 212   Chapter 14. Surprising Properties of L-functions 215 1.Compare and Contrast 215 2.Analytic Continuation 220 3.Functional Equation 221   Chapter 15. The Conjecture of Birch and Swinnerton-Dyer 225 1.How Big Is Big? 225 2.Influences of the Rank on the Np's 228 3.How Small Is Zero? 232 4.The BSD Conjecture 236 5.Computational Evidence for BSD 238 6.The Congruent Number Problem 240 Epilogue 245 Retrospect 245 Where DoWe Go from Here? 247   Bibliography 249 Index 251","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865531167063,"sku":"9780691163505","price":13.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691163505.jpg?v=1722274417"},{"product_id":"alan-turing-the-enigma-9780691164724","title":"Alan Turing The Enigma","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"The book that inspired the film The imitation game.\"\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eA New York Times Bestseller The Imitation Game, Winner of the 2015 Academy Award for Best Adapted Screenplay Winner of the 2015 (27th) USC Libraries Scripter Award, University of Southern California Libraries One of The Guardian's Best Popular Physical Science Books of 2014, chosen by GrrlScientist \"Scrupulous and enthralling.\"--A. O. Scott, New York Times \"One of the finest scientific biographies ever written.\"--Jim Holt, New Yorker \"Andrew Hodges' 1983 book Alan Turing: The Enigma, is the indispensable guide to Turing's life and work and one of the finest biographies of a scientific genius ever written.\"--Michael Hiltzik, Los Angeles Times \"Turing's rehabilitation from over a quarter-century's embarrassed silence was largely the result of Andrew Hodges's superb biography, Alan Turing: The Enigma (1983; reissued with a new introduction in 2012). Hodges examined available primary sources and interviewed surviving witnesses to elucidate Turing's multiple dimensions. A mathematician, Hodges ably explained Turing's intellectual accomplishments with insight, and situated them within their wider historical contexts. He also empathetically explored the centrality of Turing's sexual identity to his thought and life in a persuasive rather than reductive way.\"--Michael Saler, Times Literary Supplement \"On the face of it, a richly detailed 500-page biography of a mathematical genius and analysis of his ideas, might seem a daunting proposition. But fellow mathematician and author Hodges has acutely clear and often extremely moving insight into the humanity behind the leaping genius that helped to crack the Germans' Enigma codes during World War II and bring about the dawn of the computer age... This melancholy story is transfigured into something else: an exploration of the relationship between machines and the soul and a full-throated celebration of Turing's brilliance, unselfconscious quirkiness and bravery in a hostile age.\"--Sinclair McKay, Wall Street Journal \"A first-class contribution to history and an exemplary work of biography.\"--I. J. Good, Nature \"An almost perfect match of biographer and subject... [A] great book.\"--Ray Monk, Guardian \"A superb biography... Written by a mathematician, it describes in plain language Turing's work on the foundations of computer science and how he broke the Germans' Enigma code in the Second World War. The subtle depiction of class rivalries, personal relationships, and Turing's tragic end are worthy of a novel. But this was a real person. Hodges describes the man, and the science that fascinated him--which once saved, and still influences, our lives.\"--Margaret Boden, New Scientist \"Andrew Hodges's magisterial Alan Turing: The Enigma ... is still the definitive text.\"--Joshua Cohen, Harper's \"Andrew Hodges's biography is a meticulously researched and written account detailing every aspect of Turing's life... This account of Turing's life is a definitive scholarly work, rich in primary source documentation and small-grained historical detail.\"--Mathematics Teacher \"Tells a powerful story that combines professional success and personal tragedy.\"--Nancy Szokan, Washington Post \"[A] really excellent biography... The great thing about this book is that the author is a mathematician and can explain the details of Turing's work--as a scientist, mathematician, and a code breaker--in a way that is easy to understand. He is also wonderful at the emotional nuance of Alan's life, who was a somewhat odd--a student was assigned to him in school to help him maintain a semblance of tidiness in his appearance, rooms and school work and at Bletchley Park he was known for chaining his tea mug to a pipe--but he was also charming and intelligent and Hodges brings all the aspects of his personality and life into sharp focus.\"--Off the Shelf \"This book is an incredibly detailed and meticulously researched biography of Alan Turing. Reading it is a melancholy experience, since you know from the outset that the ending is a tragic one and that knowledge overshadows you throughout. While the author divides the text into two parts, it actually reads like a play in four acts... This book is Turing's memorial, and one that does justice to the subject.\"--Katherine Safford-Ramus, MAA Reviews \"The new paperback edition of the 1983 book that inspired the film, with an updated introduction by Oxford mathematics professor Andrew Hodges, is an exhilarating, compassionate and detailed biography of a complicated man.\"--Jane Ciabattari, BBC \"If [The Imitation Game] does nothing else but send you, as it did me, to Alan Hodges's Alan Turing: The Enigma (1983, newly prefaced in the 2014 Princeton University Press edition) it more than justifies its existence. A great read, Hodges's intellectual biography depicts Turing as a brilliant mathematician; a crucial pioneering figure in the theorization and engineering of digital computing; and the biggest brain in Bletchley Park's Hut #8.\"--Amy Taubin, Artforum \"It is indeed the ultimate biography of Alan Turing. It will bring you as close as possible to his enigmatic personality.\"--Adhemar Bultheel, European Mathematical Society \"A book whose time has finally come. I found it to be a page-turner in spite of the occasionally esoteric explanations of mathematical theories that reminded of why Brooklyn Technical High School was not the wisest choice for me.\"--Terrance, Paris Readers Circle \"Thanks to the movie The Imitation Game, Alan Turing has emerged from history's shadows, where his memory had languished for decades. For anyone whose interest in the pioneering computer scientist, mathematician, and logician was piqued by the film, the book that served as the film's source material, Andrew Hodges's exhaustive biography Alan Turing: The Enigma, has the answers.\"--Frank Caso, Simply Charly\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Plates ix  Foreword by Douglas Hofstadter xi  Preface xv  PART ONE: THE LOGICAL  1 Esprit de Corps to 13 February 1930 3  2 The Spirit of Truth to 14 April 1936 60  3 New Men to 3 September 1939 141  4 The Relay Race to 10 November 1942 202  BRIDGE PASSAGE to 1 April 1943 305  PART TWO: THE PHYSICAL  5 Running Up to 2 September 1945 325  6 Mercury Delayed to 2 October 1948 394  7 The Greenwood Tree to 7 February 1952 491  8 On the Beach to 7 June 1954 574  Postscript 665  Author's Note 666  Notes 680  Acknowledgements 714  Index 715","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865531593047,"sku":"9780691164724","price":18.27,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691164724.jpg?v=1722274421"},{"product_id":"mathematics-and-art-9780691165288","title":"Mathematics and Art","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the disciplin\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This is a marvelous coffee table book ... very well researched and documented. It touches upon so many fundamental questions that philosophers, scientists, mathematicians and artists have asked since antiquity. But yet it guides the reader smoothly through all these competing visions and theories without becoming dull or getting lost in abstraction. This is the history of Western civilization with particular interest in art and mathematics, illuminating and instructive, and all wrapped up in a rich, colorful, and fancy book.\"--Adhemar Bultheel, European Mathematical Society \"This is the beauty and power of this book: [Mathematics and Art] is an intellectual tour de force of art history and its interaction with mathematics that will draw most readers, including me, back for further reading and study.\"--Frank Swetz, MAA Reviews \"Excellent new book... Overall this is a comprehensive, valuable and detailed book. It is written in an accessible style, with enough mathematics to interest the technical reader without overwhelming one with an arts background... Its rich anthology is particularly relevant today, given the explosion of interest in the digital arts and the need for digital artists to use maths creatively. I will definitely be keeping it close at hand.\"--William Latham, New Scientist \"The author does an artful job in creating a wide-ranging and beautifully illustrated survey that mathematicians and art historians will enjoy.\"--John Barrow, The Art Newspaper \"This sumptuously illustrated book chronicles the history of mathematics through its intersection with the development of visual art... Gamwell articulates the compelling, far-reaching connections within these fields in a way that is rewarding for scholars yet accessible to non-specialists.\"--Choice \"Beautiful books that display the beauty of art are fine additions to many coffee tables; beautiful books that display the beauty of mathematics are fine additions to few coffee tables. Gamwell's impressive work integrates the beauty of these two disciplines to create a work larger than their sum... A book for all ages and of all ages: truly a brilliant 'millennial' composition!\"--Sandra L. Arlinghaus, Mathematical Reviews \"This splendidly produced volume will appeal to everybody interested in mathematics and art and offers room for agreement and disagreement with the author... This volume stands out by its richness in contents, its wealth of colour reproductions and, last but not least, its very affordable price.\"--Dirk Werner, Zentralblatt MATH \"This wonderful book gives a very thorough overview of the impact of mathematics (and science) of the visual arts (and architecture) over the centuries.\"--Eos \"An interesting read, filled with paradigm-shifting history and art, the book still posits a linear perspective of the relationship of art and mathematics, specifically recounting the ways math has influenced art.\"--Karie Brown, Mathematics Teacher \"A monumental volume... Excellently illustrated by 523 images... Many highlighted quotations from writings of outstanding personalities of the sciences and the arts make the volume more colourful.