Verfügbarkeit: Mathematics :: THWS Bibkatalog

Mathematics: from the birth of numbers

An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Gullberg, Jan (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York [u.a.] Norton 1997
Ausgabe:	1. ed.
Schlagworte:	Calcul infinitésimal Géométrie analytique Histoire nombre Mathématiques Mathématiques - Histoire Wiskunde Mathematik Mathematics Geschichte
Online-Zugang:	Inhaltsverzeichnis
Zusammenfassung:	An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.
Beschreibung:	XXIII, 1093 S. Ill., graph. Darst., Kt.
ISBN:	039304002X

Internformat

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Datensatz im Suchindex

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adam_text	CONTENTS PAGE CONTENTS IN BRIEF VI PREFACE VII CONTENTS IX FOREWORD: MATHEMATICS IN OUR CULTURE BY PETER HILTON XVII INFORMATION FOR THE READER XXIII CHAPTER 1 NUMBERS AND LANGUAGE 1 1.0 THE ORIGINS OF RECKONING 3 1.1 NUMBERS AND NUMERALS 5 1.2 NUMBER NAMES 7 1.3 ETYMOLOGY OF ENGLISH NUMBER NAMES 26 1.4 NUMBERS VS. INFINITY 29 2 SYSTEMS OF NUMERATION 31 2.0 FORMS OF NOTATION 32 2.1 ADDITIVE NOTATION 34 2.2 MULTIPLICATIVE NOTATION 44 2.3 POSITIONAL NOTATION 46 2.4 DECIMAL POSITION SYSTEM 48 2.5 SEXAGESIMAL NUMERATION 56 2.6 VIGESIMAL NUMERATION 58 2.7 DUODECIMAL NUMERATION 61 2.8 BINARY, OCTAL, HEXADECIMAL 62 2.9 SPECIAL FORMS OF NOTATION 66 3 TYPES OF NUMBERS 69 3.0 AN EXPANDING UNIVERSE OF NUMBERS 70 3.1 RATIONAL NUMBERS 72 3.2 PRIME NUMBERS 77 3.3 PERFECT AND AMICABLE NUMBERS 82 3.4 IRRATIONAL NUMBERS 84 3.5 IMAGINARY AND COMPLEX NUMBERS 87 3.6 THE QUEST FOR PI 89 4 CORNERSTONES OF MATHEMATICS 97 4.0 BEGINNINGS 98 4.1 SYMBOLS GALORE 101 4.2 FUNDAMENTAL OPERATIONS 113 4.3 LAWS OF ARITHMETIC AND ALGEBRA 132 4.4 POWERS AND ROOTS 134 4.5 LOGARITHMS 150 4.6 MATHEMATICAL PROOF 157 4.7 RELIABILITY OF DIGITS AND CALCULATIONS 161 4.8 SIMPLE CALCULATING DEVICES 168 5 COMBINATORICS 183 5.0 HISTORICAL NOTES 184 5.1 MULTIPLICATION PRINCIPLE 186 5.2 PERMUTATIONS 188 5.3 COMBINATIONS 196 5.4 SAMPLES WITH REPLACEMENT 199 5.5 GRAPH THEORY 201 5.6 MAGIC SQUARES AND THEIR KIN 205 6 SYMBOLIC LOGIC 215 6.0 HISTORICAL NOTES 216 6.1 PITFALLS 219 6.2 PROPOSITIONS 220 6.3 TAUTOLOGIES 225 6.4 SYLLOGISMS AND PROOFS 227 6.5 LOGIC CIRCUITS 229 7 SET THEORY 231 7.0 INTRODUCTION 232 7.1 SETS AND THEIR CONTENTS 233 7.2 VENN DIAGRAMS 242 7.3 ALGEBRA OF SETS 249 7.4 BOOLEAN ALGEBRA 252 7.5 TRANSFINITE NUMBERS 257 8 INTRODUCTION TO SEQUENCES AND SERIES 263 8.1 TERMINOLOGY 264 8.2 FINITE SEQUENCES AND SERIES 266 8.3 INFINITE SERIES 270 8.4 THE TOWER OF HANOI 285 8.5 THE FIBONACCI AND RELATED SEQUENCES 286 8.6 FIGURATE NUMBERS 289 9 THEORY OF EQUATIONS 295 9.01 HISTORY 297 9.02 GROUNDWORK 302 9.1 LINEAR EQUATIONS 307 9.2 EQUATIONS WITH ABSOLUTE VALUES 308 9.3 QUADRATIC EQUATIONS 309 9.4 INEQUALITIES 312 9.5 ROOT, EXPONENTIAL, AND LOGARITHMIC EQUATIONS 313 9.6 CUBIC EQUATIONS 316 9.7 QUARTIC EQUATIONS 320 9.8 SYSTEMS OF EQUATIONS 325 9.9 DIOPHANTINE EQUATIONS 330 10 INTRODUCTION TO FUNCTIONS 335 10.0 HISTORICAL NOTES 336 10.1 GROUNDWORK 336 10.2 ELEMENTARY FUNCTIONS 348 10.3 CONTINUITY AND LIMITS 355 11 OVERTURE TO THE GEOMETRIES 363 11.0 HISTORY 364 11.1 GEOMETRIC ABSTRACTION 370 11.2 PERSPECTIVE AND PROJECTION 372 11.3 FORM AND SHAPE 376 11.4 SURVEY OF GEOMETRIES 377 11.5 TOPOLOGY 378 11.6 EUCLIDEAN AND NON-EUCLIDEAN GEOMETRIES 381 12 ELEMENTARY GEOMETRY 385 12.0 WHAT DO WE MEAN BY ELEMENTARY GEOMETRY ? 