Mathematics for the nonmathematician:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Garden City, New York
Dover Publications
1985
|
| Ausgabe: | Unabridged republication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Nachdruck der Ausgabe Reading, Massachusetts : Addison-Wesley, 1967, die unter folgendem Titel erschienen ist: Mathematics for liberal arts |
| Beschreibung: | xiii, 641 Seiten Illustrationen, Diagramme |
| ISBN: | 9780486248233 0486248232 |
Internformat
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| 240 | 1 | 0 | |a Mathematics for liberal arts |
| 245 | 1 | 0 | |a Mathematics for the nonmathematician |c Morris Kline |
| 250 | |a Unabridged republication | ||
| 264 | 1 | |a Garden City, New York |b Dover Publications |c 1985 | |
| 264 | 4 | |c © 1967 | |
| 300 | |a xiii, 641 Seiten |b Illustrationen, Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1804145183493718016 |
|---|---|
| adam_text | MATHEMATICS FOR THE
NONMATHEMATICIAN
MORRIS KLINE
Professor of Mathematics, Emeritus
Courant Institute of Mathematical Sciences
New York University
DOVER PUBLICATIONS, INC
NEW YORK
CONTENTS
1 Why Mathematics?
2 A Historical Orientation
2-1 Introduction 11
2-2 Mathematics in early civilizations 11
2-3 The classical Greek period 14
2-4 The Alexandrian Greek period 17
2-5 The Hindus and Arabs 19
2-6 Early and medieval Europe 20
2-7 The Renaissance 20
2-8 Developments from 1550 to 1800 22
2-9 Developments from 1800 to the present 24
2- 10 The human aspect of mathematics 27
3 Logic and Mathematics
3- 1 Introduction 30
3-2 The concepts of mathematics 30
3-3 Idealization 38
3-4 Methods of reasoning 39
3-5 Mathematical proof 45
3-6 Axioms and definitions 50
3- 7 The creation of mathematics 51
4 Number: the Fundamental Concept
4- 1 Introduction 58
4-2 Whole numbers and fractions 58
4-3 Irrational numbers 65
4-4 Negative numbers 72
4- 5 The axioms concerning numbers 75
* 4-6 Applications of the number system 82
5 Algebra, the Higher Arithmetic
5- 1 Introduction 94
5-2 The language of algebra 94
5-3 Exponents 97
5-4 Algebraic transformations 102
5-5 Equations involving unknowns 106
5-6 The general second-degree equation 112
♦ 5-7 The history of equations of higher degree 119
IX
X
CONTENTS
6 The Nature and Uses of Euclidean Geometry
6-1 The beginnings of geometry 123
6-2 The content of Euclidean geometry 125
6-3 Some mundane uses of Euclidean geometry 131
* 6-4 Euclidean geometry and the study of light 138
6- 5 Conic sections 142
* 6-6 Conic sections and light 144
*6-7 The cultural influence of Euclidean geometry 149
7 Charting the Earth and the Heavens
7- 1 The Alexandrian world 153
7-2 Basic concepts of trigonometry 158
7- 3 Some mundane uses of trigonometric ratios 163
*7-4 Charting the earth 165
*7-5 Charting the heavens _ 171
* 7-6 Further progress in the study of light 176
8 The Mathematical Order of Nature
8- 1 The Greek concept of nature 187
8-2 Pre-Greek and Greek views of nature 188
8-3 Greek astronomical theories 190
8-4 The evidence for the mathematical design of nature 192
8- 5 The destruction of the Greek world 194
* 9 The Awakening of Europe
9- 1 The medieval civilization of Europe 197
9-2 Mathematics in the medieval period 199
9-3 Revolutionary influences in Europe 200
9-4 New doctrines of the Renaissance 202
9- 5 The religious motivation in the study of nature 206
* 10 Mathematics and Painting in the Renaissance
10- 1 Introduction 209
10-2 Gropings toward a scientific system of perspective 210
10-3 Realism leads to mathematics 213
10-4 The basic idea of mathematical perspective 215
10-5 Some mathematical theorems on perspective drawing 219
10-6 Renaissance paintings employing mathematical perspective 223
10- 7 Other values of mathematical perspective 229
11 Projective Geometry
11- 1 The problem suggested by projection and section 232
11-2 The work of Desargues 234
11-3 The work of Pascal 239
11^4 The principle of duality 242
11- 5 The relationship between projective and Euclidean geometries 247
12 Coordinate Geometry
12- 1 Descartes and Fermat 250
12-2 The need for new methods in geometry 253
12-3 The concepts of equation and curve 256
CONTENTS
XI
12-4 The parabola 264
12-5 Finding a curve from its equation 269
12-6 The ellipse 271
*12-7 The equations of surfaces 273
*12-8 Four-dimensional geometry 275
12- 9 Summary 277
13 The Simplest Formulas in Action
13- 1 Mastery of nature 280
13-2 The search for scientific method 281
13-3 The scientific method of Galileo 284
13-4 Functions and formulas 290
13-5 The formulas describing the motion of dropped objects 293
13-6 The formulas describing the motion of objects thrown downward 299
13- 7 Formulas for the motion of bodies projected upward 300
14 Parametric Equations and Curvilinear Motion
14- 1 Introduction 307
14-2 The concept of parametric equations 308
14-3 The motion of a projectile dropped from an airplane 310
14-4 The motion of projectiles launched by cannons 313
* 14-5 The motion of projectiles fired at an arbitrary angle 318
14- 6 Summary 323
15 The Application of Formulas to Gravitation
15- 1 The revolution in astronomy 326
15-2 The objections to a heliocentric theory 330
15-3 The arguments for the heliocentric theory 331
15-4 The problem of relating earthly and heavenly motions 334
15-5 A sketch of Newton’s life 336
