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Visualization, Explanation and Reasoning Styles in Mathematics

Paolo Mancosu ; Klaus Frovin Jørgensen ; Stig Andur Pedersen (eds.)

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-1-4020-3334-6

ISBN electrónico

978-1-4020-3335-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer 2005

Cobertura temática

matematica

Matemáticas

Tabla de contenidos

doi: 10.1007/1-4020-3335-4_1

Introduction

P. Mancosu; K.F. Jørgensen; S.A. Pedersen

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Pp. 1-9

doi: 10.1007/1-4020-3335-4_2

Visualization in Logic and Mathematics

Paolo Mancosu

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 1 - Mathematical Reasoning and Visualization | Pp. 13-30

doi: 10.1007/1-4020-3335-4_3

From Symmetry Perception to Basic Geometry

M. Giaquinto

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 1 - Mathematical Reasoning and Visualization | Pp. 31-55

doi: 10.1007/1-4020-3335-4_4

Naturalism, Pictures, and Platonic Intuitions

James Robert Brown

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 1 - Mathematical Reasoning and Visualization | Pp. 57-73

doi: 10.1007/1-4020-3335-4_5

Mathematical Activity

M. Giaquinto

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 1 - Mathematical Reasoning and Visualization | Pp. 75-87

doi: 10.1007/1-4020-3335-4_6

Tertium Non Datur: On Reasoning Styles in Early Mathematics

Jens Høyrup

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 2 - Mathematical Explanation and Proof Styles | Pp. 91-121

doi: 10.1007/1-4020-3335-4_7

The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Prescription of Computation and the Operation as Argumento

Karine Chemla

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 2 - Mathematical Explanation and Proof Styles | Pp. 123-145

doi: 10.1007/1-4020-3335-4_8

Proof Style and Understanding in Mathematics I: Visualization, Unification and Axiom Choice

Jamie Tappenden

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 2 - Mathematical Explanation and Proof Styles | Pp. 147-214

doi: 10.1007/1-4020-3335-4_9

The Varieties of Mathematical Explanation

J. Hafner; P. Mancosu

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 2 - Mathematical Explanation and Proof Styles | Pp. 215-250

doi: 10.1007/1-4020-3335-4_10

The Aesthetics of Mathematics: A Study

Reviel Netz

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

Part 2 - Mathematical Explanation and Proof Styles | Pp. 251-293