386 12.1 GEOMETRIC ELEMENTS AND FIGURES 386 12.2 UNITS OF MEASUREMENT 409 12.3 EUCLIDEAN CONSTRUCTION 413 12.4 THEOREMS AND FORMULAS 425 12.41 PLANE GEOMETRY 426 12.42 SOLID GEOMETRY 446 13 TRIGONOMETRY 457 13.0 SCOPE AND HISTORY 458 13.1 FUNDAMENTAL TRIGONOMETRIC FUNCTIONS 470 13.2 INVERSE TRIGONOMETRIC FUNCTIONS 477 13.3 SOLVING TRIANGLES 478 13.4 GRAPHS, DOMAINS, RANGES 502 13.5 TRIGONOMETRIC IDENTITIES 507 13.6 TRIGONOMETRIC EQUATIONS 516 13.7 LIMITS 528 14 HYPERBOLIC FUNCTIONS 533 14.0 INTRODUCTION 534 14.1 FUNDAMENTAL HYPERBOLIC FUNCTIONS 536 14.2 INVERSE HYPERBOLIC FUNCTIONS 539 14.3 IDENTITIES 541 15 ANALYTIC GEOMETRY 547 15.0 SCOPE AND HISTORY 548 15.1 RECTILINEAR FIGURES 549 15.2 CONIC SECTIONS 559 15.3 SHIFTING ORTHOGONAL COORDINATES 572 15.4 POLAR COORDINATE SYSTEMS 576 15.5 PARAMETRIC EQUATIONS 586 16 VECTOR ANALYSIS 599 16.0 SCOPE AND HISTORY 600 16.1 BASIC VECTOR ALGEBRA 602 16.2 SCALAR AND VECTOR COMPONENTS 607 16.3 MULTIPLICATION OF VECTORS 614 17 FRACTALS 625 17.0 WHAT ARE FRACTALS? 626 17.1 THE SNOWFLAKE CURVE 627 17.2 ANTI-SNOWFLAKE AND ANTI-SQUARE CURVES 629 17.3 THE CANTOR SET 630 17.4 SIERPINSKI TRIANGLE, CARPET, AND SPONGE 631 17.5 THE MANDELBROT SET 633 17.6 THE DIMENSION CONCEPT 635 IS MATRICES AND DETERMINANTS 637 18.0 SCOPE AND HISTORY 638 18.1 MATRICES - PRESENTATION 640 18.2 MATRICES - RULES OF OPERATION 642 18.3 DETERMINANTS 646 18.4 SPECIAL MATRICES 654 18.5 COFACTORS AND THE INVERSE OF A MATRIX 659 18.6 SOLVING SYSTEMS OF LINEAR EQUATIONS 661 19 EMBARKING ON CALCULUS 671 19.1 WHAT IS CALCULUS? 673 19.2 HISTORY 674 20 INTRODUCTION TO DIFFERENTIAL CALCULUS 683 20.1 DERIVATIVES AND DIFFERENTIALS 685 20.2 DIFFERENTIATING ALGEBRAIC FUNCTIONS 689 20.3 DIFFERENTIATING TRANSCENDENTAL FUNCTIONS 695 20.4 SPECIAL TECHNIQUES OF DIFFERENTIATION 705 20.5 PARTIAL DIFFERENTIATION 710 20.6 MEAN-VALUE THEOREMS 716 21 INTRODUCTION TO INTEGRAL CALCULUS 721 21.1 BASIC CONCEPTS 722 21.2 METHODS OF INTEGRATION 723 21.3 THE DEFINITE INTEGRAL 747 21.4 MULTIPLE INTEGRALS 753 21.5 IMPROPER OR UNRESTRICTED INTEGRALS 756 22 POWER SERIES 765 22.1 CONVERGENCE 766 22.2 TAYLOR S AND MACLAURIN S SERIES 767 22.3 EXPANDING TRANSCENDENTAL FUNCTIONS 771 22.4 BINOMIAL EXPANSION 775 22.5 THE RIEMANN ZETA FUNCTION AND HYPOTHESIS 778 23 INDETERMINATE LIMITS 779 23.1 A RETROSPECT 781 23.2 L HOSPITAL S RULE 782 24 COMPLEX NUMBERS REVISITED 24.1 INTRODUCTION 788 24.2 SUMS AND DIFFERENCES 789 24.3 PRODUCTS AND QUOTIENTS 790 24.4 POWERS 791 24.5 ROOTS 793 24.6 LOGARITHMS 794 25 EXTREMA AND CRITICAL POINTS 25.1 ONE INDEPENDENT VARIABLE 798 25.2 MORE THAN ONE INDEPENDENT VARIABLE 815 25.3 FUNCTIONS WITH RESTRICTIONS 822 26 ARC LENGTH 26.1 BASIC PRINCIPLE 829 26.2 THE CATENARY 831 26.3 ARC LENGTH IN PARAMETRIC FORM 832 26.4 ARC LENGTH IN A POLAR COORDINATE SYSTEM 835 27 CENTROIDS 27.1 MASS POINT SYSTEMS 838 27.2 PLANE FIGURES AND LAMINAS 842 27.3 CENTER OF MASS OF SOLIDS OF REVOLUTION 847 28 AREA 28.1 PLANE SURFACES 852 28.2 SURFACE OF REVOLUTION 860 28.3 WORK 867 29 VOLUME 