History of mathematics Books

Book Synopsis**The First Ever Maths Book to be a No.1 Bestseller**''Wonderful ... superb'' Daily MailWhat makes a bridge wobble when it''s not meant to? Billions of dollars mysteriously vanish into thin air? A building rock when its resonant frequency matches a gym class leaping to Snap''s 1990 hit I''ve Got The Power? The answer is maths. Or, to be precise, what happens when maths goes wrong in the real world.As Matt Parker shows us, our modern lives are built on maths: computer programmes, finance, engineering. And most of the time this maths works quietly behind the scenes, until ... it doesn''t. Exploring and explaining a litany of glitches, near-misses and mishaps involving the internet, big data, elections, street signs, lotteries, the Roman empire and a hapless Olympic shooting team, Matt Parker shows us the bizarre ways maths trips us up, and what this reveals about its essential place in our world.Mathematics doesn''t have good ''people skills'', but we would all be better off, he argues, if we saw it as a practical ally. This book shows how, by making maths our friend, we can learn from its pitfalls. It also contains puzzles, challenges, geometric socks, jokes about binary code and three deliberate mistakes. Getting it wrong has never been more fun.Trade ReviewMatt Parker has pulled off something wonderful . . . his stories are superb. -- Marcus Berkmann * The Daily Mail *Parker is consistently very funny . . . highly entertaining. * The Guardian *Numbers to die for. Four stars. -- Simon Griffith * Mail on Sunday *Bought it yesterday, enjoying it enormously, well done! -- Dara Ó Briain * Twitter *I just finished the new book by irrepressible maths enthusiast @standupmaths, and it's GREAT! -- Adam Savage, ex-host of 'Mythbusters' * Twitter *An entertaining and often alarming journey through the numerical blunders made over the years. * The Big Issue *Very funny. . . a compendium of stories about mathematical failures; some are amusing, others alarming, as in the case of the passenger aircraft that ran out of fuel because it had been measured in the wrong units * Telegraph Books of the Year *The surprise bestseller that makes maths fun * Sunday Times Magazine *Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations - that also gives you permission to feel a little better about some of your own mistakes -- Ryan North, author of How to Invent Everything

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Book SynopsisThe innovative, dramatic graphic novel based on the life of the philosopher and mathematician Bertrand Russell.

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Book SynopsisPlease note that this Floris Books edition has been revised for UK and European notation, language and metric systems.From the early peoples who marvelled at the geometry of nature -- the beehive and bird's nest -- to ancient civilisations who questioned beautiful geometric forms and asked 'why?', the story of geometry spans thousands of years. Using only three simple tools -- the string, the straight-edge and the shadow -- human beings revealed the basic principles and constructions of elementary geometry. Weaving history and legend, this fascinating book reconstructs the discoveries of mathematics's most famous figures. Through illustrations and diagrams, readers are able to follow the reasoning that lead to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, or the construction of the five regular solids.This insightful and engaging book makes geometry accessible to everyone. Readers will be fascinated with how the knowledge and wisdom of so many cultures helped shape our civilisation today.String, Straight-edge and Shadow is also a useful and inspiring book for those teaching geometry in Steiner-Waldorf classrooms.Trade Review'Shows us what we don't realise we know, what civilisations before us learnt and passed down to us. It brings an awe and magic back to our learning… Those that advanced knowledge of geometry had a grounded and practical understanding of where it came from. This book helps us to do that.'-- The Smart Happy Project'This was an enjoyable read for the everyday person of curious mind.' - Amazon.com'Fantastic, accurate, readable, teachable and Classical.' -- Amazon.com'The well constructed narrative brings these people and their excitement over these discoveries to life. I learned about the patterns in math from a new perspective and it made me wonder why math is always taught in the abstract format. These people understood it in a completely different way and I would think that some people would learn it better if it were explained this way.' -- Goodreads'This gem is about ancient Geometry that has definite application today. Knowing the stories behind many great discoveries make them so much more interesting and really helps math to come alive.' -- Goodreads'Whether you are learning geometry for the first time, teaching it to students at home or in the classroom, or are parents helping your children through their first geometry course, this is a must-read for everyone! You will be fascinated with the graphic illustrations and written depiction of how the knowledge and wisdom of so many cultures helped shape our civilization today.' -- Waldorf Books‘String, Straight-edge and Shadow (is) an interesting and informative book and its numerous diagrams and illustrations are part of its appeal. Anyone interested in learning how discoveries made thousands of years ago still underpin much of our modern day science and mathematics will find this a useful and engaging read.’-- New View

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Book SynopsisA FINANCIAL TIMES AND TLS BOOK OF THE YEARAn exhilarating new biography of John von Neumann: the lost genius who invented our world''A sparkling book, with an intoxicating mix of pen-portraits and grand historical narrative. Above all it fizzes with a dizzying mix of deliciously vital ideas. . . A staggering achievement'' Tim HarfordThe smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Self-replicating moon bases and nuclear weapons. All bear the fingerprints of one remarkable man: John von Neumann.Born in Budapest at the turn of the century, von Neumann is one of the most influential scientists to have ever lived. His colleagues believed he had the fastest brain on the planet - bar none. He was instrumental in the Manhattan Project and helped formulate the bedrock of Cold War geopolitics and modern economic theory. He created the first ever programmable digital computer. He prophesied the potential of nanotechnology and, from his deathbed, expounded on the limits of brains and computers - and how they might be overcome.Taking us on an astonishing journey, Ananyo Bhattacharya explores how a combination of genius and unique historical circumstance allowed a single man to sweep through so many different fields of science, sparking revolutions wherever he went.Insightful and illuminating, The Man from the Future is a thrilling intellectual biography of the visionary thinker who shaped our century.

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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 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 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 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 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 SynopsisGOD CREATED THE INTEGERS is Stephen Hawking''s personal choice of the greatest mathematical works in history. He allows the reader to peer into the mind of genius by providing us with excerpts from original mathematical proofs and results. He also helps us understand the progression of mathematical thought, and the very foundations of our presentday technologies. The book includes landmark discoveries spanning 2500 years and representing the work of mathematicians such as Euclid, Georg Cantor, Kurt Godel, Augustin Cauchy, Bernard Riemann and Alan Turing. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication, many in new translations.

