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Playing with Infinity

by

Playing with Infinity Cover

 

Synopses & Reviews

Publisher Comments:

This popular account of the many mathematical concepts relating to infinity is one of the best introductions to this subject and to the entire field of mathematics. Dividing her book into three parts — The Sorcerer's Apprentice, The Creative Role of Form, and The Self-Critique of Pure Reason — Peter develops her material in twenty-two chapters that sound almost too appealing to be true: playing with fingers, coloring the grey number series, we catch infinity again, the line is filled up, some workshop secrets, the building rocks, and so on.

Yet, within this structure, the author discusses many important mathematical concepts with complete accuracy: number systems, arithmetical progression, diagonals of convex polygons, the theory of combinations, the law of prime numbers, equations, negative numbers, vectors, operations with fractions, infinite series, irrational numbers, Pythagoras' Theorem, logarithm tables, analytical geometry, the line at infinity, indefinite and definite integrals, the squaring of the circle, transcendental numbers, the theory of groups, the theory of sets, metamathematics, and much more. Numerous illustrations and examples make all the material readily comprehensible.

Without being technical or superficial, the author writes with complete clarity and much originality on the whole range of topics from counting to mathematical logic. Using little algebra and no mathematical formulas, she has written an unusual book that will interest even mathematicians and teachers. Beginning mathematics students and people in the humanities and other fields will find the book particularly outstanding for their purposes.

Synopsis:

Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.

Table of Contents

INTRODUCTION

PART I THE SORCERER'S APPRENTICE

1 PLAYING WITH FINGERS

2 THE 'TEMPERATURE CHARTS' OF THE OPERATIONS

3 THE PARCELLING OUT OF THE INFINITE NUMBER SERIES

4 THE SORCERER'S APPRENTICE

5 VARIATIONS ON A FUNDAMENTAL THEME

    POSTSCRIPT ON GEOMETRY WITHOUT MEASUREMENTS

6 WE GO THROUGH ALL POSSIBILITIES

7 COLOURING THE GREY NUMBER SERIES

8 I HAVE THOUGHT OF A NUMBER'

PART II THE CREATIVE ROLE OF FORM

9 DIVERGING NUMBERS

10 LIMITLESS DENSITY

11 WE CATCH INFINITY AGAIN

12 THE LINE IS FILLED UP

13 THE CHARTS GET SMOOTHED OUT

14 MATHEMATICS IS ONE

    POSTSCRIPT ABOUT WAVES AND SHADOWS

15 WRITE IT DOWN' ELEMENTS

16 SOME WORKSHOP SECRETS

17 MANY SMALL MAKE A GREAT'

PART III THE SELF-CRITIQUE OF PURE REASON

18 AND STILL THERE ARE DIFFERENT KINDS OF MATHEMATICS

    POSTSCRIPT ABOUT THE FOURTH DIMENSION

19 THE BUILDING ROCKS

20 FORM BECOMES INDEPENDENT

21 AWAITING JUDGEMENT BY METAMATHEMATICS

    POSTSCRIPT ON PERCEPTION PROJECTED TO INFINITY

22 WHAT IS MATHEMATICS NOT CAPABLE OF?

  AFTER USE

Product Details

ISBN:
9780486232652
Author:
Peter, Rozsa
Publisher:
Dover Publications
Author:
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Author:
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Author:
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Author:
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Author:
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Author:
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Author:
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Location:
New York :
Subject:
General
Subject:
General science
Subject:
Mathematics
Subject:
Popular works
Subject:
Mathematics -- Popular works.
Subject:
Mathematics - General
Subject:
Applied
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20100831
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
288
Dimensions:
8.5 x 5.38 in 0.68 lb

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Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Popular Surveys and Recreational
Science and Mathematics » Nature Studies » General

Playing with Infinity Used Trade Paper
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Product details 288 pages Dover Publications - English 9780486232652 Reviews:
"Synopsis" by ,
Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.
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