The history of mathematics: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
McGraw-Hill
2007
|
| Ausgabe: | 6. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xii, 788 p. Ill., graph. Darst. 25 cm |
| ISBN: | 0071106359 0073051896 |
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| 245 | 1 | 0 | |a The history of mathematics |b an introduction |c David M. Burton |
| 250 | |a 6. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b McGraw-Hill |c 2007 | |
| 300 | |a xii, 788 p. |b Ill., graph. Darst. |c 25 cm | ||
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| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x History | |
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Datensatz im Suchindex
| _version_ | 1804135213439123456 |
|---|---|
| adam_text | Titel: The history of mathematics
Autor: Burton, David M
Jahr: 2007
Contents
Preface xi-xvi
Chapter 1
Early Number Systems and
Symbols 1
1.1 Primitive Counting 1
A Sense of Number 1
Notches as Tally Marks 2
The Peruvian Quipus: Knots as Numbers 6
1.2 Number Recording of the Egyptians and Greeks 9
The History of Herodotus 9
Hieroglyphic Representation of Numbers 11
Egyptian Hieratic Numeration 15
The Greek Alphabetic Numeral System 16
1.3 Number Recording of the Babylonians 20
Babylonian Cuneiform Script 20
Deciphering Cuneiform: Grotefend and Rawlinson 21
The Babylonian Positional Number System 23
Writing in Ancient China 27
Chapter 2
Mathematics in Early
Civilizations 33
2.1 The Rhind Papyrus 33
Egyptian Mathematical Papyri 33
A Key to Deciphering: The Rosetta Stone 35
2.2 Egyptian Arithmetic 37
Early Egyptian Multiplication 37
The Unit Fraction Table 40
Representing Rational Numbers 43
2.3 Four Problems from the Rhind Papyrus 46
The Method of False Position 46
A Curious Problem 49
Egyptian Mathematics as Applied Arithmetic 50
2.4 Egyptian Geometry 53
Approximating the Area of a Circle 53
The Volume of a Truncated Pyramid 56
Speculations About the Great Pyramid 58
2.5 Babylonian Mathematics 63
A Tablet of Reciprocals 63
The Babylonian Treatment of Quadratic Equations 65
Two Characteristic Babylonian Problems 70
2.6 Plimpton 322 73
A Tablet Concerning Number Triples 73
Babylonian Use of the Pythagorean Theorem 77
The Cairo Mathematical Papyrus 78
Chapter 3
The Beginnings of Greek
Mathematics 85
3.1 The Geometrical Discoveries of Thales 85
Greece and the Aegean Area 85
The Dawn of Demonstrative Geometry:
Thales of Miletos 88
Measurements Using Geometry 89
3.2 Pythagorean Mathematics 92
Pythagoras and His Followers 92
Nicomachus s Introductio Arithmetics 96
The Theory of Figurative Numbers 99
Zeno s Paradox 103
Contents
3.3 The Pythagorean Problem 107
Geometric Proofs of the Pythagorean Theorem 107
Early Solutions of the Pythagorean Equation 109
The Crisis of Incommensurable Quantities 111
Theon s Side and Diagonal Numbers 113
Eudoxus of Cnidos 117
3.4 Three Construction Problems of Antiquity 122
Hippocrates and the Quadrature of the Circle 122
The Duplication of the Cube 126
The Triscction of an Angle 127
3.5 The Quadrarrix of Hippias 132
Rise of the Sophists 132
Hippias of Elis 133
The Grove of Academia: Platos Academy 136
Chapter 4
The Alexandrian School:
Euclid 143
4.1 Euclid and the Elements 143
A Center of Learning: The Museum 143
Euclid s Life and Writings 145
4-2 Euclidean Geometry 146
Euclid s Foundation for Geometry 146
Postulates 148
Common Notions 148