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Book SynopsisIn a series of 50 accessible essays, Tony Crilly explains and introduces the mathematical laws and principles - ancient and modern, theoretical and practical, everyday and esoteric - that allow us to understand the world around us.From Pascal's triangle to money management, ideas of relativity to the very real uses of imaginary numbers, 50 Maths Ideas is a complete introduction to the most important mathematical concepts in history.

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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 SynopsisTrade ReviewFull of interesting ideas, insightful and thought-provoking ... A stimulating book that perhaps leaves the reader with more questions than answers. That, in case you are wondering, is intended as praise -- Tony Mann * Times Higher Education *

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Book SynopsisA Nobel Prize-winning physicist argues that beauty is the fundamental organizing principle for the entire universeIn this scientific tour de force, world-class physicist Frank Wilczek argues that beauty is at the heart of the logic of the universe. As the quest to find the beauty embodied in the universe has connected all scientific pursuit, from Pythagoras to Einstein, Wilczek shows us just how deeply intertwined our ideas about beauty and art are with our understanding of the cosmos. A Beautiful Question is a mind-expanding book combining the age-old human quest for beauty with the age-old human quest for truth.Trade ReviewA truly beautiful book ... Why do physicists call their theories beautiful? Immerse yourself in this book, wallow in it, sit back and relax as you wander through it, and you'll soon understand. -- Richard Muller, author of Physics for Future PresidentsAnyone who wants to see how science and transcendence can be compatible must read this book. Wilczek has caught the winds of change, and his thinking breaks through some sacred boundaries with curiosity, insight, and intellectual power. -- Deepak Chopra, M.D.Illuminating ... A fresh perspective on modern scientific thinking from an expert with a flair for jargon-free exposition ... Wilczek writes A Beautiful Question with bracing pizzazz ... Contains more beef than many a finely written scientific potboiler. -- Graham Farmelo * Guardian *The first book I've read in which I've felt that almost vertiginous sensation of peering through layers of theories down to the true nature of the universe ... At times this is a challenging text, but it is well worth the effort. Wilczek is admirably clear in his explanations. -- Lewis Dartnell * Telegraph *It's rare that scientists as brilliant as Wilczek give us a glimpse of what goes on inside their heads ... Expect to come away pretty dazzled. * BBC Focus *[A] searching and earnest book ... The book of a love-struck physicist ... A Beautiful Question is a meditation. -- Amy X. Wang * Slate *A Beautiful Question is both a brilliant exploration of largely uncharted territories and a refreshingly idiosyncratic guide to developments in particle physics. * Nature *Wilczek's sheer pleasure in the beauty of mathematics is the engine and joy of this book ... [A] rewarding read ... There is a lot of food for the mind here, but also some for the eye. -- Andrea Wulf * Financial Times *[An] eccentrically brilliant book -- Steven Poole * Spectator *

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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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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 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 SynopsisMathematics is a fundamental human activity that can be practised and understood in a multitude of ways; indeed, mathematical ideas themselves are far from being fixed, but are adapted and changed by their passage across periods and cultures. In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day. Arranged thematically, to exemplify the varied contexts in which people have learned, used, and handed on mathematics, she also includes illustrative case studies drawn from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewStimulating and accessible. * Mathematical Gazette *Table of ContentsFURTHER READING

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Book SynopsisProbably the most celebrated controversy in all of the history of science was that between Newton and Leibniz over the invention of the calculus. Philosophers at War reveals how the dispute arose and became embittered, the dispositions of the chief actors, and the shifts in their opinions of each other.Table of ContentsPreface; Chronological outline; 1. Introduction; 2. Beginnings in Cambridge; 3. Newton states his claim: 1685; 4. Leibniz encounters Newton: 1672–1676; 5. The emergence of the calculus: 1677–1699; 6. The outbreak: 1693–1700; 7. Open warfare: 1700–1710; 8. The philosophical debate; 9. Thrust and parry: 1710–1713; 10. The dogs of war: 1713–1715; 11. War beyond death: 1715–1722; Appendix; Notes; Index.

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Book SynopsisIn this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians.By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.Trade Review“The text is written in an easy to read format which generously incorporates narratives from the history of mathematics as well as rigorous proofs of the concepts presented. The appendices and references to other texts provide the reader with numerous sources of supplementary information for those wishing to delve into a subject at a deeper level … . chapters are organized and clearly labeled to express which sections are appropriate for a beginning learner, an intermediate learner, or the specialist.” (Tom French, MAA Reviews, October 3, 2021)“Each chapter comes with several exercises from easy to difficult, the latter with complete solutions in the appendix. To accommodate the book to readers with different backgrounds and goals, the authors provide a guide which gives paths through the book for several courses. The exposition is always clear and motivating, no prerequisites are presumed, all terms and concepts are defined precisely, and there are many look-and-see proofs.” (Dieter Riebesehl, zbMATH 1465.68004, 2021)Table of ContentsIntroduction.- “Doing” Mathematics: A Toolkit for Mathematical Reasoning.- Sets and Their Algebras: The Stem Cells of Mathematics.- Numbers I: The Basics of Our Number System.- Arithmetic: Putting Numbers to Work.- Summations: Complex Operations from Simple Components.- The Vertigo of Infinity: Handling the Very Large and the Infinite.- Numbers II: Building the Integers and Building with the Integers.- Recurrences: Rendering Complex Structure Manageable.- Numbers III: Operational Representations and Their Consequences.- The Art of Counting: Combinatorics, Probability, and Statistics.- Graphs I: Representing Relationships Mathematically.- Graphs II: Graphs Within Computation and Communication.- Solutions to Exercises.- App. A, Pairing Functions.- App. B, A Deeper Look at the Fibonacci Numbers.- App. C, Two Recurrence-Defined Number Families.- App. D, Signed-Digit Numerals: Carry-Free Addition.- App. E, The Diverse Delights of de Bruijn Networks.- List of Symbols.- References.- Index.

