History of mathematics Books

Book SynopsisLockhart’s Mathematician’s Lament outlined how we introduce math to students in the wrong way. Measurement explains how math should be done. With plain English and pictures, he makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living.Trade ReviewA love song and a philosophical manifesto about the pleasures and frustrations, but mainly the pleasures, of doing math.In place of the usual boxed and high-lighted formulas and tricks, Measurement offers questions to be pondered. Lockhart invites readers to trade tutorial fake problems about actual objects, which lead students to abhor school mathematics, for real problems about fantastical objects, which lead mathematicians to love math. * Science *A conversational book about mathematics as an art that invites the reader to join in the fun. Sounding every bit the teacher whose love for his subject is infectious, he guides us through exercises in geometry and calculus—giving information and hints along the way while always encouraging us to ask, and answer, ‘Why?’ Lockhart does not try to make math seem easy; instead he wants his readers to understand that the difficulty brings rewards. * Scientific American *This invitation to tackle mathematical questions is infused with the joys of the rarefied reality of maths. Paul Lockhart largely avoids complex formulae and the wilder shores of jargon, opting instead for simple geometric drawings, lucid instructions and honest warnings about the hurdles. Covering size, shape, space and time, Lockhart, a maths teacher, gets through scores of problems, from showing that a cone in a hemisphere occupies half the volume to determining the size of the largest circle that can sit at the bottom of a parabola. Elegant, amusing and challenging. * Nature *This book forced me to use mental muscles I haven’t exercised in a long time, but it felt fantastic! Paul Lockhart is a mathematics evangelist; his passion for his subject is evident on every page, in every line. Looking at the subject of Measurement, he takes the reader on a journey that covers geometry, algebra, trigonometry, and on through differential calculus. He has a conversational tone and self-deprecating humor that sets the reader at ease. He understands that many people have been turned off of mathematics. His attitude is playful and joyous… Math is usually taught in such a compartmentalized way that it loses any meaning or coherence, and certainly any sense of wonder or beauty, but Measurement restores the connection. Paul Lockhart feels that math is the most beautiful, abstract and pure art form, and that it is actually fun! By the end of the book, you come to agree with him. * Sacramento Book Review *There are many books available these days on what mathematicians do, and this is one of the best… Lockhart’s approach is fresh and effective. * Choice *Lockhart presents math as an art and argues that just as there is no systematic way to create beautiful and meaningful art, there is also no method for producing beautiful and meaningful mathematical arguments. Doing mathematics, according to Lockhart, is to make a discovery (by, say, physical objects like string or rubber bands) and then to explain it in the simplest and most elegant way possible. Using illustrations of various shapes and mathematical formulas, he leads readers through several problems step by step, encouraging them to collaborate with others in working through the problem. Measuring, for example, is relative because it involves comparing the object being measured to another object. Measurement is only one of the many rivers in the ‘vast, ever-expanding jungle’ of mathematics, which for Lockhart satisfies our need to find patterns as well as our curiosity… His playful and ingenious approach not only takes the fear out of math but also elegantly illustrates that universe and the joy he finds in it. * Publishers Weekly *No matter what mathematical education you had, or didn’t have, you will be delighted by this enticing book if you take up Paul Lockhart’s invitation to engage in the mathematical sensibility that radiates from its pages, and try your own hand—not only at answering, but even more fruitfully, at formulating questions as you explore the world of mathematics.

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Book SynopsisThe Science of Secrecy from Ancient Egypt to Quantum Cryptography From the best-selling author of Fermat’s Last Theorem, The Code Book is a history of man’s urge to uncover the secrets of codes, from Egyptian puzzles to modern day computer encryptions. As in Fermat’s Last Theorem, Simon Singh brings life to an anstonishing story of puzzles, codes, languages and riddles that reveals man’s continual pursuit to disguise and uncover, and to work out the secret languages of others. Codes have influenced events throughout history, both in the stories of those who make them and those who break them. The betrayal of Mary Queen of Scots and the cracking of the enigma code that helped the Allies in World War II are major episodes in a continuing history of cryptography. In addition to stories of intrigue and warfare, Simon Singh also investigates other codes, the unravelling of genes and the rediscovery of ancient languages and most tantalisingly, the Beale ciphers, an unbroken code that could hold the key to a $20 million treasure.Trade Review‘A fascinating meander through the centuries; replete with tales of intrigue, political chicanery, military secrecy and academic rivalry.’The Times

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Book Synopsis20 years later The Music of the Primes is still a groundbreaking popular science book. This new edition features updates from the author and a foreword by actor and director, Simon McBurney. In 1859, the German mathematician Bernhard Riemann presented a paper to the Berlin Academy which would change the history of mathematics. The subject was the strange and enigmatic prime numbers. At the heart of the presentation was an idea, a hypothesis, that Riemann had not yet proved but which has come to obsess mathematicians for the last 150 years. No one knows if he ever found the proof; on his death his housekeeper burnt all the personal papers. Today, the hypothesis is considered by many the holy grail of mathematics but has significance far beyond maths. At the of the heart of the enigma is a prize much larger than just intellectual glory; not only is there a $1 million reward for the person who can crack it but also is the key to all banking and e-commerce security. It is the idea that brings together many other areas of science and has ramifications within Quantum Mechanics, Chaos Theory and the future of computing. In 'The Music of the Primes', one of Britain's leading mathematicians, Marcus du Sautoy, recounts the history of these elusive numbers. It is a story of eccentric and brilliant men, last minute escapes from death, strange journeys, dangerous ideas and the unquenchable thirst for knowledge that drove some men mad and others to unparalleled glory. du Sautoy also tells a coruscating history of Mathematics. Combining in-depth knowledge as a practitioner in the field with narrative flair, this book will become a classic of popular science writing and will rank alongside 'Chaos' and 'Fermat's Last Theorem' within the genre. The Riemann Hypothesis:• Compared to Fermat's Last Theorem, the Hypothesis is mathematicians’ real Holy Grail• Is the only problem from Hilbert's 1900 Centenary Problems that was unproved in the 20th century and now has a $1 million reward for the person who cracks it.• The Hypothesis is the key to all Internet and e-commerce securityTrade Review'Du Sautoy is a contagious enthusiast, a populist with a staunch faith in the public's intelligence…he has uncovered a wealth of intriguing anecdotes that he has woven into a compelling narrative.' Observer 'He laces the ideas with history, anecdote and personalia – an entertaining mix that renders an austere subject palatable…valiant and ingenious…Even those with a mathematical allergy can enjoy du Sautoy's depictions of his cast of characters' The Times 'He brings hugely enjoyable writing, full of zest and passion, to the most fundamental questions in the pursuit of true knowledge.' Sunday Times 'A mesmerising journey into the world of mathematics and its mysteries.' Daily Mail 'A brilliant storyteller.' Independent

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Book SynopsisTrade Review"In this intriguing study, maths historian Eli Maor traces those echoes, along with the trajectories of the ‘scientists, inventors, composers, and occasional eccentrics’ behind them."---Barbara Kiser, Nature"The prolific author Eli Maor has released yet another very readable and enjoyable book on the history of mathematics from Princeton University Press. . . . As with all of Maor’s books, this one belongs in your library so that leading students can learn about unknowns like Joseph Sauveur in the fascinating story of how mathematics and music intersect."---Karl-Dieter Crisman, MAA Reviews"Maor is an experienced storyteller. His mixture of musical, mathematical, and physical history, enriched with personal experiences and some unexpected links and bridges are nice reading for anybody with a slight interest in music and science. No mathematical training required."---Adhemar Bultheel, European Mathematical Society"This is a fascinating study of the reciprocal relationship between music and mathematics in the West."---David Lorimer, Paradigm Explorer"For anyone who ponders the role mathematics has in music, this short and delightful book is a joy to read from cover to cover. It is full of anecdotes and interesting facts and, being by Eli Maor is intensely readable."---Phil Dyke, Leonardo Reviews"[Music by the Numbers] is enjoyable and readable"---Owen Toller, Mathematical Gazette