Book I of the Elements 150
Euclid s Proof of the Pythagorean Theorem 158
Book 11 on Geometric Algebra 161
Construction of the Regular Pentagon 167
4.3 Euclid s Number Theory 172
Euclidean Divisibility Properties 172
The Algorithm of Euclid 175
The Fundamental Theorem of Arithmetic 179
An Infinity of Primes 182
4.4 Eratosthenes, the Wise Man of Alexandria 185
The Sieve of Eratosthenes 185
Measurement of the Earth 188
The Almagest of Claudius Ptolemy 190
Ptolemy s Geographical Dictionary 192
4.5 Archimedes 196
The Ancient World s Genius 196
Estimating the Value of n 200
The Sand-Reckoner 205
Quadrature of a Parabolic Segment 207
Apollonius of Perga: The Conies 209
Chapter 5
The Twilight of Greek
Mathematics: Diophantus 215
5.1 The Decline of Alexandrian Mathematics 215
The Waning of the Golden Age 215
The Spread of Christianity 217
Constantinople, A Refuge for Greek Learning 219
5.2 The Arithmetica 219
Diophantus s Number Theory 219
Problems from the Ariihmetica 222
5.3 Diophantine Equations in Greece, India,
and China 225
The Cattle Problem of Archimedes 225
Early Mathematics in India 227
The Chinese Hundred Fowls Problem 230
5.4 The Later Commentators 234
The Mathematical Collection of Pappus 234
Hypatia, the First Woman Mathematician 235
Roman Mathematics: Boethius and Cassiodorus 237
5.5 Mathematics in the Near and Far East 240
The Algebra of al-Khowarizmi 240
Abu Kamil and Thabit ibn Qurra 244
Contents
vii
Omar Khayyam 249
The Astronomers al-Tusi and al-Karashi 251
The Ancient Chinese Nine Chapters 254
Later Chinese Mathematical Works 262
Chapter 6
The First Awakening:
Fibonacci 271
6.1 The Decline and Revival of Learning 271
The Carolingian Pre-Renaissance 271
Transmission of Arabic Learning to the West 274
The Pioneer Translators: Gerard and Adelard 276
6.2 The Liber Abaci and Liber Quadratorum 279
The Hindu-Arabic Numerals 279
Fibonacci s Liber Quadratorum 282
The Works of Jordanus de Nemore 285
6.3 The Fibonacci Sequence 289
The Liber Abaci s Rabbit Problem 289
Some Properties of Fibonacci Numbers 291
6.4 Fibonacci and the Pythagorean Problem 295
Pythagorean Number Triples 295
Fibonacci s Tournament Problem 299
Chapter 1
The Renaissance of Mathematics:
Cardan and Tartaglia 303
7.1 Europe in the Fourteenth and Fifteenth
Centuries 303
The Italian Renaissance 303
Artificial Writing: The Invention of Printing 305
Founding of the Great Universities 309
A Thirst for Classical Learning 312
7.2 The Battle of the Scholars 315
Restoring the Algebraic Tradition: Robert Recorde 315
The Italian Algebraists: Pacioli, del Ferro, and
Tartaglia 317
Cardan, A Scoundrel Mathematician 321
7.3 Cardan s Ars Magna 322
Cardan s Solution of the Cubic Equation 322
Bombelli and Imaginary Roots of the Cubic 327
7.4 Ferrari s Solution of the Quartic Equation 330
The Resolvant Cubic 330
The Story of the Quintic Equation:
Ruffini, Abel, and Galois 333
Chapter 8
The Mechanical World:
Descartes and Newton 339
8.1 The Dawn of Modern Mathematics 339
The Seventeenth Century Spread of Knowledge 339
Galileo s Telescopic Observations 341
The Beginning of Modern Notation:
Francois Vieta 347
The Decimal Fractions of Simon Stevin 350
Napier s Invention of Logarithms 352
The Astronomical Discoveries of Brahe and
Kepler 357
8-2 Descartes: The Discours de la Methode 364
The Writings of Descartes 364
Inventing Cattesian Geometry 368
The Algebraic Aspect of La Geometrie 373