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Book SynopsisOther refinements in the new edition include an enlarged biography of Emmy Noether's life and work, parallels drawn between the present approach and Noether's original 1918 paper, and a summary of the logic behind Noether's theorem.Trade ReviewAs this book is well written and contains a very good set of exercises, it can serve as the primary text for a special topics course.—ChoiceNadis gives no technical details, but Neuenschwander does, in a book for physics majors with a strong background in mathematics; the book does not shy away from Lie groups and the study of invariants. This new edition delves into distinctions between two Noether theorems and adds more exercises, references, and details.—Mathematics MagazineNeuenschwander sets out from the beginning to help the reader who must be familiar with calculus and a few other standard topics, but who is not yet fluent in these areas... His role is to be the teacher on the side, prompting the reader with interesting observations and questions... He anticipates problems, guides you yet also makes you think things through... Not only a very worthwhile read for its content but also for its style.—Ken Zetie, St. Paul's School, Mathematical GazetteWell-written... Throughout there is reference to the life of Emmy Noether, including the many difficulties related to being a woman in a man's world... I am glad her story is given an airing here as she fails to be as famous as she undoubtedly should be.—Phil Dyke, FIMA, Mathematics TodayTechnical and yet ultimately poetic book on Emmy Neother's wonderful theorems... Neuenschwander's work is recommended for anyone who wants to gain a deeper understanding and appreciation of the physics and mathematics behind Emmy Noether's work, as well as the particular challenges she faced in her life.—Miriam R. Aczel, Centre for Environmental Policy, Imperial College London, Contemporary PhysicsTable of ContentsPrefaceAcknowledgmentsQuestionsPart I. When Functionals Are External 1. Symmetry1.1. Symmetry, Invariances, and Conservation Laws1.2. Meet Emmy Noether2. Functionals2.1. Single-Integral Functionals2.2. Formal Definition of a Functional3. Extremals3.1. The Euler-Lagrange Equation3.2. Conservation Laws as Corollariesto the Euler-Lagrange Equation3.3. On the Equivalence of Hamilton's Principleand Newton's Second Law3.4. Where Do Functional Extremal PrinciplesCome From?3.5. Why Kinetic Minus Potential Energy?3.6. Extremals with External ConstraintsPart II. When Functionals Are Invariant 4. Invariance4.1. Formal Definition of Invariance4.2. The Invariance Identity4.3. A More Liberal Definition of Invariance5. Emmy Noether's Elegant (First) Theorem5.1. Invariance + Extremal = Noether's Theorem5.2. Executive Summary of Noether's Theorem5.3. "Extremal" or "Stationary"?5.4. An Inverse Problem5.5. Adiabatic Invariance in Noether's TheoremPart III. The Invariance of Fields6. Noether's Theorem and Fields6.1. Multiple-Integral Functionals6.2. Euler-Lagrange Equations for Fields6.3. Canonical Momentum and the HamiltonianTensor for Fields6.4. Equations of Continuity6.5. The Invariance Identity for Fields6.6. Noether's Theorem for Fields6.7. Complex Fields6.8. Global Gauge Transformations7. Local Gauge Transformations of Fields7.1. Local Gauge Invariance and Minimal Coupling7.2. Electrodynamics as a Gauge Theory,Part 17.3. Pure Electrodynamics, Spacetime Invariances,and Conservation Laws7.4. Electrodynamics as a Gauge Theory,Part 27.5. Local Gauge Invariance and Noether Currents7.6. Internal Degrees of Freedom7.7. Noether's Theorem and GaugedInternal Symmetries8. Emmy Noether's Elegant (Second) Theorem8.1. Two Noether Theorems8.2. Noether's Second Theorem8.3. Parametric Invariance8.4. Free Fall in a Gravitational Field8.5. The Gravitational Field Equations8.6. The Functionals of General Relativity8.7. Gauge Transformations on Spacetime8.8. Noether's Resolution of an Enigma inGeneral RelativityPart IV. Trans-Noether Invariance9. Invariance in Phase Space9.1. Phase Space9.2. Hamilton's Principle in Phase Space9.3. Noether's Theorem and Hamilton's Equations9.4. Hamilton-Jacobi Theory10. The Action as a Generator10.1. Conservation of Probabilityand Continuous Transformations10.2. The Poetry of NatureAppendixesA. Scalars, Vectors, and TensorsB. Special RelativityC. Equations of Motion in Quantum MechanicsD. Conjugate Variables and Legendre TransformationsE. The JacobianF. The Covariant DerivativeBibliographyIndex

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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 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 SynopsisNumber theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.Table of ContentsList of illustrations List of tables 1: What is number theory? 2: Divisibility 3: Primes I 4: Congruences I 5: Diophantine equations 6: Congruences II 7: Primes II 8: The Riemann hypothesis Appendix Further reading Index

