The Problem Of Infinity In Mathematics

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The Mathematics of Infinity

Author : Theodore G. Faticoni
Publisher : John Wiley & Sons
ISBN 13 : 111824382X
Total Pages : 361 pages
Book Rating : 4.1/5 (182 download)

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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 2012-04-23 with total page 361 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.

The Great Mathematical Problems

Author : Ian Stewart
Publisher : Profile Books
ISBN 13 : 1847653510
Total Pages : 468 pages
Book Rating : 4.8/5 (476 download)

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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 468 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 Poincaré 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
ISBN 13 : 1786782340
Total Pages : 256 pages
Book Rating : 4.7/5 (867 download)

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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 256 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!

Roads to Infinity

Author : John Stillwell
Publisher : CRC Press
ISBN 13 : 1439865507
Total Pages : 202 pages
Book Rating : 4.4/5 (398 download)

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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

Infinity

Author : Ian Stewart
Publisher : Oxford University Press
ISBN 13 : 0198755236
Total Pages : 161 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Infinity by : Ian Stewart

Download or read book Infinity written by Ian Stewart and published by Oxford University Press. This book was released on 2017 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ian Stewart considers the concept of infinity and the profound role it plays in mathematics, logic, physics, cosmology, and philosophy. He shows that working with infinity is not just an abstract, intellectual exercise, and analyses its important practical everyday applications.

God and the Mathematics of Infinity

Author : H. Chris Ransford
Publisher : Columbia University Press
ISBN 13 : 3838270193
Total Pages : 127 pages
Book Rating : 4.8/5 (382 download)

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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 127 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.

Naming Infinity

Author : Loren Graham
Publisher : Harvard University Press
ISBN 13 : 0674032934
Total Pages : 252 pages
Book Rating : 4.6/5 (74 download)

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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.

The Infinite

Author : A.W. Moore
Publisher : Routledge
ISBN 13 : 1351381253
Total Pages : 332 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis The Infinite by : A.W. Moore

Download or read book The Infinite written by A.W. Moore and published by Routledge. This book was released on 2018-10-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor’s remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Gödel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, ‘Infinity superseded’, which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.

Infinity

Author : Michael Heller
Publisher : Cambridge University Press
ISBN 13 : 9781107685482
Total Pages : 0 pages
Book Rating : 4.6/5 (854 download)

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Book Synopsis Infinity by : Michael Heller

Download or read book Infinity written by Michael Heller and published by Cambridge University Press. This book was released on 2014-01-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite." - David Hilbert This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world‐renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity.

Beyond Infinity

Author : Eugenia Cheng
Publisher : Profile Books
ISBN 13 : 1782830812
Total Pages : 191 pages
Book Rating : 4.7/5 (828 download)

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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 191 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.

Love and Math

Author : Edward Frenkel
Publisher : Basic Books
ISBN 13 : 0465069959
Total Pages : 314 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis Love and Math by : Edward Frenkel

Download or read book Love and Math written by Edward Frenkel and published by Basic Books. This book was released on 2013-10-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

How Big is Infinity?

Author : Tony Crilly
Publisher : Quercus Publishing
ISBN 13 : 9781782069485
Total Pages : 0 pages
Book Rating : 4.0/5 (694 download)

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Book Synopsis How Big is Infinity? by : Tony Crilly

Download or read book How Big is Infinity? written by Tony Crilly and published by Quercus Publishing. This book was released on 2014-07-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: What are the strangest numbers? Where do numbers come from? Can maths guarantee riches? Why are three dimensions not enough? Can a butterfly's wings really cause a hurricane? Can maths predict the future? In How Big is Infinity?, acclaimed writer Tony Crilly distills the wisdom of some of the greatest minds in history to help provide answers some of the most perplexing, stimulating and surprising questions in mathematics.

Things to Make and Do in the Fourth Dimension

Author : Matt Parker
Publisher : Farrar, Straus and Giroux
ISBN 13 : 0374710376
Total Pages : 465 pages
Book Rating : 4.3/5 (747 download)

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Book Synopsis Things to Make and Do in the Fourth Dimension by : Matt Parker

Download or read book Things to Make and Do in the Fourth Dimension written by Matt Parker and published by Farrar, Straus and Giroux. This book was released on 2014-12-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book from the stand-up mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond. Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it.

Advanced Problems in Mathematics

Author : Stephen Siklos
Publisher :
ISBN 13 : 9781783747764
Total Pages : 188 pages
Book Rating : 4.7/5 (477 download)

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Book Synopsis Advanced Problems in Mathematics by : Stephen Siklos

Download or read book Advanced Problems in Mathematics written by Stephen Siklos and published by . This book was released on 2019-10-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Drawing Theories Apart

Author : David Kaiser
Publisher : University of Chicago Press
ISBN 13 : 0226422658
Total Pages : 376 pages
Book Rating : 4.2/5 (264 download)

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Book Synopsis Drawing Theories Apart by : David Kaiser

Download or read book Drawing Theories Apart written by David Kaiser and published by University of Chicago Press. This book was released on 2009-11-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2007 Pfizer Prize from the History of Science Society. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process. Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calculational skills, David Kaiser frames his story around the crafting and stabilizing of the basic tools in the physicist's kit—thus offering the first book to follow the diagrams once they left Feynman's hands and entered the physics vernacular.

Bridges to Infinity

Author : Michael Guillen
Publisher : Tarcher
ISBN 13 : 9780874773453
Total Pages : 222 pages
Book Rating : 4.7/5 (734 download)

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Book Synopsis Bridges to Infinity by : Michael Guillen

Download or read book Bridges to Infinity written by Michael Guillen and published by Tarcher. This book was released on 1983 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an endlessly fascinating journey through a mathematician's looking glass.

Leibniz and Kant

Author : Brandon C. Look
Publisher : Oxford University Press
ISBN 13 : 0199606366
Total Pages : 403 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Leibniz and Kant by : Brandon C. Look

Download or read book Leibniz and Kant written by Brandon C. Look and published by Oxford University Press. This book was released on 2021 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although it is common to see Kant's philosophy as at its core a reaction to (and partial rejection of) the dogmatism and rationalism of Leibniz, Wolff, and their followers, it is surprising how little detailed and critical study there has been of the relation between Leibniz and Kant. How did Kant understand Leibniz's philosophy? Did he correctly understand Leibniz's philosophy? Since only a portion of Leibniz's philosophical writings were published prior to Kant's critical period, is there a "true Leibniz" that Kant did not know? Are all of Kant's criticisms of Leibniz in particular and Leibnizian rationalism in general justified? Or does Leibniz have an answer to Kant's philosophy? Moreover, how should we understand the reception of Leibniz's philosophy in 18th-century Enlightenment Germany? Leibniz and Kant seeks to examine the relation between Leibniz and Kant by collecting essays written by some of the leading scholars of the history of modern philosophy, all of whom have in common a deep knowledge of both philosophers. This anthology further aims to create a dialogue between scholars of early modern philosophy and Kantians and to fill a lacuna in historical and philosophical scholarship. The essays contained here address fundamental questions of metaphysics, epistemology, and philosophical theology in Leibniz and Kant and address Kant's understanding and interpretation of his philosophical predecessor.