Descartes s Principia Philosophiae 376
Perspective Geometry: Desargues and Poncelet 379
8.3 Newton: The Principia Mathematica 382
The Textbooks of Oughtred and Harriot 382
Wallis s Arithmetica Infinitorum 384
viii
The Lucasian Professorship: Barrow and Newton 387
Newton s Golden Years 393
The Laws of Motion 399
Later Years: Appointment to the Mint 405
8.4 Gottfried Leibniz: The Calculus Controversy 410
The Early Work of Leibniz 410
Leibniz s Creation of the Calculus 414
Newton s Fluxional Calculus 417
The Dispute over Priority 425
Maria Agnesi and Emilie du Chatelet 430
Chapter 9
The Development of Probability
Theory: Pascal, Bernoulli,
and Laplace 439
9.1 The Origins of Probability Theory 439
Graunt s Bills of Mortality 439
Games of Chance: Dice and Cards 443
The Precocity of the Young Pascal 446
Pascal and the Cycloid 452
De Mere s Problem of Points 454
9.2 Pascal s Arithmetic Triangle 456
The Traitc du Triangle Arithmetic 456
Mathematical Induction 461
Francesco Maurolico s Use of Induction 463
9.3 The Bernoullis and Laplace 468
Christiaan Huygens s Pamphlet on Probability 468
The Bernoulli Brothers: John and James 470
De Moivre s Doctrine of Chances 477
The Mathematics of Celestial Phenomena:
Laplace 477
Mary Fairfax Somerville 481
Laplace s Research in Probability Theory 482
Daniel Bernoulli, Poisson, and Chebyshev 489
Contents
Chapter 10
The Revival of Number Theory:
Fermat, Euler, and Gauss 497
10.1 Marin Mersenne and the Search
for Perfect Numbers 497
Scientific Societies 497
Marin Mersenne s Mathematical Gathering 499
Numbers, Perfect and Not So Perfect 502
10.2 From Fermat to Euler 511
Fermat s Arithmetica 511
The Famous Last Theorem of Fermat 516
The Eighteenth-Century Enlightenment 520
Maclaurin s Treatise on Fluxions 5 24
Euler s Life and Contributions 527
10.3 The Prince of Mathematicians: Carl
Friedrich Gauss 539
The Period of the French Revolution:
Lagrange and Monge 539
Gauss s Disquisitiones Arithmeticae 543
The Legacy of Gauss: Congruence Theory 549
Dirichlet and Jacobi 555
Chapter J J
N ineteentb-Century
Contributions: Lobachevsky to
Hilbert 561
11.1 Attempts to Prove the Parallel Postulate 561
The Efforts of Proclus, Playfair, and Wallis 561
Saccheri Quadrilaterals 564
The Accomplishments of Legendre 569
Legendre s Elements de giomivrie 572
11.2 The Founders of Non-Euclidean Geometry 582
Contents
ix
Gauss s Attempt at a New Geometry 582
The Struggle of John Bolyai 587
Creation of Non-Euclidean Geometry: Lobachevsky 591
Models of the New Geometry: Riemann,
Beltrami, and Klein 596
Grace Chisholm Young 601
11.3 The Age of Rigor 602
D Alembert and Cauchy on Limits 602
Fourier s Series 608
The Father of Modern Analysis, Weierstrass 612
Sonya Kovalevsky 615
The Axiomatic Movement: Pasch and Hilbert 618
11.4 Arithmetic Generalized 624
Babbage and the Analytical Engine 624
Peacock s Treatise on Algebra 62 7
The Representation of Complex Numbers 628
Hamilton s Discovery of Quaternions 631
Matrix Algebra: Cayley and Sylvester 637
Boole s Algebra of Logic 643
Chapter 12
Transition to the Twentieth
Century: Cantor and
Kronecker 653
12.1 The Emergence of American Mathematics 653
Ascendency of the German Universities 653
American Mathematics Takes Root: 1800-1900 655
The Twentieth-Century Consolidation 662
12.2 Counting the Infinite 666
The Last Universalist: Poincare 666
Cantor s Theory of Infinite Sets 668
Kronecker s View of Set Theory 673