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Book SynopsisTrade ReviewBestselling physicist Carlo Rovelli argues in this enjoyable and provocative little book that a little-known Greek philosopher invented the idea of the cosmos -- Tim Adams * Observer *Carlo Rovelli’s Anaximander is a knockout: there’s nobody like Rovelli for bridging the Two Cultures, and I was enlarged by his lucid, optimistic account, full of fascinating historical nuggets, of what scientists do and why it’s exciting -- Sam Leith * TLS , Best Books of the Year *Rovelli is a very good scientist and a very good writer. He explains some of the most conceptually difficult and densest areas of physics lightly and breezily. Here, he tells the story of an ancient thinker who had a revolutionary idea about the Earth's place in the cosmos -- Tom Whipple * The Times *Anaximander is a delight and so is this book -- James McConnachie * Sunday Times *As Rovelli's fans will expect, this book is excellent. It is never less than engaging, and enviably compendious -- Tim Smith-Laing * The Telegraph *A celebration of the scientific spirit of inquiry and the remarkable achievements of one man more than 2,500 years ago -- John Sellars * TLS *A bold and persuasive case that this ancient Greek philosopher scientist was the founder of critical thinking -- Adam Rutherford * Start the Week, BBC Radio 4 *This is seriously astounding. So lucid, so imaginative, so subtle, and so large in scope. It's like the best primer you can imagine for the non-scientist on why what you think you know about Ptolemy and Copernicus, or Popper and Kuhn, is not quite right -- Sam Leith * Twitter *

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Book SynopsisNearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th-century mathematician Oliver Byrne employed the color scheme for his 1847 edition of Euclid’s mathematical and geometric treatise Elements. Byrne’s idea was to use color to make learning easier and “diffuse permanent knowledge.” The result has been described as one of the oddest and most beautiful books of the 19th century. The facsimile of Byrne’s seminal publication is now available in a beautiful new edition. A masterwork of art and science, it is as remarkable in the boldness of its red, yellow, and blue figures and diagrams as it is in the mathematical precision of its theories. In the simplicity of forms and colors, the pages anticipate the vigor of De Stijl and Bauhaus design. In making complex information at once accessible and aesthetically engaging, this work is a forerunner to the information graphics that today define much of our data consumption.Trade Review“Every graphic designer, book lover and math nerd will be awestruck.” * The New York Times *

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Book SynopsisAll the Math Your 4th Grader Needs to SucceedThis book will help your elementary school student develop the math skills needed to succeed in the classroom and on standardized tests. The user-friendly, full-color pages are filled to the brim with engaging activities for maximum educational value. The book includes easy-to-follow instructions, helpful examples, and tons of practice problems to help students master each concept, sharpen their problem-solving skills, and build confidence.Features include:â A guide that outlines national standards for Grade 4â Concise lessons combined with lot of practice that promote better scoresâin class and on achievement testsâ A pretest to help identify areas where students need more workâ End-of-chapter tests to measure studentsâ progressâ A helpful glossary of key terms used in the bookâ More than 1,000 math problems with answersTopics covered:â Adding and

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Book SynopsisAll the Math Your 5th Grader Needs to SucceedThis book will help your elementary school student develop the math skills needed to succeed in the classroom and on standardized tests. The user-friendly, full-color pages are filled to the brim with engaging activities for maximum educational value. The book includes easy-to-follow instructions, helpful examples, and tons of practice problems to help students master each concept, sharpen their problem-solving skills, and build confidence.Features include:â A guide that outlines national standards for Grade 5â Concise lessons combined with lot of practice that promote better scoresâin class and on achievement testsâ A pretest to help identify areas where students need more workâ End-of-chapter tests  to measure studentsâ progressâ A helpful glossary of key terms used in the bookâ More than 1,000 math problems with answersTopics covered:â Opera

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Book SynopsisTrade Review"A volume that should be on every scientist's reading list."—Barbara Kiser, Nature"A terrific book."—Mathematics Magazine"Fun and entertaining to read."—MAA Reviews"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."—David M. Bressoud, UMAP Journal"A very enriching journey. Your vision will be broadened."—Adhemar Bultheel, European Mathematical Society"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."—ZME Science

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Book SynopsisIn this book, Johnny Ball tells one of the most important stories in world history the story of mathematics. By introducing us to the major characters and leading us through many historical twists and turns, Johnny slowly unravels the tale of how humanity built up a knowledge and understanding of shapes, numbers and patterns from ancient times, a story that leads directly to the technological wonderland we live in today. As Galileo said, Everything in the universe is written in the language of mathematics', and Wonders Beyond Numbers is your guide to this language. Mathematics is only one part of this rich and varied tale; we meet many fascinating personalities along the way, such as a mathematician who everyone has heard of but who may not have existed; a Greek philosopher who made so many mistakes that many wanted his books destroyed; a mathematical artist who built the largest masonry dome on earth, which builders had previously declared impossible; a world-renowned pTrade ReviewThe great strength of this book is probably its wide coverage of practical applications of mathematics, especially in engineering and architecture. * The Mathematical Gazette *Johnny Ball's trademark enthusiasm for mathematics bubbles off every page. Clear, simple, readable, and informative – just as I expected. It's a winner! -- Ian Stewart, author of Significant FiguresI became an instant Johnny Ball fan when his TV series Think of a Number first aired in the UK, and I saw how he engaged and delighted my two young daughters in a way I, their maths professor dad, could not. With this new book, his passion for, and sheer enjoyment of, mathematics will surely entice yet more generations to the subject we both love. -- Keith Devlin, Stanford University mathematician, award-winning author and the 'Math Guy' on America's radio.I always found maths intriguing and baffling in equal measure - and the latter triumphed. If only I'd had Wonders Beyond Numbers when growing up. But I now have it and it is a re-awaking into a world of delight and wonder. It is a wonderful book. -- Anthony Seldon, Vice-Chancellor of the University of BuckinghamTable of ContentsPreface: Mathematics means everything to me... Wow Factor Mathematical Index Explained Introduction: Russian Sums in an English Pub, Circa 1946 Chapter 1: The Most Ancient Mathematical Legend Chapter 2: The First Two Great Mathematicians Chapter 3: The Great Age of Grecian Geeks Chapter 4: Archimedes – the Greatest Greek of Them All Chapter 5: The Glory That Was Alexandria Chapter 6: Total Eclipse of the Greeks Chapter 7: Maths Origins, Far and Wide Chapter 8: Mathematics Was Never a Religion Chapter 9: Discovering the Unknown World Chapter 10: The Huge Awakening and a New Age of Learning Chapter 11: The New Age of Mathematical Discovery Chapter 12: How to Calculate Anything and Everything Chapter 13: A Mathematician With Gravitas Chapter 14: The Simple Mathematics That Underpins Science Chapter 15: The Many Tentacles of Mathematics Wow Factor Mathematical Index Bibliography Image credits Index

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Book SynopsisTrade ReviewWinner of the 2016 PROSE Award in Mathematics, Association of American Publishers One of Choice's Outstanding Academic Titles for the Year Winner of the 2016 PROSE Award in Mathematics, Association of American Publishers One of Choice's Outstanding Academic Titles for 2015 "Mathematics without Apologies is a kaleidoscope of philosophical, sociological, historical and literary perspectives on what mathematicians do, and why."--Amir Alexander, Nature "A wry and insightful look at what being a pure mathematician is all about, as seen from the inside."--Steven Strogatz, Physics Today "If you are interested at all in what mathematics really is and what the best mathematicians really do (and you're up for an intellectual challenge), I highly recommend that you get a copy and set some time aside for delving into this unusual book... Harris manages to move back and forth between the deepest ideas about mathematics at the frontiers of the subject, insightful takes on the sociology of mathematical research, and a variety of topics pursued in a sometimes gonzo version of post-modern academic style. You will surely sometimes be baffled, but definitely will come away knowing about many things you'd never heard of before, and with a lot of new ideas to think about."--Peter Woit, Not Even Wrong "Harris is the kind of mathematician one hopes to meet at an intimate dinner party. By sharing his professional and personal relationship to mathematics, [he] links art, philosophy, music, and literature to academic culture and research problems."--Library Journal "Extraordinary, extravagant... Harris is a polyglot, deeply learned. Threading through his remarkable book, unifying it, is Hardy's lament regarding whether a pure mathematician can make a claim that the vocation has a philosophically 'useful' purpose. Harris's reply is multivalent, persuasive, and profound. A book to be read and then read again."--Choice "The erudition displayed by Harris in this book is amazing... The satisfaction it gives is more than rewarding."--A. Bultheel, Adhemar Bultheel Blog "This book is a rich tapestry interweaving various aspects of culture and tradition--social, economic, religious, aesthetic--in an attempt to explicate the three basic philosophical questions underlying mathematics as a human endeavor: the What, Why and How of it."--Swami Vidyanathananda, Prabuddha Bharata "Michael Harris is more than a mathematician; he is a Parisian intellectual."--Brendan Larvor, London Mathematical Society Newsletter "Even apprentice number theorists can understand and enjoy this well-written book. Harris's theories are coherent and rational, and he provides lay readers clarity into what contemporary mathematicians really do."--Bernadette Trainer, Mathematics TeacherTable of ContentsPreface ix Acknowledgments xix Part 1 Chapter 1. Introduction: The Veil 3 Chapter 2. How I Acquired Charisma 7 Chapter alpha. How to Explain Number Theory at a Dinner Party 41 (First Session: Primes) 43 Chapter 3. Not Merely Good, True, and Beautiful 54 Chapter 4. Megaloprepeia 80 Chapter ss. How to Explain Number Theory at a Dinner Party 109 (Second Session: Equations) 109 Bonus Chapter 5. An Automorphic Reading of Thomas Pynchon's Against the Day (Interrupted by Elliptical Reflections on Mason & Dixon) 128 Part II 139 Chapter 6. Further Investigations of the Mind-Body Problem 141 Chapter ss.5. How to Explain Number Theory at a Dinner Party 175 (Impromptu Minisession: Transcendental Numbers) 175 Chapter 7. The Habit of Clinging to an Ultimate Ground 181 Chapter 8. The Science of Tricks 222 Part III 257 Chapter gamma. How to Explain Number Theory at a Dinner Party 259 (Third Session: Congruences) 259 Chapter 9. A Mathematical Dream and Its Interpretation 265 Chapter 10. No Apologies 279 Chapter delta. How to Explain Number Theory at a Dinner Party 311 (Fourth Session: Order and Randomness) 311 Afterword: The Veil of Maya 321 Notes 327 Bibliography 397 Index of Mathematicians 423 Subject Index 427

