Exploring the Real Numbers / Edition 1

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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.
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Product Details

  • ISBN-13: 9780130402615
  • Publisher: Pearson
  • Publication date: 12/28/1999
  • Edition number: 1
  • Pages: 365
  • Product dimensions: 6.25 (w) x 9.35 (h) x 0.77 (d)

Table of Contents

1. The Natural Numbers.
The Basics. The Fundamental Theorem of Arithmetic. Searching for Primes. Number Fascinations.

2. The Integers.
Diophantine Equations. Congruence Arithmetic. Pell and Pythagoras. Factoring Large Numbers.

3. The Rational Numbers.
Rational Numbers as Decimals. Decimals as Rational Numbers. Continued Fractions. Solving Equations on the Rational Plane

4. The Real Numbers.
Algebraic Representations. Geometric Representations. Analytic Representations. Searching for Transcendental Numbers.

5. Mathematical Projects.
Rings of Factors. Sums of Consecutive Numbers. Measuring Abundance. Inside the Fibonacci Numbers. Pictures at an Iteration. Eenie Meenie Miney Mo. Factoring with the Pollard …r Method. Charting the Integral Universe. Triangles on the Integral Lattice. The Gaussian Integers. Writing Fractions the Egyptian Way. Building Polygons with Dots. The Decimal Universe of Fractions, I. The Decimal Universe of Fractions, II. The Making of a Star. Making Your Own Real Numbers. Building 1 the Egyptian Way. Continued Fraction Expansions of x1/2 N. A Special Kind of Triangle. Polygon Numbers. Continued Fraction Expansions.

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