\"--Gyorgy Darvas, Symmetry \"Mathematics and Art is an enjoyable read accessible to anyone interested in the history of mathematics and art.\"--Andre Michael Hahn, British Journal for the History of Science\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFOREWORD by Neil deGrasse Tyson IX  PREFACE XI  1 Arithmetic and Geometry 1  2 Proportion 73  3 Infinity 109  4 Formalism 151  5 Logic 197  6 Intuitionism 225  7 Symmetry 249  8 Utopian Visions after World War I 277  9 The Incompleteness of Mathematics 321  10 Computation 355  1 1 Geometric Abstraction after World War II 385  12 Computers in Mathematics and Art 455  13 Platonism in the Postmodern Era 499  NOTES 512  ACKNOWLEDGMENTS 547  CREDITS 548  INDEX 549","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865531855191,"sku":"9780691165288","price":46.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691165288.jpg?v=1722274421"},{"product_id":"an-imaginary-tale-9780691169248","title":"An Imaginary Tale","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIn the title, \"[the square root of minus one]\" appears as a radical over \"-1.\"\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Choice's Outstanding Academic Titles for 1999 Honorable Mention for the 1998 Award for Best Professional\/Scholarly Book in Mathematics, Association of American Publishers \"A book-length hymn of praise to the square root of minus one.\"--Brian Rotman, Times Literary Supplement \"An Imaginary Tale is marvelous reading and hard to put down. Readers will find that Nahin has cleared up many of the mysteries surrounding the use of complex numbers.\"--Victor J. Katz, Science \"[An Imaginary Tale] can be read for fun and profit by anyone who has taken courses in introductory calculus, plane geometry and trigonometry.\"--William Thompson, American Scientist \"Someone has finally delivered a definitive history of this 'imaginary' number... A must read for anyone interested in mathematics and its history.\"--D. S. Larson, Choice \"Attempting to explain imaginary numbers to a non-mathematician can be a frustrating experience... On such occasions, it would be most useful to have a copy of Paul Nahin's excellent book at hand.\"--A. Rice, Mathematical Gazette \"Imaginary numbers! Threeve! Ninety-fifteen! No, not those kind of imaginary numbers. If you have any interest in where the concept of imaginary numbers comes from, you will be drawn into the wonderful stories of how i was discovered.\"--Rebecca Russ, Math Horizons \"There will be something of reward in this book for everyone.\"--R.G. Keesing, Contemporary Physics \"Nahin has given us a fine addition to the family of books about particular numbers. It is interesting to speculate what the next member of the family will be about. Zero? The Euler constant? The square root of two? While we are waiting, we can enjoy An Imaginary Tale.\"--Ed Sandifer, MAA Online \"Paul Nahin's book is a delightful romp through the development of imaginary numbers.\"--Robin J. Wilson, London Mathematical Society Newsletter \"You will definitely enjoy it. In fact it clearly reflects the the joy and delight that the author experienced when he was confronted with complex analysis during his engineering studies.\"--Adhemar Bultheel, European Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*A Note to the Reader, pg. vii*Contents, pg. ix*Illustrations, pg. xi*Preface to the Paperback Edition, pg. xiii*Preface, pg. xxi*Introduction, pg. 1*CHAPTER ONE The Puzzles of Imaginary Numbers, pg. 8*CHAPTER TWO. A First Try at Understanding the Geometry of  -1, pg. 31*CHAPTER THREE. The Puzzles Start to Clear, pg. 48*CHAPTER FOUR. Using Complex Numbers, pg. 84*CHAPTER FIVE. More Uses of Complex Numbers, pg. 105*CHAPTER SIX. Wizard Mathematics, pg. 142*CHAPTER SEVEN. The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory, pg. 187*APPENDIX A. The Fundamental Theorem of Algebra, pg. 227*APPENDIX B. The Complex Roots of a Transcendental Equation, pg. 230*APPENDIX C. ( -1)( -1) to 135 Decimal Places, and How It Was Computed, pg. 235*APPENDIX D. Solving Clausen's Puzzle, pg. 238*APPENDIX E. Deriving the Differential Equation for the Phase-Shift Oscillator, pg. 240*APPENDIX F. The Value of the Gamma Function on the Critical Line, pg. 244*Notes, pg. 247*Name Index, pg. 261*Subject Index, pg. 265*Acknowledgments, pg. 269","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865534017879,"sku":"9780691169248","price":13.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691169248.jpg?v=1722274434"},{"product_id":"the-golden-ticket-9780691175782","title":"The Golden Ticket","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Amazon.com's 2013 Best Science Books One of Choice's Outstanding Academic Titles for 2013 Honorable Mention for the 2013 PROSE Award in Popular Science \u0026amp; Mathematics, Association of American Publishers \"As Fortnow describes... P versus NP is 'one of the great open problems in all of mathematics' not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, 'from cures to deadly diseases to the nature of the universe,' even 'an algorithmic process to recognize greatness.'... To postulate that P ? NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration--but also of discovery and inquiry, of pleasures pleasingly delayed.\"--Alexander Nazaryan, New Yorker \"Fortnow effectively initiates readers into the seductive mystery and importance of P and NP problems.