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Book SynopsisCalculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.Trade ReviewA masterpiece... Packed with insights, both historical and mathematical. * Steven Strogatz, professor of mathematics, Cornell University, and author of The Joy of X and Infinite Powers *This is the book on calculus I wish I'd written. It's a beautifully simple, friendly guide that's bursting at the seams with glorious, persuasive explanations as to why calculus is one of the most powerful ideas ever conceived by mankind. * Hannah Fry, Broadcaster, lecturer, and author of The Mathematics of Love *A splendid little book ... accessible to a very wide audience ... The book is highly recommended. * Adam McBride, Mathematical Gazette *A remarkably expansive and frictionless tour of mathematical history and theory... The calculus story is no textbook... It is the antithesis of the dreary way calculus is too often taught at schools and universities... a supplement for a high school student, the parents of such a student, or an adult wishing to reacquaint herself painlessly with material long forgotten. * Henrik Latter, Plus *This is a very readable book... It offers an illuminating perspective on calculus... A very enjoyable book for the layperson or the user of calculus. * Alex Chaplin, School Science Review *Wish I'd had it as a maths student! * Tim Harford, Undercover Economist *Another wonderful book. * Mark McCartney, LMS Newsletter *A very clear explanation of calculus ([I] wish I'd had it as a maths student!) along with some history of the subject. * Tim Harford, The Undercover Economist *Superb introduction to calculus that should be in every young mathematician's bookcase. * Peter Ransom, Symmetry Plus *Don't panic if your mathematical muscles appear to have withered away (or you never truly cracked differentiation), David Acheson's The Calculus Story could be just the thing... A roller-coaster read, constantly climbing and diving through the wonderful world of calculus... There's something for everyone, from the inexperienced integrator to the seasoned solver of equations... His enthusiasm for calculus is almost palpable. * Timothy Revell, New Scientist *Dazzling. * Matthew Reisz, Times Higher Education *I would have killed for this book when I was 13 ... he [David Acheson] belongs in the league of great authors of popular works on mathematics. * George Matthews, Mathematics Today *A worthy successor to 1089 and All That. * Adhemar Bult heel, European Mathematical Society *A simple guide to calculus - where it came from, how it works, what it's good for, and where it went. Brief, informative, charming, and a model of clarity. Ideal motivation for beginners, and recommended to anyone who wonders what the subject is about. * Ian Stewart, author of Seventeen Equations that Changed the World *This wide-ranging picture of calculus and its applications, from antiquity to the present, reveals the method as both the key to much of modern science and engineering, and something of a mathematical adventure. * Science *Acheson offers a much-needed short account of the big picture of calculus as a whole, illustrated with examples and reproductions from historic publications [...] Short pages, many illustrations, and a sense of telling a big story contribute to the success of the book. * Paul J. Campbell, Mathematical Magazine *Table of ContentsREFERENCES; FURTHER READING; INDEX

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Book SynopsisThis 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 disciplinTrade Review"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 ScienceTable of ContentsFOREWORD 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

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Book SynopsisInthe tradition of Fermat’s Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematics—the formula to predict prime numbers.Oliver Sacks, author of The Man Who Mistook His Wife for a Hat, calls TheMusic of the Primes “an amazing book. . . . I could not put it down once Ihad started.” Simon Winchester, author of The Professor and the Madman,writes, “this fascinating account, decoding the inscrutable language of themathematical priesthood, is written like the purest poetry. Marcus du Sautoy''s enthusiasm shines through every line of this hymnto the joy of high intelligence, illuminating as it does so even the darkestcorners of his most arcane universe.”

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Book SynopsisOriginally published between 1880 and 1886, this two-volume work by George Shoobridge Carr (1837–1914) was intended as an aid to students preparing for the Cambridge Mathematical Tripos. Most notably, it played an important part in the mathematical education of the Indian prodigy Srinivasa Ramanujan (1887–1920).Table of ContentsPart I. 1. Mathematical tables; 2. Algebra; 3. Theory of equations; 4. Plane trigonometry; 5. Spherical trigonometry; 6. Elementary geometry; 7. Geometrical conics.

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Book SynopsisPresents 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.Trade Review"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 MathematicaTable of ContentsPreface 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

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Book SynopsisProviding insight into one of the most fascinating and unique subjects in statistics, this book examines classic problems of probability that have both contributed to the field and have been of historical significance, including Parrondo's Amazing Paradox, Laplace's Rule of Succession, and Jacob Bernoulli and His Golden Theorem.Trade Review“Thus, the book can be highly recommend to every lecturer in this field and every student interested in probability and statistics.” (Zentralblatt Math, 1 September 2013)Table of ContentsPreface ix Acknowledgments xi 1 Cardano and Games of Chance (1564) 1 2 Galileo and a Discovery Concerning Dice (1620) 9 3 The Chevalier de Méré Problem I: The Problem of Dice (1654) 13 4 The Chevalier de Méré Problem II: The Problem of Points (1654) 20 5 Huygens and the Gambler’s Ruin (1657) 39 6 The Pepys–Newton Connection (1693) 49 7 Rencontres with Montmort (1708) 54 8 Jacob Bernoulli and his Golden Theorem (1713) 62 9 De Moivre’s Problem (1730) 81 10 De Moivre, Gauss, and the Normal Curve (1730, 1809) 89 11 Daniel Bernoulli and the St. Petersburg Problem (1738) 108 12 d’Alembert and the “Croix ou Pile” Article (1754) 119 13 d’Alembert and the Gambler’s Fallacy (1761) 124 14 Bayes, Laplace, and Philosophies of Probability (1764, 1774) 129 15 Leibniz’s Error (1768) 156 16 The Buffon Needle Problem (1777) 159 17 Bertrand’s Ballot Problem (1887) 169 18 Bertrand’s Strange Three Boxes (1889) 175 19 Bertrand’s Chords (1889) 179 20 Three Coins and a Puzzle from Galton (1894) 186 21 Lewis Carroll’s Pillow Problem No. 72 (1894) 189 22 Borel and a Different Kind of Normality (1909) 194 23 Borel’s Paradox and Kolmogorov’s Axioms (1909, 1933) 199 24 Of Borel, Monkeys, and the New Creationism (1913) 208 25 Kraitchik’s Neckties and Newcomb’s Problem (1930, 1960) 215 26 Fisher and the Lady Tasting Tea (1935) 224 27 Benford and the Peculiar Behavior of the First Significant Digit (1938) 233 28 Coinciding Birthdays (1939) 240 29 Lévy and the Arc Sine Law (1939) 247 30 Simpson’s Paradox (1951) 253 31 Gamow, Stern, and Elevators (1958) 260 32 Monty-Hall, Cars, and Goats (1975) 264 33 Parrondo’s Perplexing Paradox (1996) 271 Bibliography 277 Photo Credits 296 Index 299

