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Exploring Topics in Elementary Number Theory Through A Computational Experiment

  • Sergei AbramovichEmail author
Chapter
  • 1.1k Downloads
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 3)

Abstract

Chapter 8 considers topics in the elementary theory of numbers that span from the time of Pythagoras to the time of Euler and connects ancient ideas about the properties of numbers that concerned Pythagoras and Euclid with more sophisticated interpretation of those ideas by Fermat and Euler. Whereas mathematical explorations that can be included in a computational experiment can be quite significant, software tools allow for hiding some of the complexity and formal structure of mathematics involved. This feature of computing is especially important for mathematics teacher education programs for it enables teacher candidates true engagement in dealing with rather advanced content without the need to have full understanding of the content and command of rigorous argument expected from future professional mathematicians.

Keywords

Number theory Unit fractions Diophantine equations Summation formulas Maximum Minimum Prime numbers Pythagorean triples Empirical induction Formal demonstration Negative transfer Rigor Proving Spreadsheet modeling The Geometer’s Sketchpad, Wolfram Alpha 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.State University of New York at PotsdamPotsdamUSA

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