Introducing Infinity

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Introducing Infinity

Brian Clegg
Introducing Infinity Book PDF

Author : Brian Clegg
Publisher : Icon Books Ltd
Page : 314 pages
File Size : 45,7 Mb
Release : 2014-12-01
Category : Mathematics
ISBN : 9781848318830

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Introducing Infinity by Brian Clegg Pdf

Infinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers – and provoked and shocked others. The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers. Brian Clegg and Oliver Pugh's brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.

Infinity

Ian Stewart
Infinity Book PDF

Author : Ian Stewart
Publisher : Oxford University Press
Page : 161 pages
File Size : 42,6 Mb
Release : 2017
Category : Infinite
ISBN : 9780198755234

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Infinity by Ian Stewart Pdf

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.

Introduction to Infinity-Categories

Markus Land
Introduction to Infinity Categories Book PDF

Author : Markus Land
Publisher : Springer Nature
Page : 300 pages
File Size : 54,9 Mb
Release : 2021-04-21
Category : Mathematics
ISBN : 9783030615246

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Introduction to Infinity-Categories by Markus Land Pdf

This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more advanced results such as the very important adjoint functor theorems. The book is based on lectures given by the author on the topic. While the material itself is well-known to experts, the presentation of the material is, in parts, novel and accessible to non-experts. Exercises complement this textbook that can be used both in a classroom setting at the graduate level and as an introductory text for the interested reader.

An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics

Matthew Katz,Jan Reimann
An Introduction to Ramsey Theory Fast Functions Infinity and Metamathematics Book PDF

Author : Matthew Katz,Jan Reimann
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 55,9 Mb
Release : 2018-10-03
Category : Combinatorial analysis
ISBN : 9781470442903

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An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics by Matthew Katz,Jan Reimann Pdf

This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”

Introduction to Analysis of the Infinite

Leonhard Euler
Introduction to Analysis of the Infinite Book PDF

Author : Leonhard Euler
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210214

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Introduction to Analysis of the Infinite by Leonhard Euler Pdf

From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

An Introduction to Infinite Products

Charles H. C. Little,Kee L. Teo,Bruce van Brunt
An Introduction to Infinite Products Book PDF

Author : Charles H. C. Little,Kee L. Teo,Bruce van Brunt
Publisher : Springer Nature
Page : 258 pages
File Size : 48,9 Mb
Release : 2022-01-10
Category : Mathematics
ISBN : 9783030906467

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An Introduction to Infinite Products by Charles H. C. Little,Kee L. Teo,Bruce van Brunt Pdf

This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

The Beginning of Infinity

David Deutsch
The Beginning of Infinity Book PDF

Author : David Deutsch
Publisher : Penguin UK
Page : 571 pages
File Size : 40,9 Mb
Release : 2011-03-31
Category : Science
ISBN : 9780141969695

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The Beginning of Infinity by David Deutsch Pdf

'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

The Infinite Game

Simon Sinek
The Infinite Game Book PDF

Author : Simon Sinek
Publisher : Penguin
Page : 272 pages
File Size : 50,8 Mb
Release : 2019-10-15
Category : Business & Economics
ISBN : 9780735213524

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The Infinite Game by Simon Sinek Pdf

From the New York Times bestselling author of Start With Why and Leaders Eat Last, a bold framework for leadership in today’s ever-changing world. How do we win a game that has no end? Finite games, like football or chess, have known players, fixed rules and a clear endpoint. The winners and losers are easily identified. Infinite games, games with no finish line, like business or politics, or life itself, have players who come and go. The rules of an infinite game are changeable while infinite games have no defined endpoint. There are no winners or losers—only ahead and behind. The question is, how do we play to succeed in the game we’re in? In this revelatory new book, Simon Sinek offers a framework for leading with an infinite mindset. On one hand, none of us can resist the fleeting thrills of a promotion earned or a tournament won, yet these rewards fade quickly. In pursuit of a Just Cause, we will commit to a vision of a future world so appealing that we will build it week after week, month after month, year after year. Although we do not know the exact form this world will take, working toward it gives our work and our life meaning. Leaders who embrace an infinite mindset build stronger, more innovative, more inspiring organizations. Ultimately, they are the ones who lead us into the future.