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Book SynopsisTrade ReviewPublishers Weekly "Stewart shares his enthusiasm as well as his knowledge in this tour of ground-breaking equations and the research they supported... An entertaining and illuminating collection of curious facts and histories suitable for random dipping-in or reading straight through." Kirkus Reviews "Stewart provides clear, cogent explanations of how the equations work without burdening the reader with cumbersome derivations... He gives a fascinating explanation of how Newton's laws, when extended to three-body problems, are still used by NASA to calculate the best route from Earth to Mars and have laid the basis for chaos theory. Throughout, Stewart's style is felicitous." Discover "Seemingly basic equations have enabled us to predict eclipses, engineer earthquake-proof buildings, and invent the refrigerator. In this lively volume, mathematician Ian Stewart delves into 17 equations that shape our daily existence, including those dreamed up by the likes of Einstein, Newton, and Erwin Schrodinger." Maclean's "Stewart is the finest living math popularizer-a writer who can tackle eye-spraining mathematical topics approachably, and yet dazzle hard-core nerds with new and surprising information. It is hard not to get your money's worth from him, and in a book like this he is at his best because of the very wide ground covered." Library Journal "Stewart's expertise and his well-developed style (enhanced by a nice sense of humor) make for enjoyable reading... [A] worthwhile and entertaining book, accessible to all readers. Recommended for anyone interested in the influence of mathematics on the development of science and on the emergence of our current technology-driven society." Washington Independent Review of Books "Stewart has managed to produce a remarkably readable, informative and entertaining volume on a subject about which few are as well informed as they would like to be." New York Journal of Books "Stewart is a genius in the way he conveys his excitement and sense of wonder... He has that valuable grasp of not only what it takes to make equations interesting, but also to make science cool."Table of ContentsWhy Equations? 1. The squaw on the hippopotamus 2. Shortening the proceedings 3. Ghosts of departed quantities 4. The system of the world 5. Portent of the ideal world 6. Much ado about knotting 7. Patterns of chance 8. Good vibrations 9. Ripples and blips 10. The ascent of humanity 11. Waves in the ether 12. Law and disorder 13. One thing is absolute 14. Quantum weirdness 15. Codes, communications, and computers 16. The imbalance of nature 17. The Midas formula Where Next?

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Book SynopsisIn his monumental 1687 work, Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. This is a modern translation based on the 1726 edition.

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Book SynopsisA gently guided, profusely illustrated Grand Tour of the world of mathematics.

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Book SynopsisTrade Review"A historical and philosophical tour of major insights in the development of probability theory."---James Ryerson, New York Times Book Review"A volume that should be on every scientist’s reading list."---Barbara Kiser, Nature"Mathematically rigorous, yet also reasonably accessible; informative, yet fun and entertaining to read. Both students and faculty should find reading this to be a rewarding experience." * MAA Reviews *"The audience is quite specific, but for them it will be a gem. . . . I would recommend this to any student studying or having studied anything statistics related at university."---Jonathan Shock, Mathemafrica"A very enriching journey. Your vision will be broadened assimilating all these issues and solutions as well as open problems from the early history of probability, game theory, financial markets, politics, thermodynamics, quantum theory and much much more."---Adhemar Bultheel, European Mathematical Society"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." * ZME Science *"This book will not increase your odds of winning at games of chance, but it will give you some greater understanding of why you lose." * Cosmos *"Ten Great Ideas about Chance isn’t just about 18th century philosophical arguments, World War II events or tests of expensive, hard-to-pronounce drugs. The book’s ideas are as down to earth and as current as your busted bracket for NCAA Men’s Basketball." * Herald Business Journal *"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, written in a conversational style with many examples and asides and an emphasis throughout on the people who have built the theory."---David M. Bressoud, UMAP Journal"A terrific book. The authors explain 10 great ideas in probability, starting from their history and pursuing their philosophical implications."---Eric S. Rosenthal, Mathematics Magazine

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Book SynopsisThe Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.Trade ReviewA remarkable book. Mr. Franklin writes clearly and exhibits a wry wit. But he also ranges knowledgeably across many disciplines and over many centuries. Wall Street Journal The Science of Conjecture opens an old chest of human attempts to draw order from havoc and wipes clean the rust from some cast-off classical tools that can now be reused to help build a framework for the unpredictable future. Science Franklin's style is clear and fluent, with an occasional sly Gibbonian aside to make the reader chuckle. New Criterion An admirably accessible study written in a crisp prose. It presents the reader with anarching historical perspective throughout many a century of human action. -- Giora Hon Centaurus Franklin gives a magisterial account of matters as diverse as the Talmud, Justinian's Digest, torture, witch hunts, Tudor treason trials, ancient and medieval astronomy and physics, humanist historiography, scholastic philosophy, speculations in public debt, and 17th century mathematics. His treatment of medieval law is among the best I have ever read. International Journal of Evidence and Proof Franklin's book is magnificent... Think of [it] as a non-fiction equivalent of Tolstoy's War and Peace. -- Peter Tillers The Jurist The Science of Conjecture is a masterly work, beautifully written, and based on encyclopaedic research... It is simply a tour de force that is unlikely to be surpassed for many a year. -- Barry Miller The Thomist Statistics teachers who like to sprinkle a little history and philosophy into their classes will find much here to delight and challenge them... This is a serious and scholarly work that I expect often will inform my teaching. -- Richard J. Cleary Journal of the American Statistical Association [This book has given me] sheer enjoyment in its density of strange information, in the wit and clarity if its writing, and in the vigour of its argumentation. I recommend it unreservedly to all interested in its subject. -- Oliver Mayo Australian and New Zealand Journal of Statistics This is the intellectual book of the year, and it ought to become one of the great classics of intellectual history. -- Scott Campbell Interdisciplinary Science Reviews The strength of The Science of Conjecture lies in its panoramic exposition of developments across the centuries and across intellectual disciplines and human endeavors. It is, as one reviewer wrote, 'a magesterial account of matters as diverse as the Talmud, Justinian's Digest, torture, witch hunts, Tudor treason trials, ancient and medieval astronomy and physics, humanist histriography, scholastic philosophy, speculations in public debt, and 17th century mathematics.' -- D. H. Kaye Law and History Review A remarkable book. Mr. Franklin writes clearly and exhibits a wry wit. But he also ranges knowledgeably across many disciplines and over many centuries. There are several reasons to read this book, but perhaps the best reason is its contemporary relevance. The lessons he discusses have pertinence to an age like ours, which has witnessed a gradual waning of faith in the objectivity of the relation of uncertain evidence to conclusion. Wall Street Journal In The Science of Conjecture, James Franklin shows us how deeply and subtly jurists and philosophers from ancient Greece onwards have explored how we can deal rationally with real-life cases (law cases, for instance, or scientific experiments) where the link between cause and effect is not obvious. -- J.M. Coetzee The Australian Since many in the nominalist/empiricist/positivist tradition deny that we can know natures, this book has a place in teacher education as well as legal education for the challenges it poses the reader on how we know, and how well we know, through induction, perception and abstraction. Metascience The text has an even wider importance in that it signals the need for more, not less, study of the history, philosophy and social studies in science to occupy a greater space in undergraduate degrees so that an educated electorate is better able to evaluate what the STEM community tells us is good for the progress of society. MetascienceTable of ContentsContents: Preface Chapter 1: The Ancient Law of Proof Egypt and Mesopotamia; The Talmud; Roman Law; Proof and Presumptions; Indian LawChapter 2: The Medieval Law of Evidence: Suspicion, Half-proof, and the Inquisition Dark Age Ordeals; The Gregorian Revolution; The Glossators Invent Half-Proof; Presumptions in Canon Law; Grades of Evidence and Torture; The Postglossators Bartolus and Baldus; The Competed Theory; The Inquisition; Law in the EastChapter 3: Renaissance Law Henry VIII Presumed Wed; Tudor Treason Trials; Continental Laws: The Treatises on Presumptions; The Witch Inquisitors; English Legal Theory and the Reasonable ManChapter 4: The Doubting Conscience and Moral Certainty Penance and Doubts; The Doctrine of Probabilism; Suarez: Negative and Positive Doubt; Grotius, Silhon, and the Morality of the State; Hobbes and the Risk of Attack; The Scandal of Laxism; English Casuists Pursue the Middle Way; Juan Caramuel Lobkowitz, Prince of Laxists; Pascal's Provincial LettersChapter 5: Rhetoric, Logic, Theory The Greek Vocabulary of Probability; The Sophists and the Art of Persuasion; Aristotle's Rhetoric and Logic; The Rhetoric to Alexander; Roman Rhetoric: Cicero and Quintilian; Islamic Logic; The Scholastic Dialectical Syllogism; Probability in Ordinary Language; Humanist Rhetoric; Late Scholastic LogicChapter 6: Hard Science Observation and Theory; Aristotle's Not-by-Chance Argument; Averaging of Observations in Greek Astronomy; The Simplicity of Theories; Nicole Oresme on Relative Frequency; Copernicus; Kepler Harmonizes Observations; Galileo on the Probability of Copernican HypothesisChapter 7: Soft Science and History The Physiognomics; Divination and Astrology; The Empiric School of Medicine on Drug Testing; The Talmud and Maimonides on Majorities; Vernacular Averaging and Quality Control; Experimentation in Biology; The Authority of Histories; The Authenticity of Documents; Valla and the Donation of Constantine; Cano and the Signs of True HistoriesChapter 8: Philosophy: Action and Induction Carneades's Mitigated Skepticism; The Epicureans on Inference from Signs; Inductive Skepticism and Avicenna's Reply; Aquinas on Tendencies; Scotus and Ockham on Induction; Nicholas of Autrecourt; The Decline of the West; Bacon and Descartes: Certainty? or Moral Certainty?; The Jesuits and Hobbes on Induction; Pascal's Deductivist Philosophy of ScienceChapter 9: Religion: Laws of God, Laws of Nature The Argument from Design; The Church Fathers; Inductive Skepticism by Revelation; John of Salisbury; Maimonides on Creation; Are Laws of Nature Necessary?; The Reasonableness of Christianity; Pascal's WagerChapter 10: Aleatory Contracts: Insurance, Annuities, and Bets The Price of Peril; Doubtful Claims in Jewish Law; Olivi on Usury and Future Profits; Pricing Life Annuities; Speculation in Public Debt; Insurance Rates; Renaissance Bets and Speculation; Lots and Lotteries; Commerce and the CasuistsChapter 11: Dice Games of Chance in Antiquity; The Medieval Manuscript on the Interrupted Game; Cardano; Gamblers and Casuists; Galileo's Fragment; De Mere and Roberval; The Fermat-Pascal Correspondence; Huygens' Reckoning in Games of Chance; CaramuelChapter 12: Conclusion Subsymbolic Probability and the Transition to Symbols; Kinds of Probability and the Stages of Discovering Them; Why Not Earlier?; Two Parallel Histories; The Genius of the Scholastics and the Orbit of Aristotle; The Place of Law in the history of IdeasEpilogue: The Survival of Unquantified Probability The Port-Royal Logic; Leibniz's Logic of Probability; To the PresentAppendix: Review of Work before 1660

