Patterns of change: linguistic innovations in the development of classical mathematics
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2008
|
| Schriftenreihe: | Science networks
36 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016604458&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVIII, 261 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783764388393 |
Internformat
MARC
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|---|---|---|---|
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| 245 | 1 | 0 | |a Patterns of change |b linguistic innovations in the development of classical mathematics |c Ladislav Kvasz |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XVIII, 261 S. |b Ill., graph. Darst. |c 24 cm | ||
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Datensatz im Suchindex
| _version_ | 1819250167250944000 |
|---|---|
| adam_text | Contents
Acknowledgements V
Preface
VII
Introduction
1
1
Re-coding as the First Pattern of Change
in Mathematics
11
1.1
Historical Description of Re-codings
........ 14
1.1.1
Elementary Arithmetic
............ 17
1.1.2
Synthetic Geometry
.............. 23
1.1.3
Algebra
.................... 29
1.1.4
Analytic Geometry
.............. 37
1.1.5
The Differential and Integral Calculus
. ... 47
1.1.6
Iterative Geometry
.............. 56
1.1.7
Predicate Calculus
.............. 67
1.1.8
Set Theory
.................. 76
XVI
Contents
1.2
Philosophical Reflections on Re-Codings
...... 85
1.2.1
Relation between Logical and Historical
Reconstructions of Mathematical Theories
. 89
1.2.2
Perception of Shape and Motion
....... 94
1.2.3
Epistemic
Tension and the Dynamics of the
Development of Mathematics
........ 98
1.2.4
Technology and the Coordination of
Activities
................... 99
1.2.5
The Pre-History of Mathematical Theories
. 102
2
Relativizations as the Second Pattern
of Change in Mathematics
107
2.1
Historical Description of Relativizations in
Synthetic Geometry
.................
Ill
2.1.1
The Perspectivist Form of Language of
Synthetic Geometry
.............. 114
2.1.2
The
Projective
Form of Language of
Synthetic Geometry
.............. 118
2.1.3
The Interpretative Form of Language of
Synthetic Geometry
.............. 124
2.1.4
The
Integrative Form
of Language of
Synthetic Geometry
.............. 133
2.1.5
The Constitutive Form of Language of
Synthetic Geometry
.............. 143
2.1.6
The Conceptual Form of Language of
Synthetic Geometry
.............. 154
2.1.7
An Overview of Relativizations in the
Development of Synthetic Geometry
..... 159
2.2
Historical Description of Relativizations in
Algebra
........................ 160
2.2.1
The Perspectivist Form of the Language of
Algebra
.................... 165
2.2.2
The
Projective
Form of the Language of
Algebra
.................... 167
2.2.3
The
Coordinative Form
of the Language of
Algebra
.................... 173
Contents
XVII
2.2.4
The Compositive Form of the Language of
Algebra
.................... 177
2.2.5
The Interpretative Form of the Language of
Algebra
.................... 180
2.2.6
The
Integrative Form
of the Language of
Algebra
.................... 184
2.2.7
The Constitutive Form of the Language of
Algebra
.................... 192
2.2.8
The Conceptual Form of the Language of
Algebra
.................... 197
2.2.9
An Overview of Relativizations in the
Development of Algebra
........... 198
2.3
Philosophical Reflections on Relativizations
.... 201
2.3.1
Comparison of the Development of Algebra
with the Development of Geometry
..... 202
2.3.2
Form of Language and the Development of
Mathematical Theories
............ 205
2.3.3
The Notion of the Form of Language and
Philosophy of Mathematics
.......... 210
2.3.4
The Changes of the Form of Language and
the Development of Subjectivity
....... 215
2.3.5
The Problem of Understanding Mathematical
Concepts
................... 220
2.3.6
A Gap of Two Centuries in the Curricula
. . 222
3
Re-Formulations as a Third Pattern
of Change in Mathematics
225
3.1
Re-Formulations and Concept-Formation
..... 228
3.2
Re-Formulations and Problem-Solving
...... 232
3.3
Re-Formulations and Theory-Building
....... 235
XVIII
Contents
4
Mathematics and Change
239
4.1
Revolutions in Mathematics
(Kuhn)........ 240
4.1.1
What Kind of Changes Should we Consider
Revolutionary?
................ 240
4.1.2
The Distinction between Revolutions and
Epistemological Ruptures
.......... 241
4.1.3
Possible Refinements of the Kuhnian Picture
243
4.2
Mathematical Research Programmes
(Lakatos)
. 245
4.2.1
The Lack of Connection between the Two
Major Parts of Proofs and Refutations
. . . . 246
4.2.2
Reduction of the Development of
Mathematics to Re-Formulations
....... 247
4.3
Stages of Cognitive Development
(Piaget)
..... 249
4.3.1
The Problem of the Omitted Stages
..... 249
4.3.2
The Relation of Ontogenesis and
Phylogenesis
................. 250
Bibliography
253
|
| any_adam_object | 1 |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.14 |
| dewey-search | 510.14 |
| dewey-sort | 3510.14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Book |
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| id | DE-604.BV023422038 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:16:00Z |
| institution | BVB |
| isbn | 9783764388393 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016604458 |
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| owner_facet | DE-210 DE-12 DE-355 DE-BY-UBR DE-11 DE-703 DE-20 |
| physical | XVIII, 261 S. Ill., graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Science networks |
| series2 | Science networks |
| spellingShingle | Kvasz, Ladislav Patterns of change linguistic innovations in the development of classical mathematics Science networks Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd Fachsprache (DE-588)4016216-3 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4016216-3 |
| title | Patterns of change linguistic innovations in the development of classical mathematics |
| title_auth | Patterns of change linguistic innovations in the development of classical mathematics |
| title_exact_search | Patterns of change linguistic innovations in the development of classical mathematics |
| title_full | Patterns of change linguistic innovations in the development of classical mathematics Ladislav Kvasz |
| title_fullStr | Patterns of change linguistic innovations in the development of classical mathematics Ladislav Kvasz |
| title_full_unstemmed | Patterns of change linguistic innovations in the development of classical mathematics Ladislav Kvasz |
| title_short | Patterns of change |
| title_sort | patterns of change linguistic innovations in the development of classical mathematics |
| title_sub | linguistic innovations in the development of classical mathematics |
| topic | Mathematik Mathematics Mathematik (DE-588)4037944-9 gnd Fachsprache (DE-588)4016216-3 gnd |
| topic_facet | Mathematik Mathematics Fachsprache |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016604458&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT kvaszladislav patternsofchangelinguisticinnovationsinthedevelopmentofclassicalmathematics |