A Mathematician Comes of Age

Steven G. Krantz

doi:10.5948/UPO9781614445111

A Mathematician Comes of Age discusses the maturation process for a mathematics student. It describes and analyzes how a student develops from a neophyte who can manipulate simple arithmetic problems to a sophisticated thinker who can understand abstract concepts, can think rigorously, and can analyze and manipulate proofs. Most importantly, mature mathematics students can create proofs and know when the proofs that they have created are correct. Mathematics is distinct from other disciplines in the nature of its intellectual development. The book lays out these differences and discusses their significance.

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A Mathematician Comes of Age

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Contents

Frontmatter
pp i-viii

Contents
pp ix-xii

Preface
pp xiii-xvi

Acknowledgements
pp xvii-xviii

1 - Introductory Thoughts
pp 1-26

2 - Math Concepts
pp 27-40

3 - Teaching Techniques
pp 41-62

4 - Social Issues
pp 63-76

5 - Cognitive Issues
pp 77-106

6 - What is a Mathematician?
pp 107-114

7 - Is Mathematical Maturity for Everyone?
pp 115-118

The Tree of Mathematical Maturity
pp 119-120

Etymology of the Word “Maturity”
pp 121-122

Bibliography
pp 123-128

Index
pp 129-136

About the Author
pp 137-137

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A Mathematician Comes of Age

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