Infinity

Infinity

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  • Author: Ian Stewart
  • Publisher: Oxford University Press
  • ISBN: 0198755236
  • Category : Infinite
  • Languages : en
  • Pages : 161

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) isintimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas ofmathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectualexercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.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, andenthusiasm to make interesting and challenging topics highly readable.


Mathematics: A Very Short Introduction

Mathematics: A Very Short Introduction

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  • Author: Timothy Gowers
  • Publisher: Oxford Paperbacks
  • ISBN: 9780192853615
  • Category : Mathematics
  • Languages : en
  • Pages : 172

The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.


Symmetry: A Very Short Introduction

Symmetry: A Very Short Introduction

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  • Author: Ian Stewart
  • Publisher: OUP Oxford
  • ISBN: 0191652741
  • Category : Mathematics
  • Languages : en
  • Pages : 152

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. 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.


Infinity and the Mind

Infinity and the Mind

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  • Author: Rudy Rucker
  • Publisher: Princeton University Press
  • ISBN: 0691191255
  • Category : Mathematics
  • Languages : en
  • Pages :

A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.


Numbers: A Very Short Introduction

Numbers: A Very Short Introduction

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  • Author: Peter M. Higgins
  • Publisher: Oxford University Press
  • ISBN: 0199584052
  • Category : Mathematics
  • Languages : en
  • Pages : 153

In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinating role of primes, and explains their role in contemporary cryptography.


Infinity: A Very Short Introduction

Infinity: A Very Short Introduction

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  • Author: Ian Stewart
  • Publisher: Oxford University Press
  • ISBN: 019107151X
  • Category : Mathematics
  • Languages : en
  • Pages : 144

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite. 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.


From Here to Infinity

From Here to Infinity

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  • Author: Ian Stewart
  • Publisher: Oxford Paperbacks
  • ISBN: 0192832026
  • Category : Mathematics
  • Languages : en
  • Pages : 338

A retitled and revised edition of Ian Stewart's The Problem of Mathematics, this is the perfect guide to today's mathematics. Read about the latest discoveries, including Andrew Wile's amazing proof of Fermat's Last Theorem, the newest advances in knot theory, the Four Colour Theorem, Chaos Theory, and fake four-dimensial spaces. See how simple concepts from probability theory shed light on the National Lottery and tell you how to maximize your winnings. Discover howinfinitesimals become respectable, why there are different kinds of infinity, and how to square the circle with the mathematical equivalent of a pair of scissors.


Time: A Very Short Introduction

Time: A Very Short Introduction

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  • Author: Jenann Ismael
  • Publisher: Oxford University Press
  • ISBN: 0192568957
  • Category : Science
  • Languages : en
  • Pages : 137

What is time? What does it mean for time to pass? Is it possible to travel in time? What is the difference between the past and future? Until the work of Newton, these questions were purely topics of philosophical speculation. Since then we've learned a great deal about time, and its study has moved from a subject of philosophical reflection to instead became part of the subject matter of physics. This Very Short Introduction introduces readers to the current physical understanding of the direction of time, from the Second Law of Thermodynamics to the emergence of complexity and life. Jenann Ismael charts the line of development in physical theory from Newton, via Einstein's Theory of Relativity, to the current day. Einstein's innovations led to a vision of time very different from the familiar time of everyday sense. In this new vision, time is one of the dimensions in which the universe is extended alongside the spatial dimensions. The universe appears as a static block of events, in which there is no more a difference between past and future than there is between east and west. Discussing the controversy and philosophical confusion which surrounded the reception of this new vision, Ismael also covers the contemporary mixture of statistical mechanics, cognitive science, and phenomenology that point the way to reconciling the familiar time of everyday sense with the vision of time presented in Einstein's theories. Very Short Introductions: Brilliant, Sharp, Inspiring 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.


Game Theory: A Very Short Introduction

Game Theory: A Very Short Introduction

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  • Author: Ken Binmore
  • Publisher: Oxford University Press
  • ISBN: 0199218463
  • Category : Business & Economics
  • Languages : en
  • Pages : 201

Games are played everywhere: from economics to evolutionary biology, and from social interactions to online auctions. This title shows how to play such games in a rational way, and how to maximize their outcomes.


The Beginning of Infinity

The Beginning of Infinity

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  • Author: David Deutsch
  • Publisher: Penguin UK
  • ISBN: 0141969695
  • Category : Science
  • Languages : en
  • Pages : 571

'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman