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The Mathematics of Infinity

Author: Theodore G. Faticoni

Publisher: John Wiley & Sons

Published: 2012-04-17

Total Pages: 360

ISBN-13: 1118204484

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Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.

Book Synopsis The Mathematics of Infinity by : Theodore G. Faticoni

Download or read book The Mathematics of Infinity written by Theodore G. Faticoni and published by John Wiley & Sons. This book was released on 2012-04-17 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.

God and the Mathematics of Infinity

Author: H. Chris Ransford

Publisher: Columbia University Press

Published: 2017-03-28

Total Pages: 152

ISBN-13: 3838270193

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Drawing on the science and mathematics of infinity, H. Chris Ransford analyzes the traditional concept of godhood and reaches surprising conclusions. He addresses humankind's abiding core debate on the meaning of spirituality and God. Using mathematics, he explores key questions within this debate: for instance, why does evil exist if there is a God? The book fastidiously does not take sides nor proffers opinions, it only follows allowable mathematics wherever it leads. By doing so, it makes a major contribution to an understanding of the nature of reality.

Book Synopsis God and the Mathematics of Infinity by : H. Chris Ransford

Download or read book God and the Mathematics of Infinity written by H. Chris Ransford and published by Columbia University Press. This book was released on 2017-03-28 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on the science and mathematics of infinity, H. Chris Ransford analyzes the traditional concept of godhood and reaches surprising conclusions. He addresses humankind's abiding core debate on the meaning of spirituality and God. Using mathematics, he explores key questions within this debate: for instance, why does evil exist if there is a God? The book fastidiously does not take sides nor proffers opinions, it only follows allowable mathematics wherever it leads. By doing so, it makes a major contribution to an understanding of the nature of reality.

Beyond Infinity

Author: Eugenia Cheng

Publisher: Profile Books

Published: 2017-03-09

Total Pages: 204

ISBN-13: 1782830812

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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.

Book Synopsis Beyond Infinity by : Eugenia Cheng

Download or read book Beyond Infinity written by Eugenia Cheng and published by Profile Books. This book was released on 2017-03-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Naming Infinity

Author: Loren Graham

Publisher: Harvard University Press

Published: 2009-03-31

Total Pages: 252

ISBN-13: 0674032934

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In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

Book Synopsis Naming Infinity by : Loren Graham

Download or read book Naming Infinity written by Loren Graham and published by Harvard University Press. This book was released on 2009-03-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

Levels of Infinity

Author: Hermann Weyl

Publisher: Courier Corporation

Published: 2013-09-26

Total Pages: 208

ISBN-13: 0486266931

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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.

Book Synopsis Levels of Infinity by : Hermann Weyl

Download or read book Levels of Infinity written by Hermann Weyl and published by Courier Corporation. This book was released on 2013-09-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numbers and Infinity

Author: E. H. Sondheimer

Publisher: Courier Corporation

Published: 2006-01-01

Total Pages: 194

ISBN-13: 0486452980

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This fresh overview of numbers and infinity avoids tedium and controversy while maintaining historical accuracy and modern relevance. Perfect for undergraduate mathematics or science history courses. 1981 edition.

Book Synopsis Numbers and Infinity by : E. H. Sondheimer

Download or read book Numbers and Infinity written by E. H. Sondheimer and published by Courier Corporation. This book was released on 2006-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fresh overview of numbers and infinity avoids tedium and controversy while maintaining historical accuracy and modern relevance. Perfect for undergraduate mathematics or science history courses. 1981 edition.

The Invention of Infinity

Author: Judith Veronica Field

Publisher: Oxford University Press, USA

Published: 1997

Total Pages: 264

ISBN-13: 0198523947

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Fully illustrated, this story brings together the histories of arts and mathematics and shows how infinity at last acquired a precise mathematical meaning.

Book Synopsis The Invention of Infinity by : Judith Veronica Field

Download or read book The Invention of Infinity written by Judith Veronica Field and published by Oxford University Press, USA. This book was released on 1997 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully illustrated, this story brings together the histories of arts and mathematics and shows how infinity at last acquired a precise mathematical meaning.

Roads to Infinity

Author: John Stillwell

Publisher: CRC Press

Published: 2010-07-13

Total Pages: 202

ISBN-13: 1439865507

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Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h

Book Synopsis Roads to Infinity by : John Stillwell

Download or read book Roads to Infinity written by John Stillwell and published by CRC Press. This book was released on 2010-07-13 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h

The Great Mathematical Problems

Author: Ian Stewart

Publisher: Profile Books

Published: 2013-03-07

Total Pages: 340

ISBN-13: 1847653510

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There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Book Synopsis The Great Mathematical Problems by : Ian Stewart

Download or read book The Great Mathematical Problems written by Ian Stewart and published by Profile Books. This book was released on 2013-03-07 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Eight Lessons on Infinity

Author: Haim Shapira

Publisher: Watkins

Published: 2019-04-16

Total Pages: 272

ISBN-13: 1786782340

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A fun, non-technical and wonderfully engaging guide to that most powerful and mysterious of mathematical concepts: infinity.in this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. In this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. Written in clear, simple language and aimed at a lay audience, this book also offers some strategies that will allow readers to try their ability at solving truly fascinating mathematical problems. Infinity is a deeply counter-intuitive concept that has inspired many great thinkers. In this book we will meet many sages, both familiar and unfamiliar: Zeno and Pythagoras, Georg Cantor and Bertrand Russell, Sofia Kovalevskaya and Emmy Noether, al-Khwarizmi and Euclid, Sophie Germain and Srinivasa Ramanujan.The world of infinity is inhabited by many paradoxes, and so is this book: Zeno paradoxes, Hilbert's "Infinity Hotel", Achilles and the gods paradox, the paradox of heaven and hell, the Ross-Littlewood paradox involving tennis balls, the Galileo paradox and many more. Aimed at the curious but non-technical reader, this book refrains from using any fearsome mathematical symbols. It uses only the most basic operations of mathematics: adding, subtracting, multiplication, division, powers and roots – that is all. But that doesn’t mean that a bit of deep thinking won’t be necessary and rewarding. Writing with humour and lightness of touch, Haim Shapira banishes the chalky pallor of the schoolroom and offers instead a truly thrilling intellectual journey. Fasten your seatbelt – we are going to Infinity, and beyond!

Book Synopsis Eight Lessons on Infinity by : Haim Shapira

Download or read book Eight Lessons on Infinity written by Haim Shapira and published by Watkins. This book was released on 2019-04-16 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fun, non-technical and wonderfully engaging guide to that most powerful and mysterious of mathematical concepts: infinity.in this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. In this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. Written in clear, simple language and aimed at a lay audience, this book also offers some strategies that will allow readers to try their ability at solving truly fascinating mathematical problems. Infinity is a deeply counter-intuitive concept that has inspired many great thinkers. In this book we will meet many sages, both familiar and unfamiliar: Zeno and Pythagoras, Georg Cantor and Bertrand Russell, Sofia Kovalevskaya and Emmy Noether, al-Khwarizmi and Euclid, Sophie Germain and Srinivasa Ramanujan.The world of infinity is inhabited by many paradoxes, and so is this book: Zeno paradoxes, Hilbert's "Infinity Hotel", Achilles and the gods paradox, the paradox of heaven and hell, the Ross-Littlewood paradox involving tennis balls, the Galileo paradox and many more. Aimed at the curious but non-technical reader, this book refrains from using any fearsome mathematical symbols. It uses only the most basic operations of mathematics: adding, subtracting, multiplication, division, powers and roots – that is all. But that doesn’t mean that a bit of deep thinking won’t be necessary and rewarding. Writing with humour and lightness of touch, Haim Shapira banishes the chalky pallor of the schoolroom and offers instead a truly thrilling intellectual journey. Fasten your seatbelt – we are going to Infinity, and beyond!