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Numbers as a Source of Mathematical Ideas

  • Israel Kleiner
Chapter

Abstract

Number systems have been a fruitful source of concepts, results, and theories in the evolution of mathematics. In fact, it has been suggested that much even of modern mathematics has its roots in the study of number and shape [78, 79]. This chapter offers suggestions for introducing various mathematical topics related to, and often originating in, the study of number systems. The material is organized around eight themes, which vary in detail and difficulty, and may serve as source material for courses or topics of varied degrees of sophistication and be addressed to various audiences – for example teachers, mathematics majors, and liberal-arts enthusiasts. The themes deal with algebraic, analytic, geometric, number-theoretic, set-theoretic, cultural, and philosophical issues. Although the themes are interconnected, they can be read independently. In many cases, we sketch the historical origin of the mathematical ideas involved. No attempt is made to be thorough, but references to an extensive bibliography are provided throughout. Readers are invited to come up with their own themes to suit their interests, needs, and objectives. The material in the next chapter may serve as an example of a possible theme.

Keywords

Seventeenth Century Number System Algebraic Number Negative Number Division Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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