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Book SynopsisThis graphic novel is both a historical novel as well as an entertaining way of using mathematics to solve a crime. The plot, the possible motive of every suspect, and the elements of his or her character are based on actual historical figures.The 2nd International Congress of Mathematicians is being held in Paris in 1900. The main speaker, the renowned Professor X, is found dead in the hotel dining room. Foul play is suspected. The greatest mathematicians of all time (who are attending the Congress) are called in for questioning. Their statements to the police, however, take the form of mathematical problems. The Chief Inspector enlists the aid of a young mathematician to help solve the crime. Do numbers always tell the truth? Or don’t they?Trade Review“It is a detective story in which several of the greatest historic mathematicians become all suspects for a murder on a colleague. … This is a wonderful booklet of fiction, but based on historical incidents. … It is a fantastic present that you can give to anybody between 9 and 99.” (Adhemar Bultheel, euro-math-soc.eu, June, 2015)Table of ContentsThe Crime.- The Suspects: Mathematicians.- Credits.- Examination of the Statements.

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Book SynopsisTrade Review"There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction."—Ben Longstaff, New Scientist"A popular account of important ideas and their development."—Peter M. Neumann, Times Higher Education Supplement"If one has never read a book by Eli Maor, this book is a great place to start."—J. Johnson, Choice"Maor expertly tells the story of how this simple theorem known to schoolchildren is part and parcel of much of mathematics itself."—Amy Shell-Gellasch, MAA Reviews"At last, a popular book that isn't afraid to print a mathematical formula in all its symbolic glory! Thanks to Eli Maor for proving—in his delightful, playful way—the eternal importance of a three-sided idea as old as humankind."—Dava Sobel, author of Longitude

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Book SynopsisTrade Review"This is not your father’s – or grandfather’s – standard collection of conic sections."---Jim Stein, New Books Network"Undoubtedly [this book], written in the same entertaining unmistakable style of the author and containing a lot of information - mathematical, historical and general - will attract, as the previous ones, a large audience."---S. Cobzas, Studia Mathematica"What a beautiful book!"---Jonathan Shock, Mathemafrica.org"A wonderful addition to libraries where the mathematically curious find their reading." * Choice *"Havil’s narrative for each curve is a cornucopia of fun facts and rigorous explanation."---Andrew J. Simoson, Mathematical Intelligencer"Overall, the book was a delight to read. The writing is witty and entertaining, the history is at times peculiar and surprising, and the mathematics is rich and engaging. It would make a fine addition to a classroom bookcase or home coffee table, but while there are plenty of elegant diagrams and intriguing stories to give every curious reader the chance to glimpse mathematical beauty, only those with the ability to dig beneath the surface will understand just how much beauty this book has to offer."---Samuel Hewitt, Mathematical Gazette

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Book SynopsisMathematics is a product of human culture which has developed along with our attempts to comprehend the world around us. In A Brief History of Mathematical Thought, Luke Heaton explores how the language of mathematics has evolved over time, enabling new technologies and shaping the way people think. From stone-age rituals to algebra, calculus, and the concept of computation, Heaton shows the enormous influence of mathematics on science, philosophy and the broader human story.The book traces the fascinating history of mathematical practice, focusing on the impact of key conceptual innovations. Its structure of thirteen chapters split between four sections is dictated by a combination of historical and thematic considerations. In the first section, Heaton illuminates the fundamental concept of number. He begins with a speculative and rhetorical account of prehistoric rituals, before describing the practice of mathematics in Ancient Egypt, Babylon and Greece. He

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Book Synopsis Euclid's Elements of Geometry was a book that changed the world. Trade Review Praise for The Book of Wonders ‘An astonishingly readable and informative history of the greatest mathematical bestseller of all time, from ancient Greece to dark energy. The writing is vivid and the stories are gripping. Highly recommended!’Ian Stewart, author of Significant Figures ‘Benjamin Wardhaugh is an excellent storyteller and his collected short story approach to the history of The Elements works splendidly… simultaneously educational, entertaining and illuminating … A highly desirable read for all those, both professional and amateur, who interest themselves in the histories of mathematics, science and knowledge … over almost two and a half millennia’Thony Christie, The Renaissance Mathematicus ‘A fascinating tour through 2300 years of reading, re-imagining, & responding to perhaps most important textbook ever written’ Seb Falk, author of The Light Ages Praise for Benjamin Wardhaugh’s Gunpowder and Geometry ‘Meticulous yet lively biography, even those who have never heard of its subject could hardly disagree’ Sunday Times ‘Wardhaugh graphically describes the conditions Hutton escaped from and the importance of Newcastle and its coal to the changes taking place in Britain in the second half of the eighteenth century . . . like something from the pages of a Jane Austen novel . . . Wardhaugh has done a good job of rescuing Hutton from obscurity and setting the man and his achievements in the context of their times . . . This account of how “the pit boy turned professor” became “one of the most revered British scientists of his day” is well worth reading’ Literary Review