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Book SynopsisThe updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind s relationship with numbers, shapes, and patterns.Trade Review"... the book is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it." (Zentralblatt MATH, 2016) "... an 'engaging' read for the mathematically minded." (Inside OR, June 2011)Table of ContentsForeword by Isaac Asimov xi Preface to the Third Edition xiii Preface to the Second Edition xv Preface to the First Edition xvii 1 Traces 1 Concepts and Relationships 1 Early Number Bases 3 Number Language and Counting 5 Spatial Relationships 6 2 Ancient Egypt 8 The Era and the Sources 8 Numbers and Fractions 10 Arithmetic Operations 12 “Heap” Problems 13 Geometric Problems 14 Slope Problems 18 Arithmetic Pragmatism 19 3 Mesopotamia 21 The Era and the Sources 21 Cuneiform Writing 22 Numbers and Fractions: Sexagesimals 23 Positional Numeration 23 Sexagesimal Fractions 25 Approximations 25 Tables 26 Equations 28 Measurements: Pythagorean Triads 31 Polygonal Areas 35 Geometry as Applied Arithmetic 36 4 Hellenic Traditions 40 The Era and the Sources 40 Thales and Pythagoras 42 Numeration 52 Arithmetic and Logistic 55 Fifth-Century Athens 56 Three Classical Problems 57 Quadrature of Lunes 58 Hippias of Elis 61 Philolaus and Archytas of Tarentum 63 Incommensurability 65 Paradoxes of Zeno 67 Deductive Reasoning 70 Democritus of Abdera 72 Mathematics and the Liberal Arts 74 The Academy 74 Aristotle 88 5 Euclid of Alexandria 90 Alexandria 90 Lost Works 91 Extant Works 91 The Elements 93 6 Archimedes of Syracuse 109 The Siege of Syracuse 109 On the Equilibriums of Planes 110 On Floating Bodies 111 The Sand-Reckoner 112 Measurement of the Circle 113 On Spirals 113 Quadrature of the Parabola 115 On Conoids and Spheroids 116 On the Sphere and Cylinder 118 Book of Lemmas 120 Semiregular Solids and Trigonometry 121 The Method 122 7 Apollonius of Perge 127 Works and Tradition 127 Lost Works 128 Cycles and Epicycles 129 The Conics 130 8 Crosscurrents 142 Changing Trends 142 Eratosthenes 143 Angles and Chords 144 Ptolemy’s Almagest 149 Heron of Alexandria 156 The Decline of Greek Mathematics 159 Nicomachus of Gerasa 159 Diophantus of Alexandria 160 Pappus of Alexandria 164 The End of Alexandrian Dominance 170 Proclus of Alexandria 171 Boethius 171 Athenian Fragments 172 Byzantine Mathematicians 173 9 Ancient and Medieval China 175 The Oldest Known Texts 175 The Nine Chapters 176 Rod Numerals 177 The Abacus and Decimal Fractions 178 Values of Pi 180 Thirteenth-Century Mathematics 182 10 Ancient and Medieval India 186 Early Mathematics in India 186 The Sulbasutras 187 The Siddhantas 188 Aryabhata 189 Numerals 191 Trigonometry 193 Multiplication 194 Long Division 195 Brahmagupta 197 Indeterminate Equations 199 Bhaskara 200 Madhava and the Keralese School 202 11 The Islamic Hegemony 203 Arabic Conquests 203 The House of Wisdom 205 Al-Khwarizmi 206 ‘Abd Al-Hamid ibn-Turk 212 Thabit ibn-Qurra 213 Numerals 214 Trigonometry 216 Tenth- and Eleventh-Century Highlights 216 Omar Khayyam 218 The Parallel Postulate 220 Nasir al-Din al-Tusi 220 Al-Kashi 221 12 The Latin West 223 Introduction 223 Compendia of the Dark Ages 224 Gerbert 224 The Century of Translation 226 Abacists and Algorists 227 Fibonacci 229 Jordanus Nemorarius 232 Campanus of Novara 233 Learning in the Thirteenth Century 235 Archimedes Revived 235 Medieval Kinematics 236 Thomas Bradwardine 236 Nicole Oresme 238 The Latitude of Forms 239 Infinite Series 241 Levi ben Gerson 242 Nicholas of Cusa 243 The Decline of Medieval Learning 243 13 The European Renaissance 245 Overview 245 Regiomontanus 246 Nicolas Chuquet’s Triparty 249 Luca Pacioli’s Summa 251 German Algebras and Arithmetics 253 Cardan’s Ars Magna 255 Rafael Bombelli 260 Robert Recorde 262 Trigonometry 263 Geometry 264 Renaissance Trends 271 François Viète 273 14 Early Modern Problem Solvers 282 Accessibility of Computation 282 Decimal Fractions 283 Notation 285 Logarithms 286 Mathematical Instruments 290 Infinitesimal Methods: Stevin 296 Johannes Kepler 296 15 Analysis, Synthesis, the Infinite, and Numbers 300 Galileo’s Two New Sciences 300 Bonaventura Cavalieri 303 Evangelista Torricelli 306 Mersenne’s Communicants 308 René Descartes 309 Fermat’s Loci 320 Gregory of St. Vincent 325 The Theory of Numbers 326 Gilles Persone de Roberval 329 Girard Desargues and Projective Geometry 330 Blaise Pascal 332 Philippe de Lahire 337 Georg Mohr 338 Pietro Mengoli 338 Frans van Schooten 339 Jan de Witt 340 Johann Hudde 341 René François de Sluse 342 Christiaan Huygens 342 16 British Techniques and Continental Methods 348 John Wallis 348 James Gregory 353 Nicolaus Mercator and William Brouncker 355 Barrow’s Method of Tangents 356 Newton 358 Abraham De Moivre 372 Roger Cotes 375 James Stirling 376 Colin Maclaurin 376 Textbooks 380 Rigor and Progress 381 Leibniz 382 The Bernoulli Family 390 Tschirnhaus Transformations 398 Solid Analytic Geometry 399 Michel Rolle and Pierre Varignon 400 The Clairauts 401 Mathematics in Italy 402 The Parallel Postulate 403 Divergent Series 404 17 Euler 406 The Life of Euler 406 Notation 408 Foundation of Analysis 409 Logarithms and the Euler Identities 413 Differential Equations 414 Probability 416 The Theory of Numbers 417 Textbooks 418 Analytic Geometry 419 The Parallel Postulate: Lambert 420 18 Pre- to Postrevolutionary France 423 Men and Institutions 423 The Committee on Weights and Measures 424 D’Alembert 425 Bézout 427 Condorcet 429 Lagrange 430 Monge 433 Carnot 438 Laplace 443 Legendre 446 Aspects of Abstraction 449 Paris in the 1820s 449 Fourier 450 Cauchy 452 Diffusion 460 19 Gauss 464 Nineteenth-Century Overview 464 Gauss: Early Work 465 Number Theory 466 Reception of the Disquisitiones Arithmeticae 469 Astronomy 470 Gauss’s Middle Years 471 Differential Geometry 472 Gauss’s Later Work 473 Gauss’s Influence 474 20 Geometry 483 The School of Monge 483 Projective Geometry: Poncelet and Chasles 485 Synthetic Metric Geometry: Steiner 487 Synthetic Nonmetric Geometry: von Staudt 489 Analytic Geometry 489 Non-Euclidean Geometry 494 Riemannian Geometry 496 Spaces of Higher Dimensions 498 Felix Klein 499 Post-Riemannian Algebraic Geometry 501 21 Algebra 504 Introduction 504 British Algebra and the Operational Calculus of Functions 505 Boole and the Algebra of Logic 506 Augustus De Morgan 509 William Rowan Hamilton 510 Grassmann and Ausdehnungslehre 512 Cayley and Sylvester 515 Linear Associative Algebras 519 Algebraic Geometry 520 Algebraic and Arithmetic Integers 520 Axioms of Arithmetic 522 22 Analysis 526 Berlin and Göttingen at Midcentury 526 Riemann in Göttingen 527 Mathematical Physics in Germany 528 Mathematical Physics in English-Speaking Countries 529 Weierstrass and Students 531 The Arithmetization of Analysis 533 Dedekind 536 Cantor and Kronecker 538 Analysis in France 543 23 Twentieth-Century Legacies 548 Overview 548 Henri Poincaré 549 David Hilbert 555 Integration and Measure 564 Functional Analysis and General Topology 568 Algebra 570 Differential Geometry and Tensor Analysis 572 Probability 573 Bounds and Approximations 575 The 1930s and World War II 577 Nicolas Bourbaki 578 Homological Algebra and Category Theory 580 Algebraic Geometry 581 Logic and Computing 582 The Fields Medals 584 24 Recent Trends 586 Overview 586 The Four-Color Conjecture 587 Classification of Finite Simple Groups 591 Fermat’s Last Theorem 593 Poincaré’s Query 596 Future Outlook 599 References 601 General Bibliography 633 Index 647

