Which Numbers Are Real? (Classroom Resource Materials)

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9780883857779: Which Numbers Are Real? (Classroom Resource Materials)

Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics.

Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers).

Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book.

Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

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Book Description:

This book explores alternative number systems that generalise the real numbers yet stay close to the properties that make the real numbers the fundamental quantities of mathematics. These exciting and sometimes eccentric number systems are active areas of research and will be of interest to students and teachers of mathematics.

About the Author:

Michael Henle is Professor of Mathematics and Computer Science at Oberlin College and has had two visiting appointments, at Howard University and the Massachusetts Institute of Technology, as well as two semesters teaching in London in Oberlin's own program. He is the author of two books: A Combinatorial Introduction to Topology (W. H. Freeman and Co., 1978, reissued by Dover Publications, 1994) and Modern Geometries: The Analytic Approach (Prentice-Hall, 1996). He is currently editor of The College Mathematics Journal.

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Michael Henle
Editore: Mathematical Association of America, United States (2012)
ISBN 10: 0883857774 ISBN 13: 9780883857779
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Descrizione libro Mathematical Association of America, United States, 2012. Hardback. Condizione libro: New. New.. Language: English . Brand New Book. The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and numbers that represent positions in games (surreal numbers). Each system has a well-developed theory with applications in other areas of mathematics and science. They all feature in active areas of research and each has unique features that are explored in this book. Alternative number systems reveal the central role of the real numbers and motivate some exciting and eccentric areas of mathematics. What Numbers Are Real? will be an illuminating read for anyone with an interest in numbers, but specifically for advanced undergraduates, graduate students and teachers of university-level mathematics. Codice libro della libreria AAA9780883857779

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Descrizione libro The Mathematical Association of America, 2012. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria FM-9780883857779

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Descrizione libro Mathematical Association of America, United States, 2012. Hardback. Condizione libro: New. New.. Language: English . Brand New Book. The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and numbers that represent positions in games (surreal numbers). Each system has a well-developed theory with applications in other areas of mathematics and science. They all feature in active areas of research and each has unique features that are explored in this book. Alternative number systems reveal the central role of the real numbers and motivate some exciting and eccentric areas of mathematics. What Numbers Are Real? will be an illuminating read for anyone with an interest in numbers, but specifically for advanced undergraduates, graduate students and teachers of university-level mathematics. Codice libro della libreria AAA9780883857779

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Descrizione libro Condizione libro: New. Codice libro della libreria 18380507-n

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Descrizione libro Mathematical Association of America, 2012. Hardcover. Condizione libro: Brand New. 219 pages. 9.25x6.25x0.75 inches. In Stock. Codice libro della libreria __0883857774

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Descrizione libro Mathematical Association of America, United States, 2012. Hardback. Condizione libro: New. New.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and numbers that represent positions in games (surreal numbers). Each system has a well-developed theory with applications in other areas of mathematics and science. They all feature in active areas of research and each has unique features that are explored in this book. Alternative number systems reveal the central role of the real numbers and motivate some exciting and eccentric areas of mathematics. What Numbers Are Real? will be an illuminating read for anyone with an interest in numbers, but specifically for advanced undergraduates, graduate students and teachers of university-level mathematics. Codice libro della libreria APE9780883857779

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Descrizione libro 2012. Hardback. Condizione libro: NEW. 9780883857779 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0483875

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Descrizione libro Mathematical Association of America. Hardback. Condizione libro: new. BRAND NEW, Which Numbers are Real?, Michael Henle, The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and numbers that represent positions in games (surreal numbers). Each system has a well-developed theory with applications in other areas of mathematics and science. They all feature in active areas of research and each has unique features that are explored in this book. Alternative number systems reveal the central role of the real numbers and motivate some exciting and eccentric areas of mathematics. What Numbers Are Real? will be an illuminating read for anyone with an interest in numbers, but specifically for advanced undergraduates, graduate students and teachers of university-level mathematics. Codice libro della libreria B9780883857779

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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, 2012. Condizione libro: New. The set of real numbers is one of the fundamental concepts of mathematics. This book surveys. . . *** Nota: EL COSTE DE ENVÍO A CANARIAS ES 8 euros. Si ha realizado un pedido con destino a CANARIAS no podemos hacer el envío con un coste de 3,5 euros . Nos pondremos en contacto con usted para comunicar el coste total del envío a Canarias y si está de acuerdo, Abebooks le efectuará el cargo adicional. Codice libro della libreria 9636931

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Descrizione libro Mathematical Association of America, 2012. Hardcover. Condizione libro: New. book. Codice libro della libreria M0883857774

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