The Concept of Number: From Quaternions to Monads and Topological Fields


Author: Benno Artmann

Publisher: Ellis Horwood Ltd , Publisher

Category: Study

Tag: Mathematics


Posted on 2012-09-25, by sharebookfree.

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The Concept of Number: From Quaternions to Monads and Topological Fields


The Concept of Number: From Quaternions to Monads and Topological Fields
Benno Artmann | Ellis Horwood Ltd , Publisher | English | PDF

This book consists of lectures that I have given, in Darmstadt since 1974, under various titles, for beginners or students of the third semester. I have tried to concentrate on those themes concerning numbers, which seem to me to be the most important on essential and historical grounds, and which in my opinion ought to belong to any wide-ranging, general education of every mathematics student. The content of that, so it occurred to me, should be to use the study of the number systems to reveal Mathematics as a visible unity, an aspect that is just what is lost from the vision of third-semester students. In order to open up the subject of interest from all sides, tools of knowledge are used from Analysis, Algebra, Geometry and Topology. Therefore also I have preferred geometrical approaches and renounced generality, if thereby the underlying ideas of a proof became more intuitive (e.g. in Liouville's Theorem on transcendental numbers).


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