29.0 INTRODUCTION 873 29.1 DISK METHOD 873 29.2 SHELL METHOD 877 29.3 SOLIDS GENERATED BY AREA BOUNDED BY TWO CURVES 880 29.4 TRANSLATION OF AXES 882 29.5 GULDIN S SECOND RULE 884 29.6 SOLIDS WITH KNOWN CROSS-SECTION AREAS 885 29.7 TRANSFORMING DOUBLE INTEGRALS FROM ORTHOGONAL TO POL COORDINATES 887 30 MOTION 891 30.1 LAWS OF KEPLER AND NEWTON 893 30.2 DIFFERENTIATING DISTANCE AND VELOCITY 896 30.3 INTEGRATING ACCELERATION AND VELOCITY 900 30.4 VELOCITY VECTORS AND ACCELERATION VECTORS 901 30.5 SPACE-TIME; MASS AND ENERGY 904 31 HARMONIC ANALYSIS 907 31.0 HISTORICAL NOTES 909 31.1 FOURIER SERIES 910 31.2 EXPANDING DISCONTINUOUS FUNCTIONS 915 31.3 EXPANDING EVEN OR ODD FUNCTIONS 918 32 METHODS OF APPROXIMATION 923 32.1 NEGLIGIBLE TERMS 925 32.2 INTERPOLATION 926 32.3 GRAPHIC AND ITERATIVE METHODS 931 32.4 NUMERICAL INTEGRATION 947 33 PROBABILITY THEORY 961 33.0 INTRODUCTION 962 33.1 HISTORY 963 33.2 THE BASICS 966 33.3 THE PROBABILITY DENSITY FUNCTION 971 33.4 CENTRAL TENDENCY 974 33.5 DISPERSION 976 33.6 NORMAL DISTRIBUTION 979 34 DIFFERENTIAL EQUATIONS 989 34.1 FUNDAMENTAL CONCEPTS 991 34.2 FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS 994 34.3 FORMULATING DIFFERENTIAL EQUATIONS 1000 34.4 SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS 1015 BIBLIOGRAPHY 1041 WORKS CITED 1048 NAME INDEX 1053 SUBJECT INDEX 1060 SYMBOLS IN COMMON USE 1092
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spelling	Gullberg, Jan Verfasser aut Mathematics from the birth of numbers Jan Gullberg 1. ed. New York [u.a.] Norton 1997 XXIII, 1093 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions. Calcul infinitésimal Géométrie analytique Histoire nombre Mathématiques Mathématiques - Histoire Mathématiques - Histoire ram Mathématiques ram Wiskunde gtt Mathematik Mathematics Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Geschichte (DE-588)4020517-4 s DE-604 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007932774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gullberg, Jan Mathematics from the birth of numbers Calcul infinitésimal Géométrie analytique Histoire nombre Mathématiques Mathématiques - Histoire Mathématiques - Histoire ram Mathématiques ram Wiskunde gtt Mathematik Mathematics Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd
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title	Mathematics from the birth of numbers
title_auth	Mathematics from the birth of numbers
title_exact_search	Mathematics from the birth of numbers
title_full	Mathematics from the birth of numbers Jan Gullberg
title_fullStr	Mathematics from the birth of numbers Jan Gullberg
title_full_unstemmed	Mathematics from the birth of numbers Jan Gullberg
title_short	Mathematics
title_sort	mathematics from the birth of numbers
title_sub	from the birth of numbers
topic	Calcul infinitésimal Géométrie analytique Histoire nombre Mathématiques Mathématiques - Histoire Mathématiques - Histoire ram Mathématiques ram Wiskunde gtt Mathematik Mathematics Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Calcul infinitésimal Géométrie analytique Histoire nombre Mathématiques Mathématiques - Histoire Wiskunde Mathematik Mathematics Geschichte
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