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History of Mathematics: A Source-Based Approach, Volume 1 [Hardback]

  • Formāts: Hardback, 496 pages, height x width: 254x178 mm, weight: 1405 g
  • Sērija : AMS/MAA Textbooks
  • Izdošanas datums: 01-Dec-2018
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 147044352X
  • ISBN-13: 9781470443528
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  • Cena: 105,43 €
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  • Formāts: Hardback, 496 pages, height x width: 254x178 mm, weight: 1405 g
  • Sērija : AMS/MAA Textbooks
  • Izdošanas datums: 01-Dec-2018
  • Izdevniecība: American Mathematical Society
  • ISBN-10: 147044352X
  • ISBN-13: 9781470443528
Citas grāmatas par šo tēmu:
The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original--primary and secondary-source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field.

The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

Recenzijas

The current volume is a thorough, very readable, nicely illustrated, and well-balanced coverage of the history of mathematics. It is peppered with footnotes, references to up-to-date scholarship and judicious suggestions for further reading. Finally, as the subtitle suggests, the history is brought to life with numerous excerpts from original sources. This engagement with source texts gives depth and authenticity to the learning process. Original sources and artefacts are the raw material of history. Using them is a wonderful way to teach which enthuses students and challenges them to think more deeply and more critically about the past. Mark McCartney, President of the British Society for the History of Mathematics

Acknowledgments ix
Permissions & Acknowledgments x
1 Introduction
1(4)
2 Early Mathematics
5(36)
Introduction
5(1)
2.1 Early counting
6(4)
2.2 Egyptian mathematics
10(10)
2.3 Mesopotamian mathematics
20(13)
2.4 A historical case study
33(6)
2.5 Further reading
39(2)
3 Greek Mathematics: An Introduction
41(54)
Introduction
41(1)
3.1 A dialogue from Plato's Meno
42(9)
3.2 Geometry before Plato
51(8)
3.3 Plato and Aristotle
59(19)
3.4 Euclid's Elements
78(15)
3.5 Further reading
93(2)
4 Greek Mathematics: Proofs and Problems
95(30)
Introduction
95(1)
4.1 The development of proof
96(2)
4.2 Methods of proof
98(11)
4.3 Doubling the cube and trisecting an angle
109(6)
4.4 Squaring the circle
115(8)
4.5 Further reading
123(2)
5 Greek Mathematics: Curves
125(36)
Introduction
125(1)
5.1 Problems with curves
125(5)
5.2 Archimedes
130(14)
5.3 Conies
144(14)
5.4 Further reading
158(3)
6 Greek Mathematics: Later Years
161(36)
Introduction
161(1)
6.1 The Hellenistic world
161(11)
6.2 Ptolemy and astronomy
172(8)
6.3 Diophantus
180(8)
6.4 The commentating tradition
188(7)
6.5 Further reading
195(2)
7 Mathematics in India and China
197(38)
Introduction
197(3)
7.1 Indian mathematics
200(10)
7.2 Chinese mathematics
210(23)
7.3 Further reading
233(2)
8 Mathematics in the Islamic World
235(26)
Introduction
235(1)
8.1 The Islamic intellectual world
235(3)
8.2 Islamic algebra
238(14)
8.3 Islamic geometry
252(7)
8.4 Further reading
259(2)
9 The Mathematical Awakening of Europe
261(16)
Introduction
261(1)
9.1 Mathematics in the medieval Christian West
262(6)
9.2 The rise of the universities
268(7)
9.3 Further reading
275(2)
10 The Renaissance: Recovery and Innovation
277(42)
Introduction
277(1)
10.1 Early European mathematics
278(8)
10.2 Renaissance translators: Maurolico and Commandino
286(6)
10.3 Cubics and quartics in 16th-century Italy
292(16)
10.4 Bombelli and Viete
308(10)
10.5 Further reading
318(1)
11 The Renaissance of Mathematics in Britain
319(54)
Introduction
319(1)
11.1 Mathematics in the vernacular: Robert Recorde
320(13)
11.2 Mathematics for the Commonwealth: John Dee
333(8)
11.3 The mathematical practitioners
341(8)
11.4 Thomas Harriot
349(7)
11.5 Excellent briefe rules: Napier and Briggs
356(14)
11.6 Further reading
370(3)
12 The Astronomical Revolution
373(34)
Introduction
373(1)
12.1 The Copernican revolution
373(6)
12.2 Kepler
379(12)
12.3 The language of nature: Galileo
391(14)
12.4 Further reading
405(2)
13 European Mathematics in the Early 17th Century
407(46)
Introduction
407(1)
13.1 Algebra and analysis
408(10)
13.2 Fermat's number theory
418(7)
13.3 Descartes
425(10)
13.4 Pappus's locus problem
435(11)
13.5 The Cartesian challenge to Euclid
446(5)
13.6 Further reading
451(2)
14 Concluding Remarks
453(4)
15 Exercises
457(20)
Advice on tackling the exercises
457(8)
Exercises: Part A
465(9)
Exercises: Part B
474(2)
Exercises: Part C
476(1)
Bibliography 477(8)
Index 485
June Barrow-Green, The Open University, Milton Keynes, United Kingdom.

Jeremy Gray, The Open University, Milton Keynes, United Kingdom.

Robin Wilson, The Open University, Milton Keynes, United Kingdom.