Countable and Uncountable Sets 676
Transcendental Numbers 682
The Continuum Hypothesis 687
12.3 The Paradoxes of Set Theory 690
The Early Paradoxes 690
Zermelo and the Axiom of Choice 694
The Logistic School: Frege, Peano, and Russell 697
Hilbert s Formalistic Approach 701
Brouwers Institutionism 704
Chapter ] 3
Extensions and Generalizations:
Hardy, Hausdorff,
andNoether 713
13.1 Hardy and Ramanujan 713
The Tripos Examination 713
The Rejuvenation of English Mathematics 714
A Unique Collaboration: Hardy and Littlewood 717
India s Prodigy, Ramanujan 718
13.2 The Beginnings of Point-Set Topology 721
Frechet s Metric Spaces 721
The Neighborhood Spaces of Hausdorff 723
Banach and Normed Linear Spaces 725
13.3 Some Twentieth-Century Developments 727
Emmy Noether s Theory of Rings 727
Von Neumann and the Computer 733
Women in Modern Mathematics 735
A Few Recent Advances 737
General Bibliography 743
Additional Reading 746
The Greek Alphabet 747
Solutions to Selected Problems 748
Index 763
|
| adam_txt |
Titel: The history of mathematics
Autor: Burton, David M
Jahr: 2007
Contents
Preface xi-xvi
Chapter 1
Early Number Systems and
Symbols 1
1.1 Primitive Counting 1
A Sense of Number 1
Notches as Tally Marks 2
The Peruvian Quipus: Knots as Numbers 6
1.2 Number Recording of the Egyptians and Greeks 9
The History of Herodotus 9
Hieroglyphic Representation of Numbers 11
Egyptian Hieratic Numeration 15
The Greek Alphabetic Numeral System 16
1.3 Number Recording of the Babylonians 20
Babylonian Cuneiform Script 20
Deciphering Cuneiform: Grotefend and Rawlinson 21
The Babylonian Positional Number System 23
Writing in Ancient China 27
Chapter 2
Mathematics in Early
Civilizations 33
2.1 The Rhind Papyrus 33
Egyptian Mathematical Papyri 33
A Key to Deciphering: The Rosetta Stone 35
2.2 Egyptian Arithmetic 37
Early Egyptian Multiplication 37
The Unit Fraction Table 40
Representing Rational Numbers 43
2.3 Four Problems from the Rhind Papyrus 46
The Method of False Position 46
A Curious Problem 49
Egyptian Mathematics as Applied Arithmetic 50
2.4 Egyptian Geometry 53
Approximating the Area of a Circle 53
The Volume of a Truncated Pyramid 56
Speculations About the Great Pyramid 58
2.5 Babylonian Mathematics 63
A Tablet of Reciprocals 63
The Babylonian Treatment of Quadratic Equations 65
Two Characteristic Babylonian Problems 70
2.6 Plimpton 322 73
A Tablet Concerning Number Triples 73
Babylonian Use of the Pythagorean Theorem 77
The Cairo Mathematical Papyrus 78
Chapter 3
The Beginnings of Greek
Mathematics 85
3.1 The Geometrical Discoveries of Thales 85
Greece and the Aegean Area 85
The Dawn of Demonstrative Geometry:
Thales of Miletos 88
Measurements Using Geometry 89
3.2 Pythagorean Mathematics 92
Pythagoras and His Followers 92
Nicomachus's Introductio Arithmetics 96
The Theory of Figurative Numbers 99
Zeno's Paradox 103
Contents
3.3 The Pythagorean Problem 107
Geometric Proofs of the Pythagorean Theorem 107
Early Solutions of the Pythagorean Equation 109
The Crisis of Incommensurable Quantities 111
Theon's Side and Diagonal Numbers 113
Eudoxus of Cnidos 117
3.4 Three Construction Problems of Antiquity 122
Hippocrates and the Quadrature of the Circle 122
The Duplication of the Cube 126
The Triscction of an Angle 127
3.5 The Quadrarrix of Hippias 132
Rise of the Sophists 132
Hippias of Elis 133
The Grove of Academia: Platos Academy 136
Chapter 4
The Alexandrian School:
