The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    Life was a despairing time in the 1950s, as Veronica sought desperately to keep away from his cruelty. Astonishingly, to her and her mother, she won a scholarship to Ackworth Boarding School where she began to shine above her class-mates. A champion in all sports, Veronica at last found some happiness until her brother-in-law came into her life. It was as if she had stepped from the frying pan into the re: he took over control of her life removing her from the school she adored, two terms before she was due to take her GCEs, so he could put her to work as a cheap option on his market stall. Abused for many years by these two men, Veronica eventually ran away and applied to the Prison Service, knowing it was the only safe place she could trust. This is the astonishing, and true story of Veronica Bird who rose to become a Governor of Armley prison. Given a ‘basket case’ in another prison, contrary to all expectations, she turned it around within a year, to become an example for others to match. During her life inside, her ‘bird’, she met many Home Secretaries, was honoured by the Queen and was asked to help improve conditions in Russian Prisons. A deeply poignant story of eventual triumph against a staggeringly high series of setbacks, her story is filled with humour and compassion for those inside.

    Originally published in 1960, this compact book tells the true story of a German soldier: from his early childhood during the First World War, through to his harrowing experiences on the frontline during the Word War II, culminating in his capture by the Red Army on 20 December 1942…An astonishing first-hand account.

    

    Daysearlier, while traversing the Straits of Sicily the crew had discovered a crack in one ofthe nuclear reactor pipes, requiring the immediate shutting down of the reactor toprevent a potential reactor accident, an operation never before conducted on a Britishsubmarine at sea.Th e previous six days had been a difficult time for the crew of the submarine. Initialindications of a nuclear reactor defect had quickly escalated into a full scale potential nuclearreactor accident at sea, requiring decisive action by the crew to make the reactor safe, toidentify the defect and attempt to repair the reactor, and then to surface the submarine andto sail her safely back to the nearest safe harbor using emergency propulsion machinerydesigned for very limited use. The resulting lack of electrical power resulted in the crewhaving to sacrifice lighting, air-conditioning, bathing facilities and even hot food until theirreturn to harbor, and to suffer in the excessively hot interior of the boat. Throughout,there remained the fear of exposure to deadly radiation and the uncertainty that the reactormight still be one step away from a major accident.For one man onboard, this episode formed the culmination of a 25 year navalengineering career almost fated for this moment. Charge Chief Stephen Bridgman,the senior nuclear propulsion technician, had needed all of his engineering knowledgeand experience in the identification and eventual repair of the submarine reactor,subsequently being awarded an MBE together with a colleague for his services to navalengineering for his actions.This book provides an insight into a remarkable naval career starting as a 16 year oldStoker on the final proper British aircraft carrier HMS Ark Royal in 1977, throughthe Falklands War, being selected for naval technician training and submarine service,submarine training, submarine patrols in the supposed post cold-war period, theKosovo conflict, progression through the ranks, submarine refi t and refueling throughto the nuclear reactor accident onboard HMS Tireless.While there are countless accounts of naval life during wartime, this book tells theunique story of life as a British naval rating in the modern era, starting from the lowestlevel at a time of decline for the Royal Navy in the late 1970s, and paralleling the majorpolitical and military events of the 1980s and 1990s.

    A potpourri of musings assembled with a hint of practical spirituality, to be savoured passably as an oracle of hearts to the many answers, whose questions our minds are yet to comprehend. Ivory Gleam is split into three chapters of learning, longing and loving. Each chapter is a journey traversing a different road to the ultimate destination of self-reflection.

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    This sharply intelligent, consistently provocative book takes the reader on an astonishing, thought-provoking voyage into the realm of delightful uncertainty--a world of paradox in which logical argument leads to contradiction and common sense is seemingly rendered irrelevant.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    . . like a pendulum? These may not look like math questions, but they are-because they all have to do with patterns. And mathematics, at heart, is the study of patterns. That realization changed Eddie Woo's life-by turning the "dry" subject he dreaded in high school into a boundless quest for discovery. Now an award-winning math teacher, Woo sees patterns everywhere: in the "branches" of blood vessels and lightning, in the growth of a savings account and a sunflower, even in his morning cup of tea! Here are twenty-six bite-size chapters on the hidden mathematical marvels that encrypt our email, enchant our senses, and even keep us alive-from the sine waves we hear as "music" to the mysterious golden ratio. This book will change your mind about what math can be. We are all born mathematicians-and It's a Numberful World.

    The gear you select and how you use it can mean big results—or bigger disappointment.FASTER takes a scientific look at triathlon to see what truly makes you faster—and busts the myths and doublespeak that waste your money and race times. In this fascinating exploration of the forces at play in the swim-bike-run sport, astronautical engineer and triathlete Jim Gourley shows where to find free speed, speed on a budget, and the gear upgrades that are worth it.FASTER offers specific, science-based guidance on the fastest techniques and the most effective gear, answering questions like: •    Which wetsuit is best for me? •    What’s the best way to draft a swimmer? •    Should I buy a lighter bike? •    Deep dish or disc wheels? •    Are lighter shoes faster? •    Who’s right about running technique? Gourley reviews published studies in peer-reviewed journals to show what scientists have learned about swim drafting, pacing the bike leg, race strategy for short and long-course racing, and the fastest ways to handle transitions.FASTER will change how you think about your body, your gear, and the world around you. With science on your side, you'll make the smart calls that will make you a better, faster triathlete.

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.