A history of mathematics: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Pearson
[2018]
|
| Ausgabe: | Third edition |
| Schriftenreihe: | Pearson modern classic
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originally published in 2009, reissued as part of Pearson's modern classic series. - Includes bibliographical references and index |
| Beschreibung: | xvi, 976 Seiten Illustrationen |
| ISBN: | 9780134689524 0134689526 |
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Datensatz im Suchindex
| _version_ | 1804177546136256512 |
|---|---|
| adam_text | Titel: A history of mathematics
Autor: Katz, Victor J
Jahr: 2018
Contents
Preface.......................... xi
PART ONE Ancient Mathematics
Chapter 1 Egypt and Mesopotamia 1
1.1 Egypt..................................................2
1.2 Mesopotamia............................................10
1.3 Conclusion..............................................27
Exercises..............................................28
References and Notes....................................30
Chapter 2 The Beginnings of Mathematics in Greece 32
2.1 The Earliest Greek Mathematics............................33
2.2 The Time of Plato........................................41
2.3 Aristotle................................................43
Exercises..............................................47
References and Notes....................................48
Chapter 3 Euclid 50
3.1 Introduction to the Elements................................51
3.2 Book I and the Pythagorean Theorem........................53
3.3 Book II and Geometric Algebra............................60
3.4 Circles and the Pentagon Construction........................66
3.5 Ratio and Proportion......................................71
3.6 Number Theory..........................................77
3.7 Irrational Magnitudes ....................................81
3.8 Solid Geometry and the Method of Exhaustion................83
3.9 Euclid s Data............................................88
Exercises..............................................90
References and Notes....................................92
94
96
101
103
112
115
127
131
133
134
145
157
168
170
172
173
176
185
189
191
192
195
196
197
201
209
222
225
226
228
230
231
233
237
Archimedes and Apollonius
4.1 Archimedes and Physics........
4.2 Archimedes and Numerical Calculations . .
4.3 Archimedes and Geometry.......
4.4 Conic Sections before Apollonius.....
4.5 The Conies of Apollonius........
Exercises..............
References and Notes.........
Mathematical Methods in Hellenistic Times
5.1 Astronomy before Ptolemy.......
5.2 Ptolemy and the Almagest........
5.3 Practical Mathematics.........
Exercises..............
References and Notes.........
The Final Chapters of Greek Mathematics
6.1 Nicomachus and Elementary Number Theory
6.2 Diophantus and Greek Algebra......
6.3 Pappus and Analysis..........
6.4 Hypatia and the End of Greek Mathematics .
Exercises..............
References and Notes.........
Medieval Mathematics
Ancient and Medieval China
7.1 Introduction to Mathematics in China
7.2 Calculations..........
7.3 Geometry...........
7.4 Solving Equations........
7.5 Indeterminate Analysis......
7.6 Transmission To and From China . .
Exercises...........
References and Notes......