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Book SynopsisShortlisted for the Royal Society Science Book Prize 2019A magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians.This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence. Filled with idiosyncratic characters from Pythagoras to Fourier, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides.Trade ReviewWarning: this book is dangerous. It will make you love mathematics. Even more, there is a nonzero risk it will turn you into a mathematician. * Nassim Nicholas Taleb, bestselling author of The Black Swan *Fascinating reading. * Scientific American *Eloquent, erudite and charming. A remarkable story. Strogatz is a world class mathematician and a world class science writer. With a light touch and razor-sharp clarity, he tells the remarkable story of a mathematical breakthrough that changed the world - and continues to do so. * Alex Bellos, bestselling author of Alex's Adventures in Numberland *Glorious! A master class in accessible maths writing and a perfect read for anyone who feels like they never quite understood what all the fuss was about. It had me leaping for joy. * Hannah Fry, bestselling author of Hello World and presenter of BBC R4’s The Curious Cases of Rutherford and Fry *Simple, lucid, amusing, informative, and a pleasure to read. If you want to know where calculus came from, how it works, what it's good for, and where it's going next, this is the book for you. * Professor Ian Stewart, author of Significant Figures *A fine, thoughtful attempt to make the greatest stories relating to calculus accessible... After reading Infinite Powers, we should no longer fear calculus. * Literary Review *The most fascinating book I have ever read. If you have even the slightest curiosity about maths and its role in this world, I implore you to read this amazing book. * Jo Boaler, professor of mathematics education, Stanford University *A wide-ranging, humane, thoroughly readable take on one of the greatest ideas our species has ever produced. * Jordan Ellenberg, author of How Not to Be Wrong *Fascinating anecdotes abound in Infinite Powers... [Strogatz] has written a romp through the history of calculus. * Nature *A tour de force. Elegant and ebullient. Strogatz speaks to everyone, reminding us why mathematics matters in a practical sense while all the time highlighting its beauty. * Lisa Randall, Professor of Physics at Harvard University and author of Dark Matter and The Dinosaurs *A highly readable account of calculus and its modern applications - all done with the human touch. * Dr David Acheson, Emeritus Fellow, Oxford University and author of The Calculus Story *An incalculable pleasure. If calculus is the language of the universe, then Steven Strogatz is its Homer. * Daniel Gilbert, author of Stumbling on Happiness *In this engaging book, Steven Strogatz illuminates the importance of calculus and explains its mysteries as only he can. * Sean Carroll, author of The Particle at the End of the Universe *Table of Contents1: Infinity 2: The Man Who Harnessed Infinity 3: Discovering the Laws of Motion 4: The Dawn of Differential Calculus 5: The Crossroads 6: The Vocabulary of Change 7: The Secret Fountain 8: Fictions of the Mind 9: The Logical Universe 10: Making Waves 11: The Future of Calculus

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Book SynopsisWho invented zero? Why 60 seconds in a minute? How big is infinity? Where do parallel lines meet? And can a butterfly's wings really cause a storm on the far side of the world? In 50 Maths Ideas You Really Need to Know, Professor Tony Crilly explains in 50 clear and concise essays the mathematical concepts - ancient and modern, theoretical and practical, everyday and esoteric - that allow us to understand and shape the world around us. Packed with diagrams, examples and anecdotes, this book is the perfect overview of this often daunting but always essential subject. For once, mathematics couldn't be simpler. Contents include: Origins of mathematics, from Egyptian fractions to Roman numerals; Pi and primes, Fibonacci numbers and the golden ratio; What calculus, statistics and algebra can actually do; The very real uses of imaginary numbers; The Big Ideas of relativity, Chaos theory, Fractals, Genetics and hyperspace; The reasoning behind Sudoku and code cracking, Lotteries and gambling, Money management and compound interest; Solving of Fermat's last theorem and the million-dollar question of the Riemann hypothesis.Table of ContentsIntroduction. Zero. Number systems. Fractions. Squares and square roots. Pi e. Infinity. Imaginary numbers. Primes. Perfect numbers. Fibonacci numbers. Golden rectangles. Pascal's triangle. Algebra. Euclid's algorithm. Logic. Proof. Sets. Calculus. Constructions. Triangles. Curves. Topology. Dimension. Fractals. Chaos. The parallel postulate. Discrete geometry. Graphs. The four-colour problem. Probability. Bayes's theory. The birthday problem. Distributions. The normal curve. Connecting data. Genetics. Groups. Matrices. Codes. Advanced counting. Magic squares. Latin squares. Money mathematics. The diet problem. The travelling salesperson. Game theory. Relativity. Fermat's last theorem. The Riemann hypothesis. Glossary. Index.

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Book SynopsisIntroducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience classics which will endure for generations to come.Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost otherworldly'In 1963, schoolboy Andrew Wiles stumbled across the world's greatest mathematical problem: Fermat's Last Theorem. Unsolved for over 300 years, he dreamed of cracking it.Combining thrilling storytelling with a fascinating history of scientific discovery, Simon Singh uncovers how an Englishman, after years of secret toil, finally solved mathematics' most challenging problem.Fermat's Last Theorem is remarkable story of human endeavour, obsession and intellectual brilliance, sealing its reputation as a classic of popular science writing.To read it is to realise that there is a world of beauty and intellectual challenge that is denied to 99.9 per cent of us who are not high-level mathematicians'The TimesTrade Review‘This is probably the best popular account of a scientific topic I have ever read’ Irish Times ‘Reads like the chronicle of an obsessive love affair. It has the classic ingredients that Hollywood would recognise’ Daily Mail ‘To read it is to realise that there is a world of beauty and intellectual challenge that is denied to 99.9 per cent of us who are not high-level mathematicians’ The Times ‘This tale has all the elements of a most exciting story: an impenetrable riddle; the ambition and frustration of generations of hopefuls; and the genius who worked for years in secrecy to realise his childhood dream’ Express

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Book SynopsisTrade Review"This book could well serve as a history of mathematics. … [Stillwell] has done an amazing job of collecting and categorizing many of the most important ideas in this area."---Jim Stein, New Books in Mathematics"Stillwell’s [The Story of Proof] joins his two other Princeton University Press books in having my highest recommendation. I just wish they had been around when I was a student."---George Hacken, Computing Reviews"I hugely enjoyed this book."---Jonathan Shock, Mathemafrica"This book would be perfect for any keen undergraduate, keen amateur, or indeed a teacher of mathematics, who wants a book to dip into to use for the classroom."---Jonathan Shock, Mathemafrica"A well-crafted, thought-provoking meditation on the concept of proof in mathematics. . . .It is a substantive book that deserves to be read and reflected upon."---Tommy Murphy, Irish Mathematical Society Bulletin"This is a work that mathematicians, historians, and philosophers will find especially engaging, as will anyone with a serious interest in mathematics and the limits of certainty that it is constantly probing."---J.W. Dauben, Choice

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Book SynopsisBest Books of 2024, The EconomistFrom the codebreakers and problem solvers, to the engineers, mathematicians and other problem-solvers what the secret world can teach us about performance and creativity How do you hire smart people who can work together to prevent terrorist attacks and decode encrypted technology?How do you come up with creative, counterintuitive solutions to solve major global problems?How do you provide the right environment for these people to thrive and work at their best when under immense pressure?Written by Robert Hannigan, the former Director of GCHQ, this book explores the role of the counter-intelligence services in history and today's world from the codebreakers and problem solvers, to innovation and creativity, secrecy and transparency and the global tech community. It will trace the history of counter-intelligence from the early days of Bletchley Park, to the ongoing work of GCHQ while reflecting on some of the unique characteristics of the engineers, mathematicians and other problem-solvers that make up the world's intelligence community.An exhaustive and authoritative account of the history of counter-intelligence from Bletchley Park to modern day GCHQ, this brilliant and unique book will appeal to business readers, history readers and fans of smart thinking and big ideas around the world.

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Book SynopsisWhat makes mathematics so special?Whether you have anxious memories of the subject from school, or solve quadratic equations for fun, David Acheson''s book will make you look at mathematics afresh. Following on from his previous bestsellers, The Calculus Story and The Wonder Book of Geometry, here Acheson highlights the power of algebra, combining it with arithmetic and geometry to capture the spirit of mathematics. This short book encompasses an astonishing array of ideas and concepts, from number tricks and magic squares to infinite series and imaginary numbers.Acheson''s enthusiasm is infectious, and, as ever, a sense of quirkiness and fun pervades the book. But it also seeks to crystallize what is special about mathematics: the delight of discovery; the importance of proof; and the joy of contemplating an elegant solution. Using only the simplest of materials, it conjures up the depth and the magic of the subject.Trade ReviewDavid Acheson captures the joy and wonder of mathematics in this little book, full of delightful and curious examples presented in a gentle, friendly way, yet packing in a number of profound ideas. * Hannah Fry, broadcaster and lecturer, author of The Mathematics of Love and The Indisputable Existence of Santa Claus *A delight. * Brian Clegg, Popular Science *[A] compendium of intriguing ideas which would fascinate and compel a keen mathematician wanting to learn more, and provide hours of intrigue and jumping-off points for further investigation. * Katie Steckles, The Aperiodical *[A] neat little book...every teacher, or at least every department, should have a copy. * Grant Macleod, Mathematics in Schools *This book is both interesting and entertaining, and it should appeal to any numerate person who has a casual interest in puzzles or mathematics. * SF2 Concatenation *Table of Contents1: Introduction 2: Whatever Happened to A, B, and C? 3: The 1089 Trick 4: Another Kind of Magic 5: Just Imagine... 6: A Most Unusual Lecture 7: Why are Mathematicians Obsessed by Proof? 8: Puzzling Mathematics 9: Why Does (-1) × (-1) = +1? 10: It's a Square World 11: Algebra in Action 12: 'Compleating the Square' 13: Slices of Pi 14: The Golden Ratio 15: Proof by Chocolate 16: The Puzzled Farmer 17: Mathematics and Snooker 18: The Wicked Schoolteacher 19: Trains, Boats, and Planes 20: I've Seen That Before, Somewhere ... 21: An Apple Falls ... 22: Rollercoaster Mathematics 23: The Electric Guitar Revisited 24: The Domino Effect 25: Real or Imaginary? 26: The Square Root of Minus One 27: Inspector Riemann Investigates ... 28: Infinite Danger 29: 1 + 1 to the Rescue! 30: And Finally ... Notes and references Further Reading Index

