Exploring the Real Numbers / Edition 1

Exploring the Real Numbers / Edition 1

by Frederick W. Stevenson
     
 

ISBN-10: 0130402613

ISBN-13: 9780130402615

Pub. Date: 12/28/1999

Publisher: Pearson

Exploring the Real Numbers helps readers understand the real number system. Stevenson brings readers up to date with the study of the nature of real numbers, and provides a sense of the historical journey that has led to our current knowledge of the subject. Presents many interesting topics that arise during study of the real numbers. Offers 21

Overview

Exploring the Real Numbers helps readers understand the real number system. Stevenson brings readers up to date with the study of the nature of real numbers, and provides a sense of the historical journey that has led to our current knowledge of the subject. Presents many interesting topics that arise during study of the real numbers. Offers 21 exploratory projects, encouraging readers to pursue concepts beyond the book. Includes over 100 carefully worked examples. Features abundant exercises throughout. For anyone interested in learning more about some of the very different and often beautiful aspects of mathematics.

Product Details

ISBN-13:
9780130402615
Publisher:
Pearson
Publication date:
12/28/1999
Pages:
365
Product dimensions:
6.25(w) x 9.35(h) x 0.77(d)

Related Subjects

Table of Contents

Preface vii
The Natural Numbers
1(64)
The Basics
2(19)
The Fundamental Theorem of Arithmetic
21(8)
Searching for Primes
29(22)
Number Fascinations
51(14)
The Integers
65(84)
Diophantine Equations
66(18)
Congruence Arithmetic
84(22)
Pell and Pythagorus
106(25)
Factoring Large Numbers
131(18)
The Rational Numbers
149(64)
Rational Numbers as Decimals
151(16)
Decimals as Rational Numbers
167(17)
Continued Fractions
184(15)
Solving Equations on the Rational Plane
199(14)
The Real Numbers
213(92)
Algebraic Representations
214(22)
Geometric Representations
236(23)
Analytic Representations
259(23)
Searching for Transcendental Numbers
282(23)
Mathematical Projects
305(56)
Rings of Factors
306(2)
Sums of Consecutive Numbers
308(2)
Measuring Abundance
310(1)
Inside the Fibonacci Numbers
311(3)
Pictures at an Iteration
314(2)
Eenie Meenie Miney Mo
316(3)
Factoring with the Pollard ρ Method
319(2)
Charting the Integral Universe
321(4)
Triangles on the Integral Lattice
325(3)
The Gaussian Integers
328(3)
Writing Fractions the Egyptian Way
331(3)
Building Polygons with Dots
334(3)
The Decimal Universe of Fractions, I
337(4)
The Decimal Universe of Fractions, II
341(1)
The Making of a Star
342(2)
Making Your Own Real Numbers
344(4)
Building 1 the Egyptian Way
348(3)
Continued Fraction Expansions of √N
351(2)
A Special Kind of Triangle
353(2)
Polygon Numbers
355(2)
Continued Fraction Expansions
357(4)
Further Reading 361(2)
Index 363

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