An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory

J.K. Hale,L.T. Magalhaes,W.M. Oliva
An Introduction to Infinite Dimensional Dynamical Systems Geometric Theory Book PDF

Author : J.K. Hale,L.T. Magalhaes,W.M. Oliva
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 41,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475744934

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An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory by J.K. Hale,L.T. Magalhaes,W.M. Oliva Pdf

Including: An Introduction to the Homotopy Theory in Noncompact Spaces

Beyond Infinity

Eugenia Cheng
Beyond Infinity Book PDF

Author : Eugenia Cheng
Publisher : Profile Books
Page : 204 pages
File Size : 48,9 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9781782830818

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Beyond Infinity by Eugenia Cheng Pdf

SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

Awesomism!

Suzy Miller
Awesomism Book PDF

Author : Suzy Miller
Publisher : iUniverse
Page : 154 pages
File Size : 48,8 Mb
Release : 2008-11
Category : Family & Relationships
ISBN : 9781440102851

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Awesomism! by Suzy Miller Pdf

You're a parent or teacher or therapist struggling to come to terms with the diagnosis of autism. You sense that drugs and behavior modification aren't the answer. But what is there? Here it is! A fresh new and boldly positive way to view autism as it really is...not a problem or mystery but a gift in your life. Suzy Miller had been a highly skilled pediatric speech pathologist for close to two decades when, through an amazing experience with a 4-year old child diagnosed with autism, she came to this break through way of understanding and working with these gifted children. She currently works with children and families bringing awareness to the various energies that make these children tick. Suzy's revolutionary thinking preserves the humanity and dignity of children, empowers the parents and makes a great deal of sense to anyone interacting with these highly aware children. Now, in Awesomism! You'll discover how to understand autism as never before. Here you will learn about the vibration behind autism and understand how to apply this awareness to experience the Awesomism in your child. Autism has been redefined as AWESOMISM!

Truth, Proof and Infinity

P. Fletcher
Truth Proof and Infinity Book PDF

Author : P. Fletcher
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 53,7 Mb
Release : 2013-06-29
Category : Philosophy
ISBN : 9789401736169

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Truth, Proof and Infinity by P. Fletcher Pdf

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.

Levels of Infinity

Hermann Weyl
Levels of Infinity Book PDF

Author : Hermann Weyl
Publisher : Courier Corporation
Page : 208 pages
File Size : 53,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486266930

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Levels of Infinity by Hermann Weyl Pdf

Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.

Fictions of Infinity

Martin Riedelsheimer
Fictions of Infinity Book PDF

Author : Martin Riedelsheimer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 256 pages
File Size : 46,7 Mb
Release : 2020-10-12
Category : Literary Criticism
ISBN : 9783110712407

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Fictions of Infinity by Martin Riedelsheimer Pdf

This study traces the connection of infinity and Levinasian ethics in 21st-century fiction. It tackles the paradox of how infinity can be (re-)presented in the finite space between the covers of a book and finds an answer that combines conceptual metaphor theory with concepts from classical narratology and beyond, such as mise en abyme, textual circularity, intertextuality or omniscient narration. It argues that texts with such structures may be conceptualised as infinite via Lakoff and Núñez’s Basic Metaphor of Infinity. The catachrestic transfer of infinity from structure to text means that the texts themselves are understood to be infinite. Taking its cue from the central role of the infinite in Emmanuel Levinas’s ethics, the function of such ‘fictions of infinity’ turns out to be ethical: infinite textuality disrupts reading patterns and calls into question the reader’s spontaneity to interpret. This hypothesis is put to the test in detailed readings of four 21st-century novels, David Mitchell’s Cloud Atlas, Jeanette Winterson’s The Stone Gods, Ian McEwan’s Saturday and John Banville’s The Infinities. This book thus combines ethical criticism with structural aesthetics to uncover ethical potential in fiction.

Introducing Game Theory

Ivan Pastine,Tuvana Pastine
Introducing Game Theory Book PDF

Author : Ivan Pastine,Tuvana Pastine
Publisher : Icon Books
Page : 273 pages
File Size : 45,8 Mb
Release : 2017-03-02
Category : Mathematics
ISBN : 9781785780837

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Introducing Game Theory by Ivan Pastine,Tuvana Pastine Pdf

When should you adopt an aggressive business strategy? How do we make decisions when we don't have all the information? What makes international environmental cooperation possible? Game theory is the study of how we make a decision when the outcome of our moves depends on the decisions of someone else. Economists Ivan and Tuvana Pastine explain why, in these situations, we sometimes cooperate, sometimes clash, and sometimes act in a way that seems completely random. Stylishly brought to life by award-winning cartoonist Tom Humberstone, Game Theory will help readers understand behaviour in everything from our social lives to business, global politics to evolutionary biology. It provides a thrilling new perspective on the world we live in.