Mathematics for liberal arts:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
1967
|
| Schriftenreihe: | Addison-Wesley series in introductory mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 577 S. Ill., graph. Darst. |
| ISBN: | 0201037718 |
Internformat
MARC
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| 100 | 1 | |a Kline, Morris |d 1908-1992 |e Verfasser |0 (DE-588)131716271 |4 aut | |
| 245 | 1 | 0 | |a Mathematics for liberal arts |c Morris Kline |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1967 | |
| 300 | |a XIII, 577 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley series in introductory mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804116906402119680 |
|---|---|
| adam_text | 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
11 ^ 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 3 59
* 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
Xii 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^ 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 xiil
* 23 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
24 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
Index 569
|
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| author | Kline, Morris 1908-1992 |
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| id | DE-604.BV002500049 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:45:57Z |
| institution | BVB |
| isbn | 0201037718 |
| language | English |
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| physical | XIII, 577 S. Ill., graph. Darst. |
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| publishDate | 1967 |
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| series2 | Addison-Wesley series in introductory mathematics |
| spelling | Kline, Morris 1908-1992 Verfasser (DE-588)131716271 aut Mathematics for liberal arts Morris Kline Reading, Mass. [u.a.] Addison-Wesley 1967 XIII, 577 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in introductory mathematics Mathematik Mathematics HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001610499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kline, Morris 1908-1992 Mathematics for liberal arts Mathematik Mathematics |
| title | Mathematics for liberal arts |
| title_auth | Mathematics for liberal arts |
| title_exact_search | Mathematics for liberal arts |
| title_full | Mathematics for liberal arts Morris Kline |
| title_fullStr | Mathematics for liberal arts Morris Kline |
| title_full_unstemmed | Mathematics for liberal arts Morris Kline |
| title_short | Mathematics for liberal arts |
| title_sort | mathematics for liberal arts |
| topic | Mathematik Mathematics |
| topic_facet | Mathematik Mathematics |
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