15-6 Newton’s key idea 337
15-7 Mass and weight 340
15-8 The law of gravitation 341
15-9 Further discussion of mass and weight 343
15- 10 Some deductions from the law of gravitation 346
*15-11 The rotation of the earth 352
*15-12 Gravitation and the Keplerian laws • 355
* 15-13 Implications of the theory of gravitation 359
* 16 The Differential Calculus
16- 1 Introduction 365
16-2 The problems leading to the calculus 365
16-3 The concept of instantaneous rate of change 367
16-4 The concept of instantaneous speed 368
16-5 The method of increments 371
16-6 The method of increments applied to general functions 374
16-7 The geometrical meaning of the derivative 379
16- 8 The maximum and minimum values of functions 382
* 17 The Integral Calculus
17- 1 Differential and integral calculus compared 388
17-2 Finding the formula from the given rate of change 389
Xll CONTENTS
17-3 Applications to problems of motion 390
17-4 Areas obtained by integration 394
17-5 The calculation of work 397
17-6 The calculation of escape velocity 401
17-7 The integral as the limit of a sum 404
17-8 Some relevant history of the limit concept 409
17- 9 The Age of Reason 412
18 Trigonometric Functions and Oscillatory Motion
18- 1 Introduction 416
18-2 The motion of a bob on a spring 417
18-3 The sinusoidal functions 418
18-4 Acceleration in sinusoidal motion 427
18-5 The mathematical analysis of the motion of the bob 429
18- 6 Summary 434
* 19 The Trigonometric Analysis of Musical Sounds
19- 1 Introduction 436
19-2 The nature of simple sounds 438
19-3 The method of addition of ordinates 442
19-4 The analysis of complex sounds 445
19- 5 Subjective properties of musical sounds 448
20 Non-Euclidean Geometries and Their Significance
20- 1 Introduction 452
20-2 The historical background 452
20-3 The mathematical content of Gauss’s non-Euclidean geometry 458
20-4 Riemann’s non-Euclidean geometry 460
20-5 The applicability of non-Euclidean geometry 462
20-6 The applicability of non-Euclidean geometry under a new interpretation
of line 464
20-7 Non-Euclidean geometry and the nature of mathematics 471
20- 8 The implications of non-Euclidean geometry for other branches of our
culture 474
21 Arithmetics and Their Algebras
21- 1 Introduction 478
21-2 The applicability of the real number system 478
21-3 Baseball arithmetic 481
21-4 Modular arithmetics and their algebras 484
21-5 The algebra of sets 491
21- 6 Mathematics and models 497
* 22 The Statistical Approach to the Social and Biological Sciences
22- 1 Introduction 499
22-2 A brief historical review 500
22-3 Averages 502
22-4 Dispersion 503
22-5 The graph and the normal curve 505
22-6 Fitting a formula to data 511
22-7 Correlation 516
22-8 Cautions concerning the uses of statistics 518
CONTENTS XUl
The Theory of Probability
23-1 Introduction 522
23-2 Probability for equally likely outcomes 524
23-3 Probability as relative frequency 529
23-4 Probability in continuous variation 530
23-5 Binomial distributions 533
23- 6 The problems of sampling 538
The Nature and Values of Mathematics
24- 1 Introduction 541
24-2 The structure of mathematics 541
24-3 The values of mathematics for the study of nature 546
24-4 The aesthetic and intellectual values 550
24-5 Mathematics and rationalism 552
24-6 The limitations of mathematics 553
Table of Trigonometric Ratios 557
Answers to Selected and Review Exercises 559
Additional Answers and Solutions 569
|
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| author | Kline, Morris 1908-1992 |
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| id | DE-604.BV026587562 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:15:24Z |
| institution | BVB |
| isbn | 9780486248233 0486248232 |
| language | English |
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| physical | xiii, 641 Seiten Illustrationen, Diagramme |
| publishDate | 1985 |
| publishDateSearch | 1985 |
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| publisher | Dover Publications |
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| spelling | Kline, Morris 1908-1992 Verfasser (DE-588)131716271 aut Mathematics for liberal arts Mathematics for the nonmathematician Morris Kline Unabridged republication Garden City, New York Dover Publications 1985 © 1967 xiii, 641 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Nachdruck der Ausgabe Reading, Massachusetts : Addison-Wesley, 1967, die unter folgendem Titel erschienen ist: Mathematics for liberal arts Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-0-486-31613-0 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022145598&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Mathematics for the nonmathematician |
| title_alt | Mathematics for liberal arts |
| title_auth | Mathematics for the nonmathematician |
| title_exact_search | Mathematics for the nonmathematician |
| title_full | Mathematics for the nonmathematician Morris Kline |
| title_fullStr | Mathematics for the nonmathematician Morris Kline |
| title_full_unstemmed | Mathematics for the nonmathematician Morris Kline |
| title_short | Mathematics for the nonmathematician |
| title_sort | mathematics for the nonmathematician |
| topic | Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik |
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