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.
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Norton
1997
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | 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. |
| Physical Description: | XXIII, 1093 S. Ill., graph. Darst., Kt. |
| ISBN: | 039304002X |
Staff View
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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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| discipline | Mathematik Philosophie |
| edition | 1. ed. |
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| id | DE-604.BV011755251 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:15:15Z |
| institution | BVB |
| isbn | 039304002X |
| language | English |
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| physical | XXIII, 1093 S. Ill., graph. Darst., Kt. |
| publishDate | 1997 |
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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 |
| subject_GND | (DE-588)4020517-4 (DE-588)4037944-9 |
| 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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