Euclid 143
4.1 Euclid and the Elements 143
A Center of Learning: The Museum 143
Euclid's Life and Writings 145
4-2 Euclidean Geometry 146
Euclid's Foundation for Geometry 146
Postulates 148
Common Notions 148
Book I of the Elements 150
Euclid's Proof of the Pythagorean Theorem 158
Book 11 on Geometric Algebra 161
Construction of the Regular Pentagon 167
4.3 Euclid's Number Theory 172
Euclidean Divisibility Properties 172
The Algorithm of Euclid 175
The Fundamental Theorem of Arithmetic 179
An Infinity of Primes 182
4.4 Eratosthenes, the Wise Man of Alexandria 185
The Sieve of Eratosthenes 185
Measurement of the Earth 188
The Almagest of Claudius Ptolemy 190
Ptolemy's Geographical Dictionary 192
4.5 Archimedes 196
The Ancient World's Genius 196
Estimating the Value of n 200
The Sand-Reckoner 205
Quadrature of a Parabolic Segment 207
Apollonius of Perga: The Conies 209
Chapter 5
The Twilight of Greek
Mathematics: Diophantus 215
5.1 The Decline of Alexandrian Mathematics 215
The Waning of the Golden Age 215
The Spread of Christianity 217
Constantinople, A Refuge for Greek Learning 219
5.2 The Arithmetica 219
Diophantus's Number Theory 219
Problems from the Ariihmetica 222
5.3 Diophantine Equations in Greece, India,
and China 225
The Cattle Problem of Archimedes 225
Early Mathematics in India 227
The Chinese Hundred Fowls Problem 230
5.4 The Later Commentators 234
The Mathematical Collection of Pappus 234
Hypatia, the First Woman Mathematician 235
Roman Mathematics: Boethius and Cassiodorus 237
5.5 Mathematics in the Near and Far East 240
The Algebra of al-Khowarizmi 240
Abu Kamil and Thabit ibn Qurra 244
Contents
vii
Omar Khayyam 249
The Astronomers al-Tusi and al-Karashi 251
The Ancient Chinese Nine Chapters 254
Later Chinese Mathematical Works 262
Chapter 6
The First Awakening:
Fibonacci 271
6.1 The Decline and Revival of Learning 271
The Carolingian Pre-Renaissance 271
Transmission of Arabic Learning to the West 274
The Pioneer Translators: Gerard and Adelard 276
6.2 The Liber Abaci and Liber Quadratorum 279
The Hindu-Arabic Numerals 279
Fibonacci's Liber Quadratorum 282
The Works of Jordanus de Nemore 285
6.3 The Fibonacci Sequence 289
The Liber Abaci's Rabbit Problem 289
Some Properties of Fibonacci Numbers 291
6.4 Fibonacci and the Pythagorean Problem 295
Pythagorean Number Triples 295
Fibonacci's Tournament Problem 299
Chapter 1
The Renaissance of Mathematics:
Cardan and Tartaglia 303
7.1 Europe in the Fourteenth and Fifteenth
Centuries 303
The Italian Renaissance 303
Artificial Writing: The Invention of Printing 305
Founding of the Great Universities 309
A Thirst for Classical Learning 312
7.2 The Battle of the Scholars 315
Restoring the Algebraic Tradition: Robert Recorde 315
The Italian Algebraists: Pacioli, del Ferro, and
Tartaglia 317
Cardan, A Scoundrel Mathematician 321
7.3 Cardan's Ars Magna 322
Cardan's Solution of the Cubic Equation 322
Bombelli and Imaginary Roots of the Cubic 327
7.4 Ferrari's Solution of the Quartic Equation 330
The Resolvant Cubic 330
The Story of the Quintic Equation:
Ruffini, Abel, and Galois 333
Chapter 8
The Mechanical World:
Descartes and Newton 339
8.1 The Dawn of Modern Mathematics 339
The Seventeenth Century Spread of Knowledge 339
Galileo's Telescopic Observations 341
The Beginning of Modern Notation:
Francois Vieta 347
The Decimal Fractions of Simon Stevin 350
Napier's Invention of Logarithms 352