Ancient and Medieval India
8.1 Introduction to Mathematics in India
8.2 Calculations..........
8.3 Geometry...........
8.4 Equation Solving........................................242
8.5 Indeterminate Analysis....................................244
8.6 Combinatorics..........................................250
8.7 Trigonometry............................................252
8.8 Transmission To and From India............................259
Exercises..............................................260
References and Notes....................................263
Chapter 9 The Mathematics of Islam 265
9.1 Introduction to Mathematics in Islam........................266
9.2 Decimal Arithmetic......................................267
9.3 Algebra................................................271
9.4 Combinatorics..........................................292
9.5 Geometry ..........................................296
9.6 Trigonometry............................................306
9.7 Transmission of Islamic Mathematics........................317
Exercises..............................................318
References and Notes....................................321
Chapter to Mathematics in Medieval Europe 324
10.1 Introduction to the Mathematics of Medieval Europe............325
10.2 Geometry and Trigonometry................................328
10.3 Combinatorics..........................................337
10.4 Medieval Algebra........................................342
10.5 The Mathematics of Kinematics............................351
Exercises..............................................359
References and Notes....................................362
Chapter it Mathematics around the World 364
11.1 Mathematics at the Turn of the Fourteenth Century..............365
11.2 Mathematics in America, Africa, and the Pacific................370
Exercises..............................................379
References and Notes....................................380
PART THREE Early Modem Mathematics_
Chapter 12 Algebra in the Renaissance 383
12.1 The Italian Abacists......................................385
12.2 Algebra in France, Germany, England, and Portugal............389
12.3 The Solution of the Cubic Equation..........................399
12.4 Viete, Algebraic Symbolism, and Analysis....................407
12.5 Simon Stevin and Decimal Fractions ........................414
Exercises..............................................418
References ...........................................420
Chapter 13 Mathematical Methods in the Renaissance 423
13.1 Perspective..............................................427
13.2 Navigation and Geography................................432
13.3 Astronomy and Trigonometry..............................435
13.4 Logarithms .............................453
13.5 Kinematics................................................457
Exercises..............................................462
References and Notes....................................464
Chapter 14 Algebra, Geometry, and Probability in the Seventeenth Century 467
14.1 The Theory of Equations............................468
14.2 Analytic Geometry ......................................473
14.3 Elementary Probability............................487
14.4 Number Theory..........................................497
14.5 Projective Geometry......................................499
Exercises..............................................501
References and Notes....................................504
Chapter 15 The Beginnings of Calculus 507
15.1 Tangents and Extrema..............................509
15.2 Areas and Volumes ...............................514
15.3 Rectification of Curves and the Fundamental Theorem..........532
Exercises..............................................539
References and Notes....................................541
Chapter 16 Newton and Leibniz 543
16.1 Isaac Newton............................................544
16.2 Gottfried Wilhelm Leibniz ................................565
16.3 First Calculus Texts......................................575
Exercises..............................................579
References and Notes....................................580
PART FOUR Modern Mathematics
Chapter 17 Analysis in the Eighteenth Century 583
17.1 Differential Equations.................. 584
17.2 The Calculus of Several Variables.............. 601
611
628
636
639
642
643
651
655
661
663
665
666
671
677
680
683
684
686
687
689
695
701
702
706
707
709
711
721
730
740
750
759
761
764
766
788
795
17.3 Calculus Texts . .............
17.4 The Foundations of Calculus.........
Exercises................
References and Notes...........
Probability and Statistics in the Eighteenth Century
18.1 Theoretical Probability...........
18.2 Statistical Inference ............
18.3 Applications of Probability.........
Exercises................
References and Notes...........
Algebra and Number Theory in the Eighteenth Century
19.1 Algebra Texts ..............
19.2 Advances in the Theory of Equations.....
19.3 Number Theory..............
19.4 Mathematics in the Americas........
Exercises................
References and Notes...........
Geometry in the Eighteenth Century
20.1 Clairaut and the Elements of Geometry.....
20.2 The Parallel Postulate...........
20.3 Analytic and Differential Geometry......
20.4 The Beginnings of Topology.........
20.5 The French Revolution and Mathematics Education
Exercises................
References and Notes...........
Algebra and Number Theory in the Nineteenth Century
21.1 Number Theory..............
21.2 Solving Algebraic Equations.........
21.3 Symbolic Algebra.............
21.4 Matrices and Systems of Linear Equations . . .
21.5 Groups and Fields—The Beginning of Structure .
Exercises.................
References and Notes............
Analysis in the Nineteenth Century
22.1 Rigor in Analysis.............
22.2 The Arithmetization of Analysis.......
22.3 Complex Analysis.............
22.4 Vector Analysis.......................................807
Exercises.......................813
References and Notes....................................815
Chapter 23 Probability and Statistics in the Nineteenth Century 818
23.1 The Method of Least Squares and Probability Distributions ... 819
23.2 Statistics and the Social Sciences............................824
23.3 Statistical Graphs........................................828
Exercises..............................................831
References and Notes....................................831
Chapter 24 Geometry in the Nineteenth Century 833
24.1 Differential Geometry....................................835
24.2 Non-Euclidean Geometry..................................839
24.3 Projective Geometry......................................852
24.4 Graph Theory and the Four-Color Problem....................858
24.5 Geometry in N Dimensions................................862
24.6 The Foundations of Geometry..............................867
Exercises..............................................870
References and Notes....................................872
Chapter 25 Aspects of the Twentieth Century and Beyond 874
25.1 Set Theory: Problems and Paradoxes........................876
25.2 Topology..............................................882
25.3 New Ideas in Algebra....................................890
25.4 The Statistical Revolution..................................903
25.5 Computers and Applications................................907
25.6 Old Questions Answered..................................919
Exercises..............................................926
References and Notes....................................928
Appendix A Using This Textbook in Teaching Mathematics 931
A.l Courses and Topics......................................931
A.2 Sample Lesson Ideas to Incorporate History....................935
A 3 Time Line..............................................939
General References in the History of Mathematics..................945
Answers to Selected Exercises..................................949
Index and Pronunciation Guide..................................961
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| spelling | Katz, Victor J. 1942- Verfasser (DE-588)1023186675 aut A history of mathematics an introduction Victor J. Katz (University of the District of Columbia) Third edition New York, NY Pearson [2018] © 2018 xvi, 976 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pearson modern classic Originally published in 2009, reissued as part of Pearson's modern classic series. - Includes bibliographical references and index Geschichte gnd rswk-swf Geschichte Mathematik Mathematics History Mathematik (DE-588)4037944-9 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 s Geschichte z DE-604 Geschichte (DE-588)4020517-4 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029728383&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title_full | A history of mathematics an introduction Victor J. Katz (University of the District of Columbia) |
| title_fullStr | A history of mathematics an introduction Victor J. Katz (University of the District of Columbia) |
| title_full_unstemmed | A history of mathematics an introduction Victor J. Katz (University of the District of Columbia) |
| title_short | A history of mathematics |
| title_sort | a history of mathematics an introduction |
| title_sub | an introduction |
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| topic_facet | Geschichte Mathematik Mathematics History |
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