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Book SynopsisThe biography of a mathematical genius. Paul Erdos was the most prolific pure mathematician in history and, arguably, the strangest too. ’A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject – he thought and wrote mathematics for nineteen hours a day until he died. He travelled constantly, living out of a plastic bag and had no interest in food, sex, companionship, art – all that is usually indispensible to a human life. Paul Hoffman, in this marvellous biography, gives us a vivid and strangely moving portrait of this singular creature, one that brings out not only Erdos’s genius and his oddness, but his warmth and sense of fun, the joyfulness of his strange life.’ Oliver Sacks For six decades Erdos had no job, no hobbies, no wife, no home; he never learnt to cook, do laundry, drive a car and died a virgin. Instead he travelled the world with his mother in tow, arriving at the doorstep of esteemed mathematicians declaring ‘My brain is open’. He travelled until his death at 83, racing across four continents to prove as many theorems as possible, fuelled by a diet of espresso and amphetamines. With more than 1,500 papers written or co-written, a daily routine of 19 hours of mathematics a day, seven days a week, Paul Erdos was one of the most extraordinary thinkers of our times.Trade Review"Hoffman's playful, plainspoken and often hilarious biography of a monkish, impish, generous genius is purest pleasure." Mail on Sunday "Paul Hoffman's wittily articulated life of the mathematical genius Paul Erdos opens a door to a sunlit upland of pure logic, populated by bungee-bouncing, bearded maniacs and absurdly intelligent men who never learnt to tie their own shoelaces...Anyone with an interest in the science of numbers should read this." Observer "The Man Who Loved Only Numbers is one of the most accessible and engaging introductions to the world of pure mathematics you are ever likely to come across." Graham Farmelo, Sunday Telegraph "A wonderful, playful, insightful life of this century's most unusual mathematician." Ian Stewart, Independent

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Book SynopsisThis is the perfect introduction for those who have a lingering fear of maths. If you think that maths is difficult, confusing, dull or just plain scary, then The Maths Handbook is your ideal companion. Covering all the basics including fractions, equations, primes, squares and square roots, geometry and fractals, Dr Richard Elwes will lead you gently towards a greater understanding of this fascinating subject. Even apparently daunting concepts are explained simply, with the assistance of useful diagrams, and with a refreshing lack of jargon. So whether you're an adult or a student, whether you like Sudoku but hate doing sums, or whether you've always been daunted by numbers at work, school or in everyday life, you won't find a better way of overcoming your nervousness about numbers and learning to enjoy making the most of mathematics.Trade Review'Elwes takes the key concepts, perfectly illustrates them with practical examples and easy-to-follow explanations, tests us with quizzes, and applies the principles to everyday situations. The effect is strangely liberating, and you might soon find yourself acquiring a love of logarithms and a respect for reflex quadrilaterals' Good Book Guide. * Good Book Guide *Table of ContentsIntroduction. The language of mathematics. Addition. Subtraction. Multiplication. Division. Primes, factors and multiples. Negative numbers and the number line. Decimals. Fractions. Arithmetic with fractions. Powers. The power of 10. Roots and logs. Percentages and proportions. Algebra. Equations. Angles. Triangles. Circles. Area and volume. Polygons and solids. Pythagoras' theorem. Trigonometry. Coordinates. Graphs. Statistics. Probability. Charts. Answers to quizzes. Index.

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Book SynopsisWhile Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds, this Steele-Prize-winning geometer’s fundamental contributions to mathematics have been far broader and more diverse than might be guessed from this one aspect of his work. His works have deep influence and lasting impact in global differential geometry, mathematical physics and beyond. By bringing together 47 of Calabi’s important articles in a single volume, this book provides a comprehensive overview of his mathematical oeuvre, and includes papers on complex manifolds, algebraic geometry, Kähler metrics, affine geometry, partial differential equations, several complex variables, group actions and topology. The volume also includes essays on Calabi’s mathematics by several of his mathematical admirers, including S.K. Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon. This book is intended for mathematicians and graduate students around the world. Calabi’s visionary contributions will certainly continue to shape the course of this subject far into the future.Trade Review“In my case, I spent several happy hours learning about affine differential geometry, something that would certainly never have happened if I had not picked up this volume. … The collected works of Eugenio Calabi are worthy of a place on the bookshelf of any person with a serious interest in differential geometry.” (Joel Fine, EMS Magazine, May 11, 2023)Table of ContentsPreface.- J.-P. Bourguignon, Eugenio Calabi’s Short Biography.- Bibliographic List of Works.- S.-T. Yau, An Essay on Eugenio Calabi.- Part I: Commentaries on Calabi’s Life and Work: B. Lawson, Reflections on the Early Work of Eugenio Calabi.- M. Berger, Encounter with a Geometer: Eugenio Calabi.- J.-P. Bourguignon, Eugenio Calabi and Kähler Metrics.- C. LeBrun, Eugenio Calabi and the Curvature of Kähler Manifolds.- X. Chen, S. Donaldson, Calabi’s Work on Affine Differential Geometry and Results of Bernstein Type.- Part II: Collected Works: E. Calabi ,Ar. Dvoretzky, Convergence- and Sum-Factors for Series of Complex Numbers (1951).- E. Calabi, D. C. Spencer, Completely Integrable Almost Complex Manifolds (1951).- E. Calabi, Metric Riemann Surfaces (1953).- E. Calabi, M. Rosenlicht, Complex Analytic Manifolds Without Countable Base (1953).- E. Calabi, B. Eckmann, A Class of Compact, Complex Manifolds Which Are Not Algebraic (1953).- E. Calabi, Isometric Imbedding of Complex Manifolds (1953).- E. Calabi, The Space of Kähler Metrics (1954).- E. Calabi, The Variation of Kähler Metrics I. The Structure of the Space (1954).- E. Calabi, The Variation of Kähler Metrics II. A Minimum Problem (1954).- E. Calabi, On Kähler Manifolds With Vanishing Canonical Class (1957).- E. Calabi, Construction and Properties of Some 6-Dimensional Almost Complex Manifolds (1958).- E. Calabi, Improper Affine Hyperspheres of Convex Type and a Generalization of a Theorem by K. Jörgens (1958).- E. Calabi, An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1958).- E. Calabi, Errata: An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1959).- E. Calabi, E. Vesentini, Sur les variétés complexes compactes localement symétriques (1959).- E. Calabi, E. Vesentini, On Compact, Locally Symmetric Kähler Manifolds (1960).- E. Calabi, On Compact, Riemannian Manifolds with Constant Curvature I. (1961).- E. Calabi, L. Markus Relativistic Space Forms (1962).- E. Calabi, Linear Systems of Real Quadratic Forms (1964).- E. Calabi, Quasi-Surjective Mappings and a Generalization of Morse Theory (1966).- E. Calabi, Minimal Immersions of Surfaces in Euclidean Spheres (1967).- E. Calabi, On Ricci Curvature and Geodesics (1967).- E. Calabi, On Differentiable Actions of Compact Lie Groups on Compact Manifolds (1968).- E. Calabi, An Intrinsic Characterization of Harmonic One-Forms (1969).- E. Calabi, On the Group of Automorphisms of a Symplectic Manifold (1970).- E. Calabi, P. Hartman, On the Smoothness of Isometries (1970).- E. Calabi, Examples of Bernstein Problems for Some Nonlinear Equations (1970).- E. Calabi, Über singuläre symplektische Strukturen (1971).- E. Calabi, Complete Affine Hyperspheres I (1972).- E. Calabi, A Construction of Nonhomogeneous Einstein Metrics (1975).- E. Calabi, H. S. Wilf, On the Sequential and Random Selection of Subspaces Over a Finite Field (1977).- E. Calabi, Métriques kählériennes et fibrés holomorphes (1978).- E. Calabi, Isometric Families of Kähler Structures (1980).- E. Calabi, Géométrie différentielle affine des hypersurfaces (1981).- E. Calabi, Linear Systems of Real Quadratic Forms II (1982).- E. Calabi, Extremal Kähler Metrics (1982).- E. Calabi, Hypersurfaces with Maximal Affinely Invariant Area (1982).- E. Calabi, Extremal Kähler Metrics II (1985).- E. Calabi, Convex Affine Maximal Surfaces (1988).- E. Calabi, Affine Differential Geometry and Holomorphic Curves (1990).- E. Calabi, J. Cao Simple Closed Geodesics on Convex Surfaces (1992).- F. Beukers, J. A. C. Kolk and E. Calabi, Sums of Generalized Harmonic Series and Volumes (1993).- E. Calabi and H. Gluck, What are the Best Almost-Complex Structures on the 6-Sphere? (1993).- E. Calabi, Extremal Isosystolic Metrics for Compact Surfaces (1996).- E. Calabi, P. J. Olver, A. Tannenbaum, Affine Geometry, Curve Flows, and Invariant Numerical Approximations (1996).- J.-P. Bourguignon, E. Calabi, J. Eells, O. Garcia-Prada, M. Gromov, Where Does Geometry Go? A Research and Education Perspective (2001).- E. Calabi, X. Chen, The Space of Kähler Metrics II (2002).- Acknowledgements.

