Mathematics and the Unexpected


Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 9780226199900
Category: Mathematics
Page: 146
View: 7369

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"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist "In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

The Best of All Possible Worlds

Mathematics and Destiny
Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 0226199959
Category: Mathematics
Page: 207
View: 430

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Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer. This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today. Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

The Broken Dice, and Other Mathematical Tales of Chance


Author: Ivar Ekeland
Publisher: University of Chicago Press
ISBN: 9780226199924
Category: Mathematics
Page: 190
View: 8731

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Ivar Ekeland extends his consideration of the catastrophe theory of the universe begun in his widely acclaimed Mathematics and the Unexpected, by drawing on rich literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory, and particle physics. "Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science

Mathematics and the Aesthetic

New Approaches to an Ancient Affinity
Author: Nathalie Sinclair,William Higginson
Publisher: Springer Science & Business Media
ISBN: 9780387381459
Category: Mathematics
Page: 288
View: 4346

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Mathematics the Truth

‘Moving mathematics teaching into the age of quantum mechanics and relativity.’
Author: Malcolm Cameron
Publisher: Malcolm Cameron
ISBN: 1925635783
Category: Mathematics
Page: 168
View: 7618

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Malcolm McDonald, FEDFA Union, State President, 1992-96

Mathematics and the Body

Material Entanglements in the Classroom
Author: Elizabeth de Freitas,Nathalie Sinclair
Publisher: Cambridge University Press
ISBN: 1107039487
Category: Education
Page: 312
View: 4333

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This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.

Grundlagen der Mathematik für Dummies


Author: Zegarelli
Publisher: John Wiley & Sons
ISBN: 352769935X
Category: Mathematics
Page: 357
View: 8571

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Mathematik ist nicht jedermanns Sache und oft sind es gerade die Grundlagen, die fehlen: Wie berechnet man nochmal den Umfang eines Kreises? Wieviel Geld spare ich bei 30 % Rabatt? Und wie geht man Textaufgaben eigentlich richtig an? Fragen über Fragen - die Antworten finden Sie in diesem Buch. Egal ob Bruch- oder Prozentrechnung, Geometrie, Algebra, Wahrscheinlichkeitsrechnung oder Statistik, Mark Zegarelli erklärt es Ihnen einfach, mit Humor und immer schnell auf den Punkt. Frischen Sie Ihr Wissen auf, lernen Sie die Grundlagen der Mathematik und werden Sie ruckzuck zum Mathe-Ass.

Mathematics and the Imagination


Author: Edward Kasner,James Newman
Publisher: Courier Corporation
ISBN: 0486320278
Category: Mathematics
Page: 400
View: 417

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With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.

Alex im Wunderland der Zahlen

Eine Reise durch die aufregende Welt der Mathematik
Author: Alex Bellos
Publisher: eBook Berlin Verlag
ISBN: 3827078083
Category: Mathematics
Page: 480
View: 6614

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Erinnern wir uns nicht alle mit Schrecken an die ratlosen Momente vor der Tafel im Matheunterricht? Mit Kurvendiskussionen und Dreisatz dürften jedenfalls nur wenige Spaß und Spannung verbinden... Bis jetzt! Denn nun wagt sich Alex Bellos in den Kaninchenbau der Mathematik: in das Reich von Geometrie und Algebra, von Wahrscheinlichkeitsrechnung, Statistik und logischen Paradoxa. Auf der anderen Seite des Erdballs, am Amazonas, zählen die Mitglieder des Indianerstammes der Munduruku nur bis fünf und halten die Vorstellung, dass dies nicht genügen solle, für reichlich lächerlich. Bei uns in Deutschland dagegen finden jährlich die Meisterschaften der besten Kopfrechner der Welt statt - 2010 wurde in Magdeburg eine elfjährige Inderin zur Nummer eins unter den "Mathleten" gekürt. Die Mathe-Weltmeisterin unter den Tieren ist hingegen die Schimpansin Ai, die Alex Bellos im japanischen Inuyama aufspürt und über deren Rechenkünste er nur staunen kann. Auch wenn er von den bahnbrechenden Überlegungen Euklids erzählt oder erklärt, warum man in Japan seine Visitenkarten keinesfalls zu Dodekaedern falten sollte - Bellos führt uns durch das wahrhaft erstaunliche Reich der Zahlen und bringt uns eine komplexe Wissenschaft spielerisch nahe. Mit seiner Mischung aus spannender Reportage, Wissenschaftsgeschichte und mathematischen Kabinettstückchen erbringt er souverän den Beweis, dass die Gleichung Mathematik = Langeweile eindeutig nicht wahr ist. Quod erat demonstrandum.

