Patterns of Change (Record no. 38625)

MARC details
000 -LEADER
fixed length control field 04290n a2200397#a 4500
001 - CONTROL NUMBER
control field 5000274
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20221213140641.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr||||||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 100301s2008 sz | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783764388409
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-3-7643-8840-9
Source of number or code doi
035 ## - SYSTEM CONTROL NUMBER
System control number 978-3-7643-8840-9
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBX
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT015000
Source bisacsh
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 510.9
090 ## - IMPA CODE FOR CLASSIFICATION SHELVES
IMPA CODE FOR CLASSIFICATION SHELVES Matemáticas Gerais-(inclusive alguns textos elementares sobre assuntos específicos)
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Kvasz, Ladislav
9 (RLIN) 9193
245 10 - TITLE STATEMENT
Title Patterns of Change
Medium [electronic resource]:
Remainder of title Linguistic Innovations in the Development of Classical Mathematics/
Statement of responsibility, etc. by Ladislav Kvasz.
260 ## - PUBLICATION, DISTRIBUTION, ETC.
Place of publication, distribution, etc. Basel:
Name of publisher, distributor, etc. Birkhäuser Basel,
Date of publication, distribution, etc. 2008.
300 ## - PHYSICAL DESCRIPTION
Other physical details digital.
490 0# - SERIES STATEMENT
Series statement Science Networks. Historical Studies;
Volume/sequential designation 36
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Preface -- Introduction -- Re-codings as the first pattern of change in mathematics -- Historical description of re-codings -- Philosophical reflections on re-codings -- Relativizations as the second pattern of change in mathematics -- A Historical description of relativizations in synthetic geometry -- Historical description of relativizations in algebra -- Philosophical reflections on relativizations -- Re-formulations as a third pattern of change in mathematics -- Re-formulations and concept-formation -- Re-formulations and problem-solving -- Re-formulations and theory-building -- Mathematics and change -- The question of revolutions in mathematics (Kuhn) -- The question of mathematical research programs (Lakatos) -- The question of stages of cognitive development (Piaget) -- Notes -- Bibliography .
520 ## - SUMMARY, ETC.
Summary, etc. This book offers a reconstruction of linguistic innovations in the history of mathematics; innovations which changed the ways in which mathematics was done, understood and philosophically interpreted. It argues that there are at least three ways in which the language of mathematics has been changed throughout its history, thus determining the lines of development that mathematics has followed. One of these patterns of change, called a re-coding, generates two developmental lines. The first of them connecting arithmetic, algebra, differential and integral calculus and predicate calculus led to a gradual increase of the power of our calculating tools, turning difficult problems of the past into easy exercises. The second developmental line connecting synthetic geometry, analytic geometry, fractal geometry, and set theory led to a sophistication of the ways we construct geometrical objects, altering our perception of form and increasing our sensitivity to complex visual patterns. Another important pattern of change, called relativization, is illustrated by the development of synthetic geometry, connecting Euclid’s geometry, projective geometry, non-Euclidean geometry, and Klein’s Erlanger Programm up to Hilbert’s Grundlagen der Geometrie. In this development the notions of space and geometric object underwent deep and radical changes culminating in the liberation of objects from the supremacy of space and so bringing to existence geometric objects which space would never tolerate. The book offers tools of analysis by means of which scholars and students of the history and philosophy of mathematics can attain better understanding of the various changes, which the subject of their study underwent in the course of history. The book brings also important insights for mathematics education connecting growth of language with the development of mathematical thought .
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Mathematics.
9 (RLIN) 43458
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Mathematics
General subdivision History.
9 (RLIN) 26817
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Humanities
9 (RLIN) 9194
697 ## - LOCAL SUBJECT
Local Subject Matemáticas Gerais-
Description subdivision (inclusive alguns textos elementares sobre assuntos específicos)
Linkage 23752
710 1# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service).
9 (RLIN) 8857
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9783764388393
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Science networks historical studies
Volume/sequential designation 36
9 (RLIN) 34859
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-3-7643-8840-9">http://dx.doi.org/10.1007/978-3-7643-8840-9</a>
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Instituto de Matemática Pura e Aplicada
Koha item type E-Book

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