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Book SynopsisThe weird and wonderful quest for unfathomably large numbersTrade Review‘A wonderful new book… if you love journeying into imagined mathematical worlds and simply exploring, then [this book] is pure, unadulterated escapism… brilliant.’ -- New Scientist‘We are taken on an amazing adventure… [with] witty humour and fascinating facts… a comprehensive read that I would struggle to find fault in and for anyone with a passion for maths, or a knack for numbers, I couldn’t recommend it enough!’ -- Astronomy Ireland‘The brilliant combination of an accomplished science writer and a young mathematical prodigy has resulted in page after page that oozes enthusiasm, clarity and intrigue.’ -- Bobby Seagull, on Weirder MathsTable of ContentsIntroduction 1 Of Sand and Stars 2 At the Limits of Reality 3 Maths Unbound 4 Up, Up and Away 5 G Whizz 6 Conway’s Chains 7 Ackermann and the Power of Recursion 8 Figure This – If You Can 9 Infinite Matters 10 Growing Fast 11 Does Not Compute! 12 The Strange World of the Googologist 13 Bridge to Beyond 14 The Biggest Number of All Acknowledgements Bibliography Useful websites and webpages References

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Book SynopsisWhat are the strangest numbers? Where do numbers come from? Can maths guarantee riches? Why are three dimensions not enough? Can a butterfly's wings really cause a hurricane? Can maths predict the future? In How Big is Infinity?, acclaimed writer Tony Crilly distills the wisdom of some of the greatest minds in history to help provide answers some of the most perplexing, stimulating and surprising questions in mathematics.Table of ContentsIntroduction. What is mathematics for? - An introduction to purposes and prospects. Where do numbers come from? - From notches on bones to hexadecimals. Why are primes the atoms of mathematics? - Building blocks and the fundamental theorem of arithmetic. Which are the strangest numbers? - Real, irrational and transcendental numbers. Are imaginary numbers truly imaginary? - From the imaginary 'I' to octonions. How big is infinity? - Set theory and the infinity revolution. Where do parallel lines meet? - The birth of new geometries. What is the mathematics of the universe? - The Calculus miracle. Are statistics lies? - Data, proof and 'damned lies'. Can mathematics guarantee riches? - Uncertainty, chance and probability theory. Is there a formula for everything? - Mathematical recipes and the search for knowledge. Why are three dimensions not enough? - Higher dimensions, monster curves and fractals. Can a butterfly's wings really cause a hurricane? - Chaos theory, weather equations and strange attractors. Can we create an unbreakable code? - Ciphers, the Enigma machine and quantum computers. Is mathematics beautiful? - Music, art, golden numbers and the Fibonacci sequence. Can mathematics predict the future? - Mathematical models, simulations and game theory. What shape is the universe? - Topology, manifolds and the Poincare conjecture. What is symmetry? - Patterns, dualities and the fundamental nature of reality. Is mathematics true? - From Plato's reality to Godel's incompleteness theorems. Is there anything left to solve? - The great unsolved problems and the future of mathematics. Glossary. Index.

