Exploring the Real Numbers

Exploring the Real Numbers

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Intended primarily for a course for future high school teachers. Can also serve as an introduction to mathematical thought, a short course in number theory, an honors course at the high school level, or an introduction to mathematical education research.As much a book about numbers as a number theory text, Exploring the Real Numbers answers the need for future teachers to understand the real number system. Experienced educator Frederick Stevenson brings students 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. Many interesting topics that arise during the study of the real numbers are presented and students are given the opportunity to study topics further on their own.show more

Product details

  • Hardback | 365 pages
  • 158.8 x 237.5 x 19.6mm | 656.9g
  • Pearson Education (US)
  • Pearson
  • United States
  • English
  • 0130402613
  • 9780130402615

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 Plane4. 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.show more

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