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Mathematics: queen and servant of science

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Bibliographic Details
Main Author:	Bell, Eric Temple 1883-1960 (Author)
Format:	Book
Language:	English
Published:	Washington, DC Mathemat. Assoc. of America 1987
Edition:	Republ.
Series:	MAA spectrum
Subjects:	matematika mathematics
Online Access:	Inhaltsverzeichnis
Physical Description:	XXIV, 437 S. Ill., graph. Darst.
ISBN:	0883854473

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MARC


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adam_text	Contents To the Reader v List of Names xiii Chapter 1 POINTS OF VIEW / 1.1 The object of mathematics 1.4 The spirit of modern mathe 1.2 A golden age matics l.S Abel s advice Chapter 2 MATHEMATICAL TRUTH 17 2.1 Descriptions of mathematics \| 2.2 The postulational method Chapter 3 BREAKING BOUNDS 29 3.1 Common algebra 3.3 Sources of postulates 3.2 Changing the rules Chapter 4 THE SAME, YET NOT THE SAME 45 4.1 Realizations of common al continuous, complex, analy gebra sis, function 4.2 Rational, real, denumerable, 4.S The end of a road non denumerable, discrete, Chapter 5 THE ART OF ABSTRACTION 55 5.1 A change of interest 5.5 Lattices or structures 5.2 An uncommon algebra 5.6 Subrings, ideals 5.3 Rings 5.7 Subfields, extensions 5.4 Homorphism, isomorphism, 5.8 Skew fields, linear algebras automorphism Chapter 6 OAKS FROM ACORNS 94 6.1 Transformations 6.4 A suggestion to the United 6.2 A problem in geometry, Nations variables again 6.5 Invariance in nature 6.3 Matrices 6.6 Sylvester s prevision xiii xiv CONTENTS Chapter 7 PICTORIAL THINKING 121 7.1 Graphs 7.4 Three suggestions 7.2 What Descartes invented 7.5 Intuition into algebra 7.3 Unnecessary difficulties 7.6 Algebra into geometry Chapter 8 LANDMARKS OLD AND NEW 141 8.1 What is geometry? 8.6 Connectedness 8.3 Further progress 8.7 Knots 8.S Space of many dimensions 8.8 One kind of topology 8.4 Duality 8.9 Abstraction again 8.5 Non metric versus metric Chapter 9 GROUPS 1U 9.1 Multiplication tables 9.5 Interpretations 9.2 Isomorphism, homorphism 9.6 Infinite groups 9.3 Complexes, cosets, normal 9.7 The icosahedron subgroups 9.8 Galois theory 9.4 Substitution groups Chapter 10 A METRICAL UNIVERSE 188 10.1 From Pythagoras to Des 10.2 From Descartes to Rie cartes mann 10.3 From Riemann to Einstein Chapter 11 THE QUEEN OF MATHEMATICS 220 11.1 An unruly domain 11.5 Algebraic numbers 11.2 Fermat and Mersenne num 11.6 Transcendental numbers hers 11.7 Waring s conjecture 11.3 A little about primes 11.8 The Queen of queens 11.4 Diophantine analysis slaves Chapter 12 ABSTRACTION AND PREDICTION 252 12.1 From Maxwell to radar 12.3 One sort of explanation 12.2 Two methods Chapter IS FROM CYZICUS TO NEPTUNE 272 13.1 A royal road 13.4 Mathematical prophecy 13.2 Kepler s faith again 18.3 Calculation plus insight CONTENTS xv Chapter U TWO KINDS OF PICTURE 297 14.1 Continuity in science 14.5 Nature in the small 14.2 Discreteness in science 14.6 The scientist intervenes 14.3 Eternal flux 14.7 Integration 14.4 Ancient philosophers and 14.8 Boundary value problems modern pedants Chapter 15 THE CHIEF INSTRUMENT OF 320 APPLIED MATHEMATICS 15.1 Rates 15.5 Fluid flow 15.2 Higher derivatives 15.6 Integrals 15.3 Partial derivatives 15.7 The fundamental theorem 15.4 Differential equations of the calculus Chapter 16 FURTHER CALCULUSES 342 16.1 Greatest or least 16.5 The complex variable 16.2 Least action 16.6 Conformal mapping 16.3 The calculus of variations 16.7 Special functions 16.4 Hamilton s prediction 16.8 Generalizations Chapter 17 WAVES AND VIBRATIONS 357 17.1 Periodicity 17.3 Fourier s theorem 17.2 The alphabet of periodicity 17.4 From particles to fields Chapter 18 CHOICE AND CHANCE 374. 18.1 Probability 18.3 Statistics and mechanics 18.2 Pies, flies, and concrete 18.4 Is probability probable? Chapter 19 STORMING THE HEAVENS 393 19.1 Toward the infinite 19.3 Counting the infinite 19.2 How the infinite entered 19.4 What is a number? mathematics 19.5 Dedekind s cut Chapter 20 BEDROCK 407 20.1 Mathematical existence 20.3 From Hilbert to GSdel 20.2 A great illusion 20.4 To our successors Index U7
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author	Bell, Eric Temple 1883-1960
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id	DE-604.BV003555182
illustrated	Illustrated
indexdate	2024-07-09T16:01:49Z
institution	BVB
isbn	0883854473
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-002260773
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owner	DE-384 DE-210
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physical	XXIV, 437 S. Ill., graph. Darst.
publishDate	1987
publishDateSearch	1987
publishDateSort	1987
publisher	Mathemat. Assoc. of America
record_format	marc
series2	MAA spectrum
spelling	Bell, Eric Temple 1883-1960 Verfasser (DE-588)119235218 aut Mathematics queen and servant of science by E. T. Bell Republ. Washington, DC Mathemat. Assoc. of America 1987 XXIV, 437 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier MAA spectrum matematika mathematics HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002260773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bell, Eric Temple 1883-1960 Mathematics queen and servant of science matematika mathematics
title	Mathematics queen and servant of science
title_auth	Mathematics queen and servant of science
title_exact_search	Mathematics queen and servant of science
title_full	Mathematics queen and servant of science by E. T. Bell
title_fullStr	Mathematics queen and servant of science by E. T. Bell
title_full_unstemmed	Mathematics queen and servant of science by E. T. Bell
title_short	Mathematics
title_sort	mathematics queen and servant of science
title_sub	queen and servant of science
topic	matematika mathematics
topic_facet	matematika mathematics
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002260773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bellerictemple mathematicsqueenandservantofscience

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