The Astronomical Discoveries of Brahe and
Kepler 357
8-2 Descartes: The Discours de la Methode 364
The Writings of Descartes 364
Inventing Cattesian Geometry 368
The Algebraic Aspect of La Geometrie 373
Descartes's Principia Philosophiae 376
Perspective Geometry: Desargues and Poncelet 379
8.3 Newton: The Principia Mathematica 382
The Textbooks of Oughtred and Harriot 382
Wallis's Arithmetica Infinitorum 384
viii
The Lucasian Professorship: Barrow and Newton 387
Newton's Golden Years 393
The Laws of Motion 399
Later Years: Appointment to the Mint 405
8.4 Gottfried Leibniz: The Calculus Controversy 410
The Early Work of Leibniz 410
Leibniz's Creation of the Calculus 414
Newton's Fluxional Calculus 417
The Dispute over Priority 425
Maria Agnesi and Emilie du Chatelet 430
Chapter 9
The Development of Probability
Theory: Pascal, Bernoulli,
and Laplace 439
9.1 The Origins of Probability Theory 439
Graunt's Bills of Mortality 439
Games of Chance: Dice and Cards 443
The Precocity of the Young Pascal 446
Pascal and the Cycloid 452
De Mere's Problem of Points 454
9.2 Pascal's Arithmetic Triangle 456
The Traitc du Triangle Arithmetic 456
Mathematical Induction 461
Francesco Maurolico's Use of Induction 463
9.3 The Bernoullis and Laplace 468
Christiaan Huygens's Pamphlet on Probability 468
The Bernoulli Brothers: John and James 470
De Moivre's Doctrine of Chances 477
The Mathematics of Celestial Phenomena:
Laplace 477
Mary Fairfax Somerville 481
Laplace's Research in Probability Theory 482
Daniel Bernoulli, Poisson, and Chebyshev 489
Contents
Chapter 10
The Revival of Number Theory:
Fermat, Euler, and Gauss 497
10.1 Marin Mersenne and the Search
for Perfect Numbers 497
Scientific Societies 497
Marin Mersenne's Mathematical Gathering 499
Numbers, Perfect and Not So Perfect 502
10.2 From Fermat to Euler 511
Fermat's Arithmetica 511
The Famous Last Theorem of Fermat 516
The Eighteenth-Century Enlightenment 520
Maclaurin's Treatise on Fluxions 5 24
Euler's Life and Contributions 527
10.3 The Prince of Mathematicians: Carl
Friedrich Gauss 539
The Period of the French Revolution:
Lagrange and Monge 539
Gauss's Disquisitiones Arithmeticae 543
The Legacy of Gauss: Congruence Theory 549
Dirichlet and Jacobi 555
Chapter J J
N ineteentb-Century
Contributions: Lobachevsky to
Hilbert 561
11.1 Attempts to Prove the Parallel Postulate 561
The Efforts of Proclus, Playfair, and Wallis 561
Saccheri Quadrilaterals 564
The Accomplishments of Legendre 569
Legendre's Elements de giomivrie 572
11.2 The Founders of Non-Euclidean Geometry 582
Contents
ix
Gauss's Attempt at a New Geometry 582
The Struggle of John Bolyai 587
Creation of Non-Euclidean Geometry: Lobachevsky 591
Models of the New Geometry: Riemann,
Beltrami, and Klein 596
Grace Chisholm Young 601
11.3 The Age of Rigor 602
D'Alembert and Cauchy on Limits 602
Fourier's Series 608
The Father of Modern Analysis, Weierstrass 612
Sonya Kovalevsky 615
The Axiomatic Movement: Pasch and Hilbert 618
11.4 Arithmetic Generalized 624
Babbage and the Analytical Engine 624
Peacock's Treatise on Algebra 62 7
The Representation of Complex Numbers 628
Hamilton's Discovery of Quaternions 631
Matrix Algebra: Cayley and Sylvester 637
Boole's Algebra of Logic 643
Chapter 12
Transition to the Twentieth
Century: Cantor and
Kronecker 653
12.1 The Emergence of American Mathematics 653
Ascendency of the German Universities 653
