Levels Of Infinity
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Author | : Hermann Weyl |
Publisher | : Courier Corporation |
Total Pages | : 258 |
Release | : 2013-09-26 |
Genre | : Mathematics |
ISBN | : 0486266931 |
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 Most have been long unavailable or previously unpublished in book form. 2012 edition.
Author | : Rudy Rucker |
Publisher | : Bantam Books |
Total Pages | : 379 |
Release | : 1983-01-01 |
Genre | : Philosophy |
ISBN | : 5885010897 |
The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."
Author | : Rudy Rucker |
Publisher | : Courier Corporation |
Total Pages | : 337 |
Release | : 2013-11-21 |
Genre | : Computers |
ISBN | : 0486492281 |
Originally published: Boston: Houghton Mifflin, 1987.
Author | : Brian Clegg |
Publisher | : Robinson |
Total Pages | : 185 |
Release | : 2013-02-07 |
Genre | : Mathematics |
ISBN | : 1472107640 |
'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.
Author | : Richard Evan Schwartz |
Publisher | : American Mathematical Soc. |
Total Pages | : 178 |
Release | : 2018 |
Genre | : Juvenile Nonfiction |
ISBN | : 1470447363 |
Mathematics professor from Brown University uses colorful illustrations and cartoons to display the concepts of infinity and large numbers.
Author | : Eugenia Cheng |
Publisher | : Profile Books |
Total Pages | : 191 |
Release | : 2017-03-09 |
Genre | : Mathematics |
ISBN | : 1782830812 |
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.
Author | : Ivan Penkov |
Publisher | : Springer Nature |
Total Pages | : 245 |
Release | : 2022-01-05 |
Genre | : Mathematics |
ISBN | : 3030896609 |
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Author | : Kate Hosford |
Publisher | : Carolrhoda Books ® |
Total Pages | : 40 |
Release | : 2013-11-01 |
Genre | : Juvenile Fiction |
ISBN | : 1467737917 |
When I looked up, I shivered. How many stars were in the sky? A million? A billion? Maybe the number was as big as infinity. I started to feel very, very small. How could I even think about something as big as infinity? Uma can't help feeling small when she peers up at the night sky. She begins to wonder about infinity. Is infinity a number that grows forever? Is it an endless racetrack? Could infinity be in an ice cream cone? Uma soon finds that the ways to think about this big idea may just be . . . infinite.
Author | : Shaughan Lavine |
Publisher | : Harvard University Press |
Total Pages | : 386 |
Release | : 1998-01-13 |
Genre | : Philosophy |
ISBN | : 0674039998 |
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
Author | : Steven Henry Strogatz |
Publisher | : Houghton Mifflin Harcourt |
Total Pages | : 333 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0547517653 |
A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."