Holdings: A history of mathematics

A history of mathematics: an introduction

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Bibliographic Details
Main Author:	Katz, Victor J. 1942- (Author)
Format:	Book
Language:	English
Published:	New York, NY Pearson [2018]
Edition:	Third edition
Series:	Pearson modern classic
Subjects:	Geschichte Mathematik Mathematics > History
Online Access:	Inhaltsverzeichnis
Item Description:	Originally published in 2009, reissued as part of Pearson's modern classic series. - Includes bibliographical references and index
Physical Description:	xvi, 976 Seiten Illustrationen
ISBN:	9780134689524 0134689526

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MARC


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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	A history of mathematics an introduction
title_auth	A history of mathematics an introduction
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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)
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title_short	A history of mathematics
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