Understanding Infinity

The Mathematics of Infinite Processes

A. Gardiner

308 pages, parution le 15/05/2003

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Résumé

Conceived by the author as an introduction to "why the calculus works" (otherwise known as "analysis"), this volume represents a critical reexamination of the infinite processes encountered in elementary mathematics.
Part I presents a broad description of the coming parts, and Part II offers a detailed examination of the infinite processes arising in the realm of number--rational and irrational numbers and their representation as infinite decimals. Most of the text is devoted to analysis of specific examples.
Part III explores the extent to which the familiar geometric notions of length, area, and volume depend on infinite processes.
Part IV defines the evolution of the concept of functions by examining the most familiar examples--polynomial, rational, exponential, and trigonometric functions.
Exercises form an integral part of the text, and the author has provided numerous opportunities for students to reinforce their newly acquired skills.

Contents

Part I From Calculus to Analysis

What's Wrong with the Calculus?
Growth and Change in Mathematics

Part II Number

Mathematics: Rational or Irrational?
Constructive and Non-constructive Methods in
Mathematics
Common Measures, Highest Common Factors and the
Game of Euclid
Sides and Diagonals of Regular Polygons
Numbers and Arithmetic—A Quick Review
Infinite Decimals (Part 1)
Infinite Decimals (Part 2)
Recurring Nines
Fractions and Recurring Decimals
The Fundamental Property of Real Numbers
The Arithmetic of Infinite Decimals
Reflections on Recurring Themes
Continued Fractions

Part III Geometry

Numbers and Geometry
The Role of Geometrical Intuition
Comparing Areas
Comparing Volumes
Curves and Surfaces

Part IV Functions

What Is a Number?
What Is a Function?
What Is an Exponential Function?

Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	A. Gardiner
Parution	15/05/2003
Nb. de pages	308
Format	15,5 x 23,5
Couverture	Broché
Poids	410g
Intérieur	Noir et Blanc
EAN13	9780486425382
ISBN13	978-0-486-42538-2