Synopses & Reviews
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.
Popular account ranges from counting to mathematical logic and covers the many mathematical concepts that relate to infinity: graphic representation of functions; pairings and other combinations; prime numbers; logarithms and circular functions; formulas, analytical geometry; infinite lines, complex numbers, expansion in the power series; metamathematics; more. 216 illustrations.
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
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?