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Book SynopsisTrade ReviewHonorable Mention for the 2015 PROSE Award in Popular Science & Popular Mathematics, Association of American Publishers "A book that stimulates the mind as well as the eye."--Scientific American "The combination of art and exposition was quite effective. The writing is accessible to most reasonably well-educated laypeople, and I imagine that many such people would derive considerable pleasure dipping into this attractive and interesting book."--Mark Hunacek, MAA Reviews "Eli Maor's lively writing benefits in equal parts from the geometry of ancient Greece and the eye-popping images conjured by artist Eugen Jost."--Bill Cannon, Scientist's Bookshelf "Graphic illustrations serve as both beautiful abstract art and helpful explanations in this overview of geometric theorems and patterns."--Science News "[Beautiful Geometry] achieves its aim to demonstrate that there is visual beauty in Mathematics. I heartily recommend it."--LSE Review of Books "The explanations are clear, and cover the background to the paintings in a manner that will be appreciated by readers whatever their level of mathematical knowledge... Anyone with any interest in visual mathematics will love this book."--Times Higher Education "A good-looking, large-format book suitable for the coffee table, but with lots of mathematical ideas packed in among the colorful illustrations... [A] handsome book for browsing and for some deep thought, and would be a superb gift for anyone (especially a young person) who has interest in mathematics."--Rob Hardy, Columbus Dispatch "It is a handsome book for browsing and for some deep thought, and would be a superb gift for anyone (especially a young person) who has interest in mathematics."--Rob Hardy, Dispatch "The book by Maor and Jost should be given to everyone--young or old--embarking on the study of mathematics or anyone teaching mathematics. The book will act as a source of inspiration and as a reminder of why it is that mathematics has fascinated the human race for millennia."--Henrik Jeldtoft Jensen, LMS Newsletter "The content is accessible to anyone with even a high school course in geometry. The writing is very clear."--Choice "Clear and lively... The mathematics in this book is first-rate, but the real surprise is how well the art reflects and illuminates the topic at hand... All of it is lovely to look at... [Beautiful Geometry] rises to the level of a coffee-table art book, only with a lot more depth."--Mathematical Reviews "[E]erily captivating book... Maor's style of writing is conversational, and the writing is engaging."--Annalisa Crannell, Journal of Mathematics and the Arts "At a very reasonable price, this is a book which would grace the coffee-table of any mathematics department, and many of the ideas in it will stimulate valuable discussions in the classroom."--Gerry Leversha, Mathematical Gazette "It presents as a coffee-table book for mathematicians and would be a good addition to a classroom library, available for students of all ages to explore."--Susan Mielechowsky, Mathematics Teaching in the Middle School "Visually stunning... [Beautiful Geometry] raises fundamental questions, answered thousands of years later and evidencing the progress made... This is an engaging book of broad appeal and a colourful approach to the history of geometry."--Mathematics TodayTable of ContentsPrefaces ix 1.Thales of Miletus 1 2.Triangles of Equal Area 3 3.Quadrilaterals 6 4.Perfect Numbers and Triangular Numbers 9 5.The Pythagorean Theorem I

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Book SynopsisFrom a review of the second edition:"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."(David Parrott, Australian Mathematical Society)This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it's accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.Trade Review“Mathematics and Its History is an original, engaging and effective book, which I think would be enjoyed by students, lay readers with the right background, or indeed mathematicians themselves.” (Danny Yee, Danny Yee's Book Reviews, dannyreviews.com, March, 2019)From the reviews of the third edition:"The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril — it is hard to put down!"(Richard Wilders, MAA Reviews)“I appreciate and recommend Stillwell’s presentation of mathematics and history written in a lively style. The author’s concept (history mostly as the means of approaching mathematics) remains a matter of interest for both the mathematician and the historian … .” (Rüdiger Thiele, Zentralblatt MATH, Vol. 1207, 2011)From the reviews of the second edition:"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."(David Parrott, Australian Mathematical Society)"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society)"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."(Denis Bonheure, Bulletin of the Belgian Society)Table of ContentsPreface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- The Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Number Theory Revival.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Non-Euclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Simple Groups.- Sets, Logic, and Computation.- Combinatorics.- Bibliography.- Index.-

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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 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 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 SynopsisDonal O'Shea is professor of mathematics and dean of faculty at Mount Holyoke College. He has written scholarly books and monographs, and his research articles have appeared in numerous journals and collections. He lives in South Hadley, Massachusetts.Trade ReviewConveys topology's mind-bending contortions with great flair * New Scientist *One can't read The Poincaré Conjecture without an overwhelming awe at the infinite depths and richness of a mathematical realm not made by us * Martin Gardner, author of The Annotated Alice *Reveals the human story behind the challenge of the conjecture, and gives us a glimpse of the weird world inhabited by mathematicians * BBC Focus *Beautifully written * American Scientist *Intriguing * The Times *A truly marvellous book * Martin Gardner *One can't read The Poincaré Conjecture without an overwhelming awe at the infinite depths and richness of a mathematical realm not made by us * Martin Gardner, author of The Annotated Alice *

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Book SynopsisThis original anthology collects 10 of Weyl''s less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl''s mentor, David Hilbert. 2012 edition.

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Book SynopsisWe all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction. In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review pi's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics.This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.Trade Review""There is something for everyone in this book and everyone should read this book because it will be for some, a revelation that mathematics can be fun and beautiful, something they may not have realized during earlier encounters. Math teachers will find a host of ideas to enrich their instruction since Pi, as you know, comes up everywhere. This book is highly recommended and should provide a major step toward increasing the popularity of mathematics.”-Education Update “A joyful exploration…written in a conversational style reminiscent of children's science books. The writing is clear and crisp and draws the reader into the author's enthusiasm…I highly recommend [this book] to high school and college students and teachers of both. The book captures the excitement and fascination of pi and can serve as a starting point for more detailed discussion.”-Mathematics Teacher“I enjoyed reading the book…for its many applications, curiosities, and anecdotes.”-Science “Readers curious about pi could start here…Recommended.” -Choice

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Book SynopsisThis volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities. Table of Contents1. The Middle East, or the Beginning.- 2. The Sages of Ancient Greece.- 3. The Chinese Middle Ages.- 4. India and Persia.- 5. From the Renaissance to the Birth of Calculus.- 6. The Age of Analysis and the French Revolution.- 7. Modern Mathematics, Modern Art.- 8. Abstraction: Mathematics Since the Twentieth Century.

