Julian Havil Livres

"In The Irrationals, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges from antiquity to the twenty-first century"--

"Among the many constants that appear in mathematics, [pi], e, and i are the most familiar. Following closely behind is [gamma] or gamma, a constant that arises in many mathematical areas yet remains profoundly mysterious. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + ... up to 1/n , minus the natural logarithm of n -- and the numerical value is 0.5772156 ... But unlike its more celebrated colleagues [pi] and e, the exact nature of gamma remains a mystery. In fact, we don't even know if gamma is a fraction. In this tantalizing blend of history and mathematics, Julian Havil takes readers on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians."--Back cover

Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly - why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion - how is this possible? This title includes some of these counterintuitive mathematical occurrences.

John Napier (1550-1617) is celebrated today as the man who invented logarithms--an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier's pioneering efforts, his life and

Ten amazing curves personally selected by one of today's most important math writersCurves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves―and now you can share in this adventure.Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

Math―the application of reasonable logic to reasonable assumptions―usually produces reasonable results. But sometimes math generates astonishing paradoxes―conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll unaided uphill? In Nonplussed! ―a delightfully eclectic collection of paradoxes from many different areas of math―popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas.Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs.Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.

Das Buch stellt eine Reihe scheinbar paradoxer mathematischer Aussagen und deren Beweise vor. Sie kommen aus verschiedenen Bereichen der Mathematik, darunter das Geburtstagsparadoxon, Conways Chequerboard-Armee und Torricellis Trompete. Angewendet werden elementare Methoden der Kombinatorik, Wahrscheinlichkeitsrechnung, Statistik, Geometrie und Analysis. Zahlreiche Abbildungen und Tabellen illustrieren die Fragen und die wesentlichen Schritte zu ihrer Lösung. Das Buch ist für mathematisch Interessierte mit Oberstufenkenntnissen verständlich.

"Julian Havil's Das gibt's doch nicht ist eine unübertroffene Auseinandersetzung mit Problemen, die ein Gymnasiast leicht verstehen kann und deren Lösungen überraschend und unmöglich erscheinen. Dazu gehören das sattsam bekannte Drei-Türen-Problem von Monty Hall, die Aufzug-Paradoxa von Gamov und Stern, der Kartentrick von Kruskal und Cantors Paradies der Alephs, das einem den Atem verschlägt. All das analysiert dieser Meister des Lehrens, ohne sich bei Gleichungen zurückzuhalten, die elegante Beweise bieten. Und es gibt fast auf jeder Seite eine Überraschung.„ (Martin Gardner) Bleibt nur hinzuzufügen, dass es um Rätsel der folgenden Art geht: um die Wahrscheinlichkeit, als Show-Kandidat das Auto und nicht die Ziegen hinter den drei verschlossenenTüren zu wählen; um die Frage, warum der Aufzug im Parterre und im obersten Stockwerk nicht gleich oft nach oben und unten zu fahren scheint; um die paradoxe Abzählbarkeit ganzer Zahlen und Brüche, die nach Cantor als Mengen gleich groß sein sollen; um ein Erkennen einer Spielkarte aus einem auf verschlungenen Wege gemischten und geordneten Stapel; und das ist nicht alles für den geneigten Leser. “Für diejenigen, die die Spannung, die der Autor während des Lesens geschickt aufbaut, auch genießen möchten, ist ‘Gamma‘ eine wahre Goldgrube …" meint WissenschaftOnline/SpektrumDirekt zu dem bereits auf Deutsch bei Springer erschienenen Havil-Titel