\"--Publishers Weekly \"Fortnow's book is just the ticket for bringing one of the major theoretical problems of our time to the level of the average citizen--and yes, that includes elected officials.\"--Veit Elser, Science \"Without bringing formulas or computer code into the narrative, Fortnow sketches the history of this class of questions, convincingly demonstrates their surprising equivalence, and reveals some of the most far-reaching implications that a proof of P = NP would bring about. These might include tremendous advances in biotechnology (for instance, more cures for cancer), information technology, and even the arts. Verdict: Through story and analogy, this relatively slim volume manages to provide a thorough, accessible explanation of a deep mathematical question and its myriad consequences. An engaging, informative read for a broad audience.\"--J.J.S. Boyce, Library Journal \"A provocative reminder of the real-world consequences of a theoretical enigma.\"--Booklist \"The definition of this problem is tricky and technical, but in The Golden Ticket, Lance Fortnow cleverly sidesteps the issue with a boiled-down version. P is the collection of problems we can solve quickly, NP is the collection of problems we would like to solve. If P = NP, computers can answer all the questions we pose and our world is changed forever. It is an oversimplification, but Fortnow, a computer scientist at Georgia Institute of Technology, Atlanta, knows his stuff and aptly illustrates why NP problems are so important.\"--Jacob Aron, New Scientist \"Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science.\"--Rob Hardy, Commercial Dispatch \"A great book... [Lance Fortnow] has written precisely the book about P vs. NP that the interested layperson or IT professional wants and needs.\"--Scott Aaronson, Shtetl-Optimized blog \"[The Golden Ticket] is a book on a technical subject aimed at a general audience... Lance's mix of technical accuracy with evocative story telling works.\"--Michael Trick, Michael Trick's Operations Research Blog \"Thoroughly researched and reviewed. Anyone from a smart high school student to a computer scientist is sure to get a lot of this book. The presentation is beautiful. There are few formulas but lots of facts.\"--Daniel Lemire's Blog \"An entertaining discussion of the P versus NP problem.\"--Andrew Binstock, Dr. Dobb's \"The Golden Ticketis an extremely accessible and enjoyable treatment of the most important question of theoretical computer science, namely whether P is equal to NP.\"--Choice \"The book is accessible and useful for practically anyone from smart high school students to specialists... [P]erhaps the interest sparked by this book will be the 'Golden Ticket' for further accessible work in this area. And perhaps P=NP will start to become as famous as E=mc2.\"--Michael Trick, INFORMS Journal of Computing \"In any case, it is excellent to have a nontechnical book about the P versus NP question. The Golden Ticket offers an inspiring introduction for nontechnical readers to what is surely the most important open problem in computer science.\"--Leslie Ann Goldberg, LMS Newsletter \"The Golden Ticket does a good job of explaining a complex concept in terms that a secondary-school student will understand--a hard problem in its own right, even if not quite NP.\"--Physics World \"[The Golden Ticket] is fun to read and can be fully appreciated without any knowledge in (theoretical) computer science. Fortnow's efforts to make the difficult material accessible to non-experts should be commended.\"--Andreas Maletti, Zentralblatt MATH \"This is a fabulous book for both educators and students at the secondary school level and above. It does not require any particular mathematical knowledge but, rather, the ability to think. Enjoy the world of abstract ideas as you experience an intriguing journey through mathematical thinking.\"--Gail Kaplan, Mathematics Teacher \"Fortnow's book provides much of the background and personal information on the main characters involved in this problem--notably Steven Cook, with a cameo appearance by Kurt Godel--that one does not get in the more technical treatments. There is a lot of information in this book, and the serious computer science student is sure to learn from it.\"--James M. Cargal, UMAP Journal\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface ix Chapter 1 The Golden Ticket 1 Chapter 2 The Beautiful World 11 Chapter 3 P and NP 29 Chapter 4 The Hardest Problems in NP 51 Chapter 5 The Prehistory of P versus NP 71 Chapter 6 Dealing with Hardness 89 Chapter 7 Proving P \u0026lt;\u0026gt; NP 109 Chapter 8 Secrets 123 Chapter 9 Quantum 143 Chapter 10 The Future 155 Acknowledgments 163 Chapter Notes and Sources 165 Index 171","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537032535,"sku":"9780691175782","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"beautiful-geometry-9780691175881","title":"Beautiful Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eHonorable Mention for the 2015 PROSE Award in Popular Science \u0026amp; Popular Mathematics, Association of American Publishers \"A book that stimulates the mind as well as the eye.\"--Scientific American \"The combination of art and exposition was quite effective. The writing is accessible to most reasonably well-educated laypeople, and I imagine that many such people would derive considerable pleasure dipping into this attractive and interesting book.