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Book SynopsisTrade Review"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities... It would be good to have more books like this."--Timothy Gowers, Nature "Nahin's tale of the formula e[pi] i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler."--Matthew Killeya, New Scientist "It is very difficult to sum up the greatness of Euler... This excellent book goes a long way to explaining the kind of mathematician he really was."--Steve Humble, Mathematics Today "What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics... This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors."--Henry Ricardo, MAA Reviews "The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content."--Robert E. O'Malley, Jr., SIAM Review "This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level."--Eberhard Knobloch, Mathematical Reviews "It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK."--Robin Wilson, London Mathematical Society NewsletterTable of Contents*FrontMatter, pg. i*Contents, pg. ix*Preface to the Paperback Edition, pg. xiii*Preface, pg. xxix*Introduction, pg. 1*Chapter 1. Complex Numbers, pg. 13*Chapter 2. Vector Trips, pg. 68*Chapter 3. The Irrationality of pi2, pg. 92*Chapter 4. Fourier Series, pg. 114*Chapter 5. Fourier Integrals, pg. 188*Chapter 6. Electronics and -1, pg. 275*Euler: The Man and the Mathematical Physicist, pg. 324*Notes, pg. 347*Acknowledgments, pg. 375*Index, pg. 377

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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 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 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 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 SynopsisThis book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.Trade Review"[Kline] is unfalteringly clear in explaining mathematical ideas; he is learned but not pedantic; he has historical discernment, a sympathetic social outlook and a nice sense of fun and irony.... The beauty and fascination and rare excellence of mathematics emerge from his story. It is an exciting, provocative book."--Scientific American "Still the best textbook for the history and philosophy of mathematics for undergraduate liberal arts students. Especially good for the age of the Scientific Revulution."--Janet A. Fitzgerald, Molloy College, NY

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Book SynopsisIn 2013, a little known mathematician in his late 50s stunned the mathematical community with a breakthrough on an age-old problem about prime numbers. Since then, there has been further dramatic progress on the problem, thanks to the efforts of a large-scale online collaborative effort of a type that would have been unthinkable in mathematics a couple of decades ago, and the insight and creativity of a young mathematician at the start of his career.Prime numbers have intrigued, inspired and infuriated mathematicians for millennia. Every school student studies prime numbers and can appreciate their beauty, and yet mathematicians'' difficulty with answering some seemingly simple questions about them reveals the depth and subtlety of prime numbers.Vicky Neale charts the recent progress towards proving the famous Twin Primes Conjecture, and the very different ways in which the breakthroughs have been made: a solo mathematician working in isolation and obscurity, and a large collaboration that is more public than any previous collaborative effort in mathematics and that reveals much about how mathematicians go about their work. Interleaved with this story are highlights from a significantly older tale, going back two thousand years and more, of mathematicians'' efforts to comprehend the beauty and unlock the mysteries of the prime numbers.Trade ReviewThe way [Closing the Gap] explores mathematics and at the same time describes the work mathematicians do, is very interesting and it keeps the reader invested in the book. It is easy to read and precise. The book could be definitely recommended to mathematics students and teachers but also to younger people with an interest in higher-level mathematics. * Panayiotis Vlamos, University of Athens, MAA *The book features a creative structure that lends itself well to the subject matter. A curious undergraduate mathematics major should enjoy this book and learn a great deal. For mathematicians who do not specialize in number theory but who are curious about the flurry of recent activity in the field, this book provides an excellent entry point. * Stephan Ramon Garcia, Notices of the American Mathematics Society *If you are looking for an introduction to the world of Polymath; if you are looking for the story of the Twin Primes Conjecture; if you are looking to show you friends and family what your life as a mathematician is; if you would like a bit of asymptotic mathematics explained to you plainly; if you would like a summary of Waring's problem; or if you just have a couple of hours and are looking for a nice diversion, then you have found it. * Deborah Chun, London Mathematical Society *The book is clearly and enthusiastically written and beautifully presented. * Owen Toller, The Mathematical Gazette *For myself, I learned a lot, even about subjects I thought I knew before... it is clear from every page in the book that Neale is superb teacher. In sum, I recommend this book highly to anyone interested in mathematics, young people and teachers but also to researchers. * Michael N. Fried, Mathematical Thinking and Learning *Written in an engaging and inclusive way, it makes a perfect read for beginners but it also picks up the pace fairly quickly, so even enthusiasts like myself are bound to enjoy it. Neale manages to take the readers on a journey to cutting edge research mathematics. * Nikoleta Kalaydzhieva and Sam Porritt, Chalkdust Magazine *Neale writes in an inviting style that draws readers into this challenging subject, convincing them that, with a little effort, they too can follow along. An enjoyable book and journey, complemented by a helpful reading list and index... Recommended. * J. Johnson, CHOICE *Closing the Gap is an excellent exposition of the study of prime numbers. Not only do we learn about the history of this area since the Greeks, but the book is the first aimed at a lay readership that provides insight into recent breakthroughs. Vicky Neale's passion in the subject is contagious and I enjoyed how she weaves together the mathematics with background on how mathematicians now work, as well as her reflections on what it is like to be a mathematician. This book would be ideal for a curious sixth former wanting to peek ahead at what might lie around the corner if they are considering studying mathematics at a higher level. * Alex Bellos, author of Alex's Adventures in Numberland and Alex Through the Looking-Glass *Her prose is clear but not patronizing, precise but accessible. The result is a very enjoyable book that can be read with profit not only by laypeople but also by mathematics students and the people who teach them. * Mark Hunacek, MAA Reviews *Closing The Gap has gone straight into my top ten books to give to interested students... The book's introduction starts with an extended analogy comparing mathematics to climbing [and] Neale sets herself up as this guide, and succeeds brilliantly. * Colin Beveridge, The Aperiodical *Closing the Gap is among the clearest popular accounts of maths I've read in a while. It's about prime numbers, as the title suggests, but it's also a master piece in the art of weaving. Apart from exploring the mathematics, the book gives an intimate description of the process of doing maths as experienced by those who do it every day, and an account of a particularly exciting, and recent, period when prime number theory made some great leaps forward. And it's a look at a completely new way of doing mathematics: in large online collaborations that anyone can join. * Marianne Freiberger, PLUS *Table of Contents1: Introduction 2: What is a prime? 3: May 2013 4: It's easy to ask hard questions 5: May 2013 6: Making hard problems easier 7: June 2013 8: How many primes are there? 9: July 2013 10: What's so mathematical about my mathematical pencil? 11: August 2013 12: If primes are hard, let's try something else 13: November 2013 14: Generalise . . . 15: April 2014 16: Where next?