American Mathematics Takes Root: 1800-1900 655
The Twentieth-Century Consolidation 662
12.2 Counting the Infinite 666
The Last Universalist: Poincare 666
Cantor's Theory of Infinite Sets 668
Kronecker's View of Set Theory 673
Countable and Uncountable Sets 676
Transcendental Numbers 682
The Continuum Hypothesis 687
12.3 The Paradoxes of Set Theory 690
The Early Paradoxes 690
Zermelo and the Axiom of Choice 694
The Logistic School: Frege, Peano, and Russell 697
Hilbert's Formalistic Approach 701
Brouwers Institutionism 704
Chapter ] 3
Extensions and Generalizations:
Hardy, Hausdorff,
andNoether 713
13.1 Hardy and Ramanujan 713
The Tripos Examination 713
The Rejuvenation of English Mathematics 714
A Unique Collaboration: Hardy and Littlewood 717
India's Prodigy, Ramanujan 718
13.2 The Beginnings of Point-Set Topology 721
Frechet's Metric Spaces 721
The Neighborhood Spaces of Hausdorff 723
Banach and Normed Linear Spaces 725
13.3 Some Twentieth-Century Developments 727
Emmy Noether's Theory of Rings 727
Von Neumann and the Computer 733
Women in Modern Mathematics 735
A Few Recent Advances 737
General Bibliography 743
Additional Reading 746
The Greek Alphabet 747
Solutions to Selected Problems 748
Index 763 |
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| id | DE-604.BV021487982 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:11:47Z |
| indexdate | 2024-07-09T20:36:56Z |
| institution | BVB |
| isbn | 0071106359 0073051896 |
| language | English |
| lccn | 2005051123 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014704852 |
| oclc_num | 60972161 |
| open_access_boolean | |
| owner | DE-12 DE-29 |
| owner_facet | DE-12 DE-29 |
| physical | xii, 788 p. Ill., graph. Darst. 25 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | McGraw-Hill |
| record_format | marc |
| spelling | Burton, David M. 1930- Verfasser (DE-588)101498372X aut The history of mathematics an introduction David M. Burton 6. ed. Boston [u.a.] McGraw-Hill 2007 xii, 788 p. Ill., graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Geschichte Mathematik Mathematics History Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Geschichte (DE-588)4020517-4 s b DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014704852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burton, David M. 1930- The history of mathematics an introduction Geschichte Mathematik Mathematics History Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4037944-9 |
| title | The history of mathematics an introduction |
| title_auth | The history of mathematics an introduction |
| title_exact_search | The history of mathematics an introduction |
| title_exact_search_txtP | The history of mathematics an introduction |
| title_full | The history of mathematics an introduction David M. Burton |
| title_fullStr | The history of mathematics an introduction David M. Burton |
| title_full_unstemmed | The history of mathematics an introduction David M. Burton |
| title_short | The history of mathematics |
| title_sort | the history of mathematics an introduction |
| title_sub | an introduction |
| topic | Geschichte Mathematik Mathematics History Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Geschichte Mathematik Mathematics History |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014704852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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