\"--Mark Hunacek, MAA Reviews \"Eli Maor's lively writing benefits in equal parts from the geometry of ancient Greece and the eye-popping images conjured by artist Eugen Jost.\"--Bill Cannon, Scientist's Bookshelf \"Graphic illustrations serve as both beautiful abstract art and helpful explanations in this overview of geometric theorems and patterns.\"--Science News \"[Beautiful Geometry] achieves its aim to demonstrate that there is visual beauty in Mathematics. I heartily recommend it.\"--LSE Review of Books \"The explanations are clear, and cover the background to the paintings in a manner that will be appreciated by readers whatever their level of mathematical knowledge... Anyone with any interest in visual mathematics will love this book.\"--Times Higher Education \"A good-looking, large-format book suitable for the coffee table, but with lots of mathematical ideas packed in among the colorful illustrations... [A] handsome book for browsing and for some deep thought, and would be a superb gift for anyone (especially a young person) who has interest in mathematics.\"--Rob Hardy, Columbus Dispatch \"It is a handsome book for browsing and for some deep thought, and would be a superb gift for anyone (especially a young person) who has interest in mathematics.\"--Rob Hardy, Dispatch \"The book by Maor and Jost should be given to everyone--young or old--embarking on the study of mathematics or anyone teaching mathematics. The book will act as a source of inspiration and as a reminder of why it is that mathematics has fascinated the human race for millennia.\"--Henrik Jeldtoft Jensen, LMS Newsletter \"The content is accessible to anyone with even a high school course in geometry. The writing is very clear.\"--Choice \"Clear and lively... The mathematics in this book is first-rate, but the real surprise is how well the art reflects and illuminates the topic at hand... All of it is lovely to look at... [Beautiful Geometry] rises to the level of a coffee-table art book, only with a lot more depth.\"--Mathematical Reviews \"[E]erily captivating book... Maor's style of writing is conversational, and the writing is engaging.\"--Annalisa Crannell, Journal of Mathematics and the Arts \"At a very reasonable price, this is a book which would grace the coffee-table of any mathematics department, and many of the ideas in it will stimulate valuable discussions in the classroom.\"--Gerry Leversha, Mathematical Gazette \"It presents as a coffee-table book for mathematicians and would be a good addition to a classroom library, available for students of all ages to explore.\"--Susan Mielechowsky, Mathematics Teaching in the Middle School \"Visually stunning... [Beautiful Geometry] raises fundamental questions, answered thousands of years later and evidencing the progress made... This is an engaging book of broad appeal and a colourful approach to the history of geometry.\"--Mathematics Today\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePrefaces ix 1.Thales of Miletus 1 2.Triangles of Equal Area 3 3.Quadrilaterals 6 4.Perfect Numbers and Triangular Numbers 9 5.The Pythagorean Theorem I","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537261911,"sku":"9780691175881","price":22.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175881.jpg?v=1722274447"},{"product_id":"heavenly-mathematics-9780691175997","title":"Heavenly Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Choice's Outstanding Academic Titles for 2013 Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics \"Once a mainstay of mathematics, spherical trigonometry no longer appears on school curricula. Here, Glen Van Brummelen reasserts the field's importance, sharing in illuminating detail how it figured in astronomy, cartography and our understanding of Earth's rotation.\"--Rosalind Metcalfe, Nature \"The present book is very well written; it leaves a clear impression that the author intended to endear--not merely present and teach--spherical trigonometry to the reader. Although not a history book, there are separate chapters shedding light on the approaches to the subject in the ancient, medieval, and modern times. There are also chapters on spherical geometry, polyhedra, stereographic projection and the art of navigation. The book is thoroughly illustrated and is a pleasant read. Chapters end with exercises; the appendices contain a long list of available and not so available textbooks and recommendations for further reading organized by individual chapters. The book made a valuable addition to my library. I freely recommend it to math teachers and curious high schoolers.\"--Alexander Bogomolny, CTK Insights \"A no-nonsense introduction to spherical trigonometry.\"--Book News, Inc. \"A beautiful popular book.\"--ThatsMaths.com \"Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun.\"--R. Balashankar, Organiser \"Heavenly Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry... As readers discover this discipline, they will also appreciate the beauty inherent in the topic.\"--Choice \"Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader.\"--Florin Diacu, Literary Review of Canada \"Van Brummelen has written a wonderful introduction ... that draws on the history of [spherical trigonometry] to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about.