Synthese Library

Visualization, Explanation and Reasoning Styles in Mathematics

Editors: Mancosu, Paolo, Jørgensen, Klaus Frovin, Pedersen, S.A. (Eds.)

Free Preview

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-1-4020-3335-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-1-4020-3334-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-90-481-6837-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc. have become the subject of intense interest. The historians and philosophers in this book agree that there is more to understanding mathematics than a study of its logical structure. How are mathematical objects and concepts generated? How does the process tie up with justification? What role do visual images and diagrams play in mathematical activity? What are the different epistemic virtues (explanatoriness, understanding, visualizability, etc.) which are pursued and cherished by mathematicians in their work? The reader will find here systematic philosophical analyses as well as a wealth of philosophically informed case studies ranging from Babylonian, Greek, and Chinese mathematics to nineteenth century real and complex analysis.

Reviews

From the reviews:

"As its title suggests, the book deals with themes that are of great interest to mathematics educators. … this book is a collection of excellent papers by distinguished authors. It also shows a high standard of book production, in its layout, paper quality, draftsmanship and binding. … this book deserves the attention of all those with an interest in mathematics education." (G. Hanna, Educational Studies in Mathematics, Vol. 64, 2007)

"This fascinating collection of essays is a must-have for those who are interested in the history and philosophy of mathematics … . this is a book that libraries will want to have, particularly if they strive to have good collections on the history and philosophy of mathematics." (Fernando Q. Gouvêa, MathDL, August, 2005)


Table of contents (10 chapters)

Table of contents (10 chapters)
  • Introduction

    Mancosu, P. (et al.)

    Pages 1-9

  • Visualization in Logic and Mathematics

    Mancosu, Paolo

    Pages 13-30

  • From Symmetry Perception to Basic Geometry

    Giaquinto, M.

    Pages 31-55

  • Naturalism, Pictures, and Platonic Intuitions

    Brown, James Robert

    Pages 57-73

  • Mathematical Activity

    Giaquinto, M.

    Pages 75-87

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-1-4020-3335-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-1-4020-3334-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-90-481-6837-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Visualization, Explanation and Reasoning Styles in Mathematics
Editors
  • Paolo Mancosu
  • Klaus Frovin Jørgensen
  • S.A. Pedersen
Series Title
Synthese Library
Series Volume
327
Copyright
2005
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-3335-3
DOI
10.1007/1-4020-3335-4
Hardcover ISBN
978-1-4020-3334-6
Softcover ISBN
978-90-481-6837-8
Edition Number
1
Number of Pages
X, 300
Topics