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Book SynopsisWhy is 7 such a lucky number and 13 so unlucky? Why does a jury traditionally have `12 good men and true', and why are there 24 hours in the day and 60 seconds in a minute? This fascinating new book explores the world of numbers from pin numbers to book titles, and from the sixfold shape of snowflakes to the way our roads, houses and telephone numbers are designated in fact and fiction. Using the numbers themselves as its starting point it investigates everything from the origins and meaning of counting in early civilizations to numbers in proverbs, myths and nursery rhymes and the ancient `science' of numerology. It also focuses on the quirks of odds and evens, primes, on numbers in popular sports - and much, much more. So whether you've ever wondered why Heinz has 57 varieties, why 999 is the UK's emergency phone number but 911 is used in America, why Coco Chanel chose No. 5 for her iconic perfume, or how the title Catch 22 was chosen, then this is the book for you. Dip in anywhere and you'll find that numbers are not just for adding and measuring but can be hugely entertaining and informative whether you're buying a diamond or choosing dinner from the menu.Table of Contents1 Introduction 8 2 Numbers of many sorts 10 3 Numbers and counting 12 4 1 - The number of unity 17 5 2 - The duality 19 6 3 - The trinity of perfection 21 7 4 - Truth and justice 23 8 5 - The number of nature 26 9 6 - Without a fault Six and the snowflake 29 10 7 - The symbol of fortune 32 11 The seven wonders of the world 35 12 Puzzles to solve 37 13 8 - Harmony and balance 38 14 9 - Unbounded 40 15 The nine muses 43 16 10 - On our fingers and toes 44 17 11 - The final hour 46 18 12 - A number in time 47 19 The twelve labours of Hercules 49 20 13 - And other teens 53 21 0 - The story of zero 54 22 Lucky - and unlucky - numbers 56 23 Odds and evens 59 24 Many favourite numbers 60 25 The secrets of numerology 62 26 Big numbers 66 27 Small numbers 68 28 The appeal of primes 69 29 Making shapes with numbers 72 30 Numbers - more different types 74 31 - the most famous number 75 32 Fibonacci - the brilliant number sequence 77 33 The golden ratio 79 34 Numbers in use 81 35 The world we live in 84 36 Our planet earth 86 37 Lines on the map 89 38 Measuring the world 94 39 A matter of weight 98 40 By volume 101 41 More about money 104 42 Inventing the calendar 106 43 Time and the circle 109 44 The living world 110 45 The human body 114 46 A number for your home 120 47 Addresses in fiction 121 48 A dark history 123 49 The streets of power 124 50 Numbers for the post 126 51 Roads to take - navigating by numbers 127 52 The number to call 130 53 PIN - what's your number? 132 54 Edible connections 134 55 Sizing up our drinks 137 56 Of yarns, fabrics and clothes 139 57 All that glitters 140 58 Beauty by numbers 142 59 For our leisure and entertainment 144 60 Proverbs and sayings 146 61 Bingo lingo 147 62 Books with numbers 149 63 In the film title 156 64 Counting in song 161 65 Jazz numbers 163 66 A musical miscellany 165 67 Poetry's secrets revealed 167 68 The beautiful game 170 69 The oval ball game - rugby football 174 70 The game of golf 176 71 Throwing darts 178 72 Cricket - bat on ball 179 73 On court - the game of tennis 182 74 Snooker and other cue games 185 75 The game of baseball 187 76 Chancing your luck 189 77 Throwing dice 192 78 Playing dominoes 194 79 Solving the square 195 80 Index 200 81 About the author 208

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Book SynopsisTrade Review"Everything in the book is very well illustrated with insightful graphics that, together with the text, make results almost like being obvious."---Adhemar Bultheel, European Mathematical Society

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Book SynopsisTrade Review"I greatly enjoyed Richeson's Tales of Impossibility. It deserves to become a classic and can be highly recommended."---Robin Wilson, Times Higher Education"Even if you never read a single proof through to its conclusion, you’ll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school."---Jim Stein, New Books in Mathematics"The whole book, both informative and amusing, is a highly recommended read."---Adhemar Bulteel, European Mathematical Society"This book was a pleasure to read and I would recommend it for anybody who wants a lovely overview of many areas of the history of mathematics, with a focus on some very easy to understand problems."---Jonathan Shock, Mathemafrica"Richeson clearly explains what it means to be impossible to solve a problem, cites other impossibility results, goes into detail about geometric constructions with various instruments, and discusses the defective proofs and the cranks that have turned up along the way." * Mathematics Magazine *"This fascinating text will appeal to all those interested in the history of mathematics, not leasy because of its helpful notes on each chapter and its two dozen pages of references for further reading"---Laurence E. Nicholas CMath FIMA, Mathematics Today"A fact-filled, insightful, panoramic view of how mathematics developed to what it is today transformed by folks thinking both inside and outside of G so as to resolve the impossible."---Andrew J. Simoson, Mathematical Intelligencer

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Book SynopsisCollins Big Cat supports every primary child on their reading journey from phonics to fluency. Top authors and illustrators have created fiction and non-fiction books that children love to read. Book banded for guided and independent reading, there are reading notes in the back, comprehensive teaching and assessment support and ebooks available.Born in 18th century France, Sophie Germain was not allowed to learn Maths, because she was a girl. Sophie went undercover to learn Maths in secret, using a boy's name as a code name. There was just one problem. Sophie was so good at Maths, people wanted to meet her. Would her cover be blown?Lime Plus/Band 11+ books provide challenging plots and vocabulary as well as opportunities to practise inference, prediction and reading stamina.Pages 46 and 47 allow children to re-visit the content of the book, supporting comprehension skills, vocabulary development and recall.Ideas for reading in the back of the book provide practical support and stimulat

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Book SynopsisGeorge Dyson''s fascinating account of the early years of computers: Turing''s Cathedral is the story behind how the PC, ipod, smartphone and almost every aspect of modern life came into being.In 1945 a small group of brilliant engineers and mathematicians gathered at the Institute for Advanced Study in Princeton, determined to build a computer that would make Alan Turing''s theory of a ''universal machine'' reality. Led by the polymath émigré John von Neumann, they created the numerical framework that underpins almost all modern computing - and ensured that the world would never be the same again.George Dyson is a historian of technology whose interests include the development (and redevelopment) of the Aleut kayak. He is the author of Baidarka; Project Orion; and Darwin Among the Machines.''Unusual, wonderful, visionary'' Francis Spufford, Guardian''Fascinating . . . the story Dyson tells is intensely human . . . a grippiTrade ReviewRiveting . . . conveys the electrifying sense of possibility that the first computers unleashed . . . a page-turner * New Scientist *Brings to life a myriad cast of extraordinary characters, each of whom contributed to ushering in today's digital age * Daily Telegraph *An engrossing and well-researched book that recounts an important chapter in the history of 20th-century computing -- Evgeny Morozov * Observer *

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