\"--Metascience \"[Heavenly Mathematics] is an excellent survey of spherical trigonometry... Simply an appreciation of a beautiful lost subject, with historical overtones... [D]istinguishable for its appealingly fresh style.\"--Mathematical Reviews \"[Heavenly Mathematics] is a lovely book to read... [A] wonderful introduction for anyone who wishes to learn more about this subject... I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it.\"--Mathematics Today \"Engaging, clear and not overly technical; you can safely lend this book to your friends in the history department... [Heavenly Mathematics] is excellent.\"--Zentralblatt MATH \"Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject.\"--Jan P. Hogendijk, Isis \"This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students.\"--Teresa Floyd, Mathematics Teacher \"Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins... Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative.\"--P.N. Ruane, Mathematical Gazette \"An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics.\"--Elizabeth Hamm, Aestimatio Critical Reviews in the History of Science\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii  1 Heavenly Mathematics 1  2 Exploring the Sphere 23  3 The Ancient Approach 42  4 The Medieval Approach 59  5 The Modern Approach: Right- Angled Triangles 73  6 The Modern Approach: Oblique Triangles 94  7 Areas, Angles, and Polyhedra 110  8 Stereographic Projection 129  9 Navigating by the Stars 151  Appendix A. Ptolemy's Determination of the Sun's Position 173  Appendix B. Textbooks 179  Appendix C. Further Reading 182  Index 189","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537327447,"sku":"9780691175997","price":17.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175997.jpg?v=1722274447"},{"product_id":"dr-eulers-fabulous-formula-9780691175911","title":"Dr. Eulers Fabulous Formula","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities... It would be good to have more books like this.\"--Timothy Gowers, Nature \"Nahin's tale of the formula e[pi] i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler.\"--Matthew Killeya, New Scientist \"It is very difficult to sum up the greatness of Euler... This excellent book goes a long way to explaining the kind of mathematician he really was.\"--Steve Humble, Mathematics Today \"What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics... This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors.\"--Henry Ricardo, MAA Reviews \"The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content.\"--Robert E. O'Malley, Jr., SIAM Review \"This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.\"--Eberhard Knobloch, Mathematical Reviews \"It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK.\"--Robin Wilson, London Mathematical Society Newsletter\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*Contents, pg. ix*Preface to the Paperback Edition, pg. xiii*Preface, pg. xxix*Introduction, pg. 1*Chapter 1. Complex Numbers, pg. 13*Chapter 2. Vector Trips, pg. 68*Chapter 3. The Irrationality of pi2, pg. 92*Chapter 4. Fourier Series, pg. 114*Chapter 5. Fourier Integrals, pg. 188*Chapter 6. Electronics and   -1, pg. 275*Euler: The Man and the Mathematical Physicist, pg. 324*Notes, pg. 347*Acknowledgments, pg. 375*Index, pg. 377","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865537360215,"sku":"9780691175911","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175911.jpg?v=1722274448"},{"product_id":"gamma-9780691178103","title":"Gamma","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAmong the many constants that appear in mathematics, ?, e, and i are the most familiar. Following closely behind is ?,, 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 harmon\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[A] wonderful book... Havil's emphasis on historical context and his conversational style make this a pleasure to read... Gamma is a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in maths will find it richly rewarding.\"--Ben Longstaff, New Scientist \"This book is a joy from start to finish.\"--Gerry Leversha, Mathematical Gazette \"Wonderful... Havil's emphasis on historical context and his conversational style make this a pleasure to read...Gammais a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in math will find it richly rewarding.\"--New Scientist\"A joy from start to finish.\"--Mathematical Gazette\"[Gamma] is not a book about mathematics, but a book of mathematics... [It] is something like a picaresque novel; the hero, Euler's constantg, serves as the unifying motif through a wide range of mathematical adventures.\"--Notices of the American Mathematical Society \"[Gamma] is enjoyable for many reasons. Here are just two. First, the explanations are not only complete, but they have the right amount of generality... Second, the pleasure Havil has in contemplating this material is infectious.\"--MAA Online \"It is only fitting that someone should write a book about gamma, or Euler's constant. Havil takes on this task and does an excellent job.\"--Choice \"Mathematics is presented throughout as something connected to reality... Many readers will find in [Gamma] exactly what they have been missing.\"--Mohammad Akbar, Plus Magazine, Millennium Mathematics Project, University of Cambridge \"This book is written in an informal, engaging, and often amusing style. The author takes pains to make the mathematics clear. He writes about the mathematical geniuses of the past with reverence and awe. It is especially nice that the mathematical topics are discussed within a historical context.