Ein Sommer auf gut Glück


Author: Morgan Matson
Publisher: cbj Verlag
ISBN: 3641200997
Category: Young Adult Fiction
Page: 688
View: 3649

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Das wunderbare Chaos der ersten Liebe Die Sommerferien stehen vor der Tür und Andie hat alles geplant: einen Sommerkurs an einer renommierten Uni als perfekte Vorbereitung auf das Medizinstudium. Kein Problem – mit ihren guten Noten und einem bekannten Politiker als Vater. Doch als ein Skandal ihren Vater zum Rücktritt zwingt und der „befreundete“ Rektor der Eliteuni seine Empfehlung zurückzieht, steht Andie zum ersten Mal in ihrem Leben ohne Plan da. So beginnt ein Sommer, in dem sie Dinge tut, die sie nie zuvor getan hat: Sie führt Hunde aus, verbringt Zeit mit ihrem Vater – und lässt den süßen Clark weiter in ihr Herz, als sie vorhatte. Aber kann das länger halten als einen Sommer?

Fluke

The Math and Myth of Coincidence
Author: Joseph Mazur
Publisher: Hachette UK
ISBN: 0465040004
Category: Mathematics
Page: 288
View: 1341

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A mathematical guide to understanding why life can seem to be one big coincidence—and why the odds of just about everything are better than we would think

The Mathematics of Harmony

From Euclid to Contemporary Mathematics and Computer Science
Author: Alexey Stakhov
Publisher: World Scientific
ISBN: 9812775838
Category: Computer science
Page: 694
View: 5608

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Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."

Mathematics


Author: Timothy Gowers
Publisher: Sterling Publishing Company, Inc.
ISBN: 9781402768972
Category: Mathematics
Page: 180
View: 2309

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Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

Unexpected Links between Egyptian and Babylonian Mathematics


Author: Jöran Friberg
Publisher: World Scientific
ISBN: 9814480401
Category: Science
Page: 308
View: 4997

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Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected. Contents:Two Curious Mathematical Cuneiform Texts from Old Babylonian MariHieratic Mathematical Papyri and Cuneiform Mathematical TextsDemotic Mathematical Papyri and Cuneiform Mathematical TextsGreek-Egyptian Mathematical Documents and Cuneiform Mathematical Texts Readership: Mathematicians, historians of science, egyptologists and assyriologists. Keywords:Babylonian Mathematics;Egyptian Mathematics;Greek Mathematics;Mathematical Cuneiform Texts;Mathematical Papyri;Ancient Mathematics;Early Mathematics;History of Mathematics;Demotic Texts;Hieratic TextsKey Features:Extensive surveys of known Egyptian mathematical textsNew interpretations of particularly difficult Egyptian or Babylonian mathematical exercisesMany detailed diagrams and figures, using computer-aided methods of presentationsInteresting observations of experiments with new ways of representing fractions in demotic and Greek-Egyptian mathematical texts

Was ist Mathematik?