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Book SynopsisIn MATH WITH BAD DRAWINGS, Ben Orlin answers math''s three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark bad drawings, which convey both his humor and his message with perfect pitch and clarity. Organized by unconventional but compelling topics such as Statistics: The Fine Art of Honest Lying, Design: The Geometry of Stuff That Works, and Probability: The Mathematics of Maybe, MATH WITH BAD DRAWINGS is a perfect read for fans of illustrated popular science.

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Book SynopsisMorel tells the story of subterranean geometry, a forgotten discipline that developed in the silver mines of early modern Europe where mining and metallurgy were of great significance. Through vivid case studies, he illustrates how geometry was used in metallic mines, from surveying to map-making, by practitioners using esoteric manuscripts.

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Book SynopsisThis Element shows that Plato keeps a clear distinction between mathematical and metaphysical realism. It also shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability. This title is also available as Open Access on Cambridge Core.Trade Review'… Landry's response to the Platonic call for collaboration with his text opens up the possibility of very fruitful debates.' Susanna Saracco, MetascienceTable of Contents1. Introduction; 2. The interprative lay of the land; 3. The divided line; 4. Book 7; 5. The good in mathematics; 6. Mathematics versus metaphysics; References.

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Book SynopsisThis book introduces prime numbers and explains the celebrated, unsolved Riemann hypothesis in a direct manner. Suitable for both scholars and those with a minimal mathematical background.Trade Review'This is an extraordinary book, really one of a kind. Written by two supreme experts, but aimed at the level of an undergraduate or curious amateur, it emphasizes the really powerful ideas, with the bare minimum of math notation and the maximum number of elegant and suggestive visuals. The authors explain why this legendary problem is so beautiful, why it is difficult, and why you should care.' Will Hearst, Hearst Corporation'This book is a soaring ride, starting from the simplest ideas and ending with one of the deepest unsolved problems of mathematics. Unlike in many popular math books puffed up with anecdotal material, the authors here treat the reader as seriously interested in prime numbers and build up the real math in four stages with compelling graphical demonstrations revealing in deeper and deeper ways the hidden music of the primes. If you have ever wondered why so many mathematicians are obsessed with primes, here's the real deal.' David Mumford, Brown University, Rhode Island'This is a delightful little book, not quite like anything else that I am aware of … a splendid piece of work, informative and valuable. Undergraduate mathematics majors, and the faculty who teach them, should derive considerable benefit from looking at it.' Mark Hunacek, MAA Reviews'This book is divided into four parts, and succeeds beautifully in giving both an overview for the general audience and a sense of the details needed to understand how quickly the number of primes grows. This is accomplished through a very clear exposition and numerous illuminating pictures.' Steven Joel Miller, MathSciNet'Where popularizers of mathematics usually succumb either to a journalist's penchant for 'man bites dog' irony and spectacle or a schoolteacher's iron will to simplify away the terror, one might call the distinctive approach here 'take a lay reader to work'. Computers now provide mathematicians a laboratory, and the authors exploit this modern power to exhibit graphics, making the key equivalence a luminous phenomenon of experimental mathematics … for its clarity and the importance of its topic, this book deserves the same classic status as A Brief History of Time (CH, Jul'88). Summing Up: Essential. All readers.' D. V. Feldman, CHOICE'Prime Numbers and the Riemann Hypothesis is an agile, unusual book written over a decade, one week per year; it can be considered a sort of collaborative work, in that each version was put online with the purpose of getting feedback.' Massimo Nespolo, Acta Crystallographica Section A: Foundations and Advances'… a great gift for a curious student. Using the graphical methods found in calculus reform texts, this beautiful little book allows a patient reader with a good grasp of first-year calculus to explore the most famous unsolved problem in mathematics, the so-called Riemann Hypothesis, and to understand why it points to as yet undiscovered regularities in the distribution of prime numbers.' Donal O'Shea, The Herald Tribune'The book under review succeeds handsomely in making the case for the Riemann Hypothesis to a wide audience … Beginning with the definition of prime numbers, the authors weave their way through concrete and picturesque presentations of elementary techniques and descriptions of unsolved problems connected with the primes. They provide many insightful footnotes, concrete and illuminating figures, pointers to arXiv pages for added information, and a rich set of endnotes that contain further descriptions and details with varying levels of sophistication. After 23 short sections (a few pages each) they have arrived at a formulation of the Riemann Hypothesis in terms of counting primes up to a given size. By this point in their masterful and compelling presentation, the Hypothesis appears to be completely natural and inevitable … I have no doubt that many newcomers to the subject who have read to the end of the book will be eager to learn more and will be drawn into this fertile playground.' Peter Sarnak, Bulletin of the AMS'I really recommend this book if you want to get a feeling for the Riemann hypothesis without sinking into technicalities.' John Baez, The n-Category Café (http://golem.ph.utexas.edu/category)Table of Contents1. Thoughts about numbers; 2. What are prime numbers?; 3. 'Named' prime numbers; 4. Sieves; 5. Questions about primes; 6. Further questions about primes; 7. How many primes are there?; 8. Prime numbers viewed from a distance; 9. Pure and applied mathematics; 10. A probabilistic 'first' guess; 11. What is a 'good approximation'?; 12. Square root error and random walks; 13. What is Riemann's hypothesis?; 14. The mystery moves to the error term; 15. Césaro smoothing; 16. A view of Li(X) - π(X); 17. The prime number theorem; 18. The staircase of primes; 19. Tinkering with the staircase of primes; 20. Computer music files and prime numbers; 21. The word 'spectrum'; 22. Spectra and trigonometric sums; 23. The spectrum and the staircase of primes; 24. To our readers of part I; 25. Slopes and graphs that have no slopes; 26. Distributions; 27. Fourier transforms: second visit; 28. Fourier transform of delta; 29. Trigonometric series; 30. A sneak preview; 31. On losing no information; 32. Going from the primes to the Riemann spectrum; 33. How many θi's are there?; 34. Further questions about the Riemann spectrum; 35. Going from the Riemann spectrum to the primes; 36. Building π(X) knowing the spectrum; 37. As Riemann envisioned it; 38. Companions to the zeta function.

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