\"--Ward R. Stewart, Mathematics Teacher\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eForeword xv  Acknowledgements xvii  Introduction xix  Chapter One  The Logarithmic Cradle 1  1.1 A Mathematical Nightmare- and an Awakening 1  1.2 The Baron's Wonderful Canon 4  1.3 A Touch of Kepler 11  1.4 A Touch of Euler 13  1.5 Napier's Other Ideas 16  Chapter Two  The Harmonic Series 21  2.1 The Principle 21  2.2 Generating Function for Hn 21  2.3 Three Surprising Results 22  Chapter Three  Sub-Harmonic Series 27  3.1 A Gentle Start 27  3.2 Harmonic Series of Primes 28  3.3 The Kempner Series 31  3.4 Madelung's Constants 33  Chapter Four  Zeta Functions 37  4.1 Where n Is a Positive Integer 37  4.2 Where x Is a Real Number 42  4.3 Two Results to End With 44  Chapter Five  Gamma's Birthplace 47  5.1 Advent 47  5.2 Birth 49  Chapter Six  The Gamma Function 53  6.1 Exotic Definitions 53  6.2 Yet Reasonable Definitions 56  6.3 Gamma Meets Gamma 57  6.4 Complement and Beauty 58  Chapter Seven  Euler's Wonderful Identity 61  7.1 The All-Important Formula 61  7.2 And a Hint of Its Usefulness 62  Chapter Eight  A Promise Fulfilled 65  Chapter Nine  What Is Gamma Exactly? 69  9.1 Gamma Exists 69  9.2 Gamma Is What Number? 73  9.3 A Surprisingly Good Improvement 75  9.4 The Germ of a Great Idea 78  Chapter Ten  Gamma as a Decimal 81  10.1 Bernoulli Numbers 81  10.2 Euler -Maclaurin Summation 85  10.3 Two Examples 86  10.4 The Implications for Gamma 88  Chapter Eleven  Gamma as a Fraction 91  11.1 A Mystery 91  11.2 A Challenge 91  11.3 An Answer 93  11.4 Three Results 95  11.5 Irrationals 95  11.6 Pell's Equation Solved 97  11.7 Filling the Gaps 98  11.8 The Harmonic Alternative 98  Chapter Twelve  Where Is Gamma? 101  12.1 The Alternating Harmonic Series Revisited 101  12.2 In Analysis 105  12.3 In Number Theory 112  12.4 In Conjecture 116  12.5 In Generalization 116  Chapter Thirteen  It's a Harmonic World 119  13.1 Ways of Means 119  13.2 Geometric Harmony 121  13.3 Musical Harmony 123  13.4 Setting Records 125  13.5 Testing to Destruction 126  13.6 Crossing the Desert 127  13.7 Shuffiing Cards 127  13.8 Quicksort 128  13.9 Collecting a Complete Set 130  13.10 A Putnam Prize Question 131  13.11 Maximum Possible Overhang 132  13.12 Worm on a Band 133  13.13 Optimal Choice 134  Chapter Fourteen  It's a Logarithmic World 139  14.1 A Measure of Uncertainty 139  14.2 Benford's Law 145  14.3 Continued-Fraction Behaviour 155  Chapter Fifteen  Problems with Primes 163  15.1 Some Hard Questions about Primes 163  15.2 A Modest Start 164  15.3 A Sort of Answer 167  15.4 Picture the Problem 169  15.5 The Sieve of Eratosthenes 171  15.6 Heuristics 172  15.7 A Letter 174  15.8 The Harmonic Approximation 179  15.9 Different-and Yet the Same 180  15.10 There are Really Two Questions, Not Three 182  15.11 Enter Chebychev with Some Good Ideas 183  15.12 Enter Riemann, Followed by Proof(s)186  Chapter Sixteen  The Riemann Initiative 189  16.1 Counting Primes the Riemann Way 189  16.2 A New Mathematical Tool 191  16.3 Analytic Continuation 191  16.4 Riemann's Extension of the Zeta Function 193  16.5 Zeta's Functional Equation 193  16.6 The Zeros of Zeta 193  16.7 The Evaluation of (x) and p(x)196  16.8 Misleading Evidence 197  16.9 The Von Mangoldt Explicit Formula-and How It Is Used to Prove the Prime Number Theorem 200  16.10 The Riemann Hypothesis 202  16.11 Why Is the Riemann Hypothesis Important? 204  16.12 Real Alternatives 206  16.13 A Back Route to Immortality-Partly Closed 207  16.14 Incentives, Old and New 210  16.15 Progress 213  Appendix A  The Greek Alphabet 217  Appendix B  Big Oh Notation 219  Appendix C  Taylor Expansions 221  C.1 Degree 1 221  C.2 Degree 2 221  C.3 Examples 223  C.4 Convergence 223  Appendix D  Complex Function Theory 225  D.1 Complex Differentiation 225  D.2 Weierstrass Function 230  D.3 Complex Logarithms 231  D.4 Complex Integration 232  D.5 A Useful Inequality 235  D.6 The Indefinite Integral 235  D.7 The Seminal Result 237  D.8 An Astonishing Consequence 238  D.9 Taylor Expansions-and an Important Consequence 239  D.10 Laurent Expansions-and Another Important Consequence 242  D.11 The Calculus of Residues 245  D.12 Analytic Continuation 247  Appendix E  Application to the Zeta Function 249  E.1 Zeta Analytically Continued 249  E.2 Zeta's Functional Relationship 253  References 255  Name Index 259  Subject Index 263","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865538539863,"sku":"9780691178103","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691178103.jpg?v=1722274454"},{"product_id":"elements-of-mathematics-9780691178547","title":"Elements of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[Stillwell] writes clearly and engagingly... [Elements of Mathematics] can appeal to various constituencies at different levels of mathematical sophistication.\"--Mark Hunacek, MAA Reviews \"A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together.\"--Antonio Cangiano, Math-Blog \"Stillwell is ... One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another... The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [Elements of Mathematics] as well.\"--MAA Reviews \"An accessible read... Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity.\"--Gemma Tarlach, Discover \"[A] sophisticated treatment of topics usually described as elementary.