Author: Richard Courant,Herbert Robbins
Publisher: Springer-Verlag
ISBN: 3662000539
Category: Mathematics
Page: N.A
View: 8585

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47 brauchen nur den Nenner n so groß zu wählen, daß das Intervall [0, IJn] kleiner wird als das fragliche Intervall [A, B], dann muß mindestens einer der Brüche m/n innerhalb des Intervalls liegen. Also kann es kein noch so kleines Intervall auf der Achse geben, das von rationalen Punkten frei wäre. Es folgt weiterhin, daß es in jedem Intervall unendlich viele rationale Punkte geben muß; denn wenn es nur eine endliche Anzahl gäbe, so könnte das Intervall zwischen zwei beliebigen benachbarten Punkten keine rationalen Punkte enthalten, was, wie wir eben sahen, unmöglich ist. § 2. Inkommensurable Strecken, irrationale Zahlen und der Grenzwertbegriff 1. Einleitung Vergleicht man zwei Strecken a und b hinsichtlich ihrer Größe, so kann es vor kommen, daß a in b genau r-mal enthalten ist, wobei r eine ganze Zahl darstellt. In diesem Fall können wir das Maß der Strecke b durch das von a ausdrücken, indem wir sagen, daß die Länge von b das r-fache der Länge von a ist.

Locks, Mahabharata And Mathematics : AnExploration Of Unexpected Parallels


Author: V Raghunathan
Publisher: Harper Collins
ISBN: 9350296446
Category: Social Science
Page: 228
View: 5731

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A delightful exercise in lateral thinking There could be no three more disparate things than locks, mathematics and the Mahabharata. However, as Locks Mahabharata Mathematics shows, this is as entertaining a combination as any. Given here is a treasure trove of stories drawn from all three subjects. What could be more beguiling than a book that mixes Draupadi, a lock with five keys, and the quirky world of polynomials? Or Jarasandha who could be split apart but whose two halves could never be kept separate - split locks and symmetries? The Mahabharata is known for its stories. Lesser known are the fascinating combinations of locks which Dr Raghu - an avid collector - throws light upon, or the esoteric world of pure mathematics that he conveys for a lay audience. Divided into ten chapters, Locks Mahabharata Mathematics has stories ranging from that of Draupadi, to Yudhishthira's gamble, to Shukrayacharya and Kacha. Keeping them company are chancy locks, interacting keys and binary stars. Profusely illustrated with drawings of locks from his personal collection, this is a neatly original book like few others. Recalling books such as The Mind's I, Fantasies and Reflections on Self and Soul, The Tipping Point, and Godel, Escher, Bach ..., underlying it is a simple principle, one might say: Pure logic is the ruin of the spirit, as Antoine de Saint-Exupery said. These are tales that combine reason with fantasy to elevate the spirit.

Die Wirklichkeit, die nicht so ist, ...

Eine Reise in die Welt der Quantengravitation
Author: Carlo Rovelli
Publisher: Rowohlt Verlag GmbH
ISBN: 3644052514
Category: Science
Page: 320
View: 6360

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Was ist Wirklichkeit? Existieren Raum und Zeit tatsächlich, wenn wir uns anschicken, die elementarsten Grundlagen unserer Existenz zu erforschen? Wie viel davon können wir überhaupt verstehen? Carlo Rovelli beschäftigt sich seit vielen Jahren damit, die Grenzen unseres Verstehens zu erweitern. In diesem Buch nimmt er uns mit auf eine Reise, die von dem Realitätsverständnis der griechischen Klassik bis zur Schleifenquantengravitation führt. Ein großer Physiker unserer Zeit macht sich auf, uns ein neues Welt-Bild zu zeichnen: mit einem physikalischen Universum ohne Zeit, einer Raumzeit, die aus Schleifen und Körnchen besteht und in der Unendlichkeit nicht existiert. Einer Kosmologie, die ohne Urknall und Paralleluniversen auskommt und hier zum ersten Mal von einem ihrer «Erfinder» für ein breites Publikum einfach und ausführlich erklärt wird. Ein Buch über «die großen Herausforderungen der gegenwärtigen Naturwissenschaften, die all unser Wissen über die Natur in Frage stellen» (Rovelli).