eBook Beyond Geometry, 1st Edition

  • Published By:
  • ISBN-10: 1438136234
  • ISBN-13: 9781438136233
  • DDC: 516
  • Grade Level Range: 9th Grade - College Senior
  • 272 Pages | eBook
  • Original Copyright 2011 | Published/Released February 2012
  • This publication's content originally published in print form: 2011
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About

Overview

BEYOND GEOMETRY describes how set-theoretic topology developed and why it now occupies a central place in mathematics. Describing axiomatic method as well as providing a definition of what a geometric property is, this new resource examines how early analysts incorporated geometric thinking into their development of the calculus. It also looks at the various mathematicians who struggled to develop a new conceptual framework for mathematics and examines one of the sub-disciplines of set-theoretic topology called dimension theory.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Dedication.
Contents.
Preface.
Acknowledgments.
Introduction.
1: Topology: a Prehistory.
2: A Failure of Intuition.
3: A New Mathematical Landscape.
4: The First Topological Spaces.
5: The Standard Axioms and Three Topological Properties.
6: Schools of Topology.
7: Dimension Theory.
8: Topology and the Foundations of Modern Mathematics.
Afterword.
Chronology.
Glossary.
Further Resources.
Index.