\"--John Allen Paulos \"[Elements of Mathematics] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!\"--Brent Yorgey, Math Less Traveled blog \"From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics.\"--Mathematical Reviews Clippings \"[A] wonderful book... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics.\"--Victor Katz, Bulletin of the American Mathematical Society \"Elements of Mathematicsis a fine ... overview of the field of mathematics... The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent... While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas... [T]his will make a fine basic addition to most mathematicians' bookshelves.\"--Math Tango \"Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning.\"--Convergence \"[A] wonderful book ... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics.\"--Victor Katz, Bulletin of the American Mathematical Society \"[Elements of Mathematics] is a book that everybody should read. You will be the better for it.\"--Reuben Hersh, American Mathematical Monthly\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*1. Elementary Topics, pg. 1*2. Arithmetic, pg. 35*3. Computation, pg. 73*4. Algebra, pg. 106*5. Geometry, pg. 148*6. Calculus, pg. 193*7. Combinatorics, pg. 243*8. Probability, pg. 279*9. Logic, pg. 298*10. Some Advanced Mathematics, pg. 336*Bibliography, pg. 395*Index, pg. 405","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865539260759,"sku":"9780691178547","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691178547.jpg?v=1722274459"},{"product_id":"the-secret-formula-9780691183671","title":"The Secret Formula","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The yeast of the story has been told already many times, but it has never been told like Toscano does in this book.\"\u003cb\u003e---Adhemar Bultheel, \u003ci\u003eEuropean Mathematical Society\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"The cubic formula will always be beyond my grasp . . . but the story of its discovery and of the men who battled over it, so memorably recounted in \u003ci\u003eThe Secret Formula\u003c\/i\u003e, is one I am glad to know.\"\u003cb\u003e---Jeff Jacoby, \u003ci\u003eBoston Globe\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Toscano weaves together his sources deftly to make the story as lively and exciting as a novel, with mathematics an organic part of the tale.\"\u003cb\u003e---Daniel J. Curtin, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Toscano is able to provide a realistic and accurate view that captures the complexity of the story of the cubic formula and the very different mathematical practices of this time. Anyone interested in learning about the history of mathematics will likely find it an interesting and informative read.\"\u003cb\u003e---Patrick Love, \u003ci\u003eLondon Mathematical Society Newsletter\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865542013271,"sku":"9780691183671","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691183671.jpg?v=1722274472"},{"product_id":"exploring-the-invisible-9780691191058","title":"Exploring the Invisible","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865542340951,"sku":"9780691191058","price":49.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691191058.jpg?v=1722274472"},{"product_id":"eulers-gem-9780691191379","title":"Eulers Gem","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Everything in the book is very well illustrated with insightful graphics that, together with the text, make results almost like being obvious.\"\u003cb\u003e---Adhemar Bultheel, \u003ci\u003eEuropean Mathematical Society\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865542504791,"sku":"9780691191379","price":16.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691191379.jpg?v=1722274474"},{"product_id":"ten-great-ideas-about-chance-9780691196398","title":"Ten Great Ideas about Chance","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"A volume that should be on every scientist's reading list.\"\u003cb\u003e—Barbara Kiser, \u003ci\u003eNature\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"A terrific book.\"\u003cb\u003e—\u003ci\u003eMathematics Magazine\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Fun and entertaining to read.\"\u003cb\u003e\u003ci\u003e—MAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"To anyone with an interest in probability or statistics, this is a book you must read. . . . [It] is far-ranging and can be read at many levels, from the novice to the expert. It is also thoroughly engaging.\"\u003cb\u003e—David M. Bressoud, \u003ci\u003eUMAP Journal\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"A very enriching journey. Your vision will be broadened.\"\u003cb\u003e—Adhemar Bultheel, \u003ci\u003eEuropean Mathematical Society\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"A great book for anyone who wants to understand some of the central tenets of probability, how they were discovered, and how they can be tamed in our day-to-day lives.\"\u003cb\u003e\u003ci\u003e—ZME Science\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865544143191,"sku":"9780691196398","price":14.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691196398.jpg?v=1722274484"}],"url":"https:\/\/bookcurl.com\/collections\/philosophy-of-mathematics.oembed?page=17","provider":"Book Curl","version":"1.0","type":"link"}