A brief history of mathematics: a promenade through the civilizations of our world
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Chinesisch |
| Veröffentlicht: |
Cham, Switzerland
Birkhäuser
[2023]
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034344405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xv, 344 Seiten Illustrationen, Karten 24 cm |
| ISBN: | 9783031268403 3031268407 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819316831557517312 |
|---|---|
| adam_text | Contents 1 The Middle East, or the Beginning............................................................ The Origins of Mathematics......................................................................... Tite Beginnings of Counting................................................................. Number Bases....................................................................................... Arabic Numerals.................................................................................. Shape and Geometry............................................................................ Civilization on the Nile River........................................................................ A Peculiar Terrain................................................................................. The Rhind Papyrus................ .............................................................. Egyptian Fractions............................................................................... Between the Rivers........................................................................................ Babylonia.............................................................................................. The Clay Tablets.................................................................................. Plimpton 322 ......................................................................................... Conclusion.................................................................................................. 1 1 1 3 5 8 9 9 12 14 16 16 18 21 23 2 The Sages of Ancient
Greece....................................................................... The Birth of Mathematicians........................................................................ The Greek Arena.................................................................................. The First Proofs.................................................................................... Pythagoras........................................................................................... The Platonic Academy.................................................................................. Zeno’s Tortoise..................................................................................... Plato’s Academy.................................................................................. Aristotle................................................................................................ The Alexandrian School............................................................................... Euclid’s Elements................................................................................. Archimedes........................................................................................... Other Mathematicians.......................................................................... Conclusion...................................................................................................... 27 27 27 29 32 38 38 41 45 48 48 51 54 58 Xi
Contents xii 3 The Chinese Middle Ages..................................................................... Prologue.......................................................................................................... The Pre֊Qin Era..................................................................................... Zhoiibi Suanjing..................................................................................... Nine Chapters on the Mathematical Art.............................................. From Circle Divisions to the Method of Four Unknowns............................ Liu Hui’s π Algorithm........................................................................... The Sun Zi-Qin Jiushao Theorem........................................................ Other Mathematicians ........................... Conclusion............... . ...................................................................................... 4 India and Arabia.................................................................................................. From the Indus River to the Ganges.............................................................. The Indo-European Past........................................................................ The Shulba Sutras and Buddhism........................................................ The Number Zero and Hindu Numerals .............................................. From North India to South India......................................... ,........................
Aryabhata................................................................................................ Brahmagupta......................................................................................... Mahāvīra................................................................................................. Bhāskara II............................................................................................. Sacred Land.................................................................................................... Tire Arabian Empire............................................................................. Tite House of Wisdom in Baghdad....................................................... The Algebra of al֊ Khwarizmi..................... . .......................... The Scholars of Persia........................................................................... Omar Khayyam................................................ ................................... Na֊sir al-Din al-Tusi............................................................................... JamshTd al-Kāshī................................................................................... Conclusion......................................................................................... 5 From the Renaissance to the Birth of Calculus.......................................... The Renaissance in Europe.............................................. -.......... Medieval Europe................................................................................... Fibonacci’s
Rabbits............................................................................... Alberti’s Perspective Method............................................................... DaVinci and Dürer............................................................................... The Invention of Calculus.............................................................................. The Awakening of New Mathematics.................................................. Analytic Geometry................................................................................ The Pioneers of Calculus..................................................................... Newton and Leibniz......... . ................................................................... Conclusion.................................................................................. 61 61 61 63 66 69 69 77 86 96 101 101 101 105 109 110 110 114 117 120 124 124 126 129 133 133 137 141 144 147 147 147 150 153 156 160 160 164 169 174 1^2
Contents 6 The Age of Analysis and the French Revolution........................................ The Age of Analysis.................................................................................... The King of the Amateurs.................................................................. The Further Development of Calculus............................................... The Influence of Calculus.................................................................. The Bernoulli Family.......................................................................... The French Revolution................................................................................. Napoleon Bonaparte........................................................................... The Lofty Pyramid.............................................................................. The French Newton............................................................................. The Emperor’s Friend.......................................................................... Conclusion.................................................................................................... 7 Modern Mathematics, Modern Art.............................................................. The Rebirth of Algebra................................................................................ Toward a Rigorous Treatment of Analysis.......................................... Abet and Galois................................................................................... The Quaternions of William Rowan
Hamilton.................................. A Revolution in Geometry........................................................................... A Scandal in Elementary Geometry.................................................... The Arrival of Non-Euclidean Geometry........................................... Riemannian Geometry........................................................................ A New Era of Art..................................................................................... Edgar Allan Poe................................................................................... Baudelaire........................................................................................... From Imitation to Wit.................... Conclusion.................................................................................................... 8 Abstraction: Mathematics Since the Twentieth Century........................ The Road to Abstraction.............................................................................. Set Theory and Axiomatic Systems.................................................... The Abstraction of Mathematics........................................................ Abstraction in Art......................................................................... Applications of Mathematics....................................................................... Theoretical Physics ............................................................................. Biology and Economics.......................................................................
Computers and Chaos Theory.......... . ................................................ Mathematics and Logic................................................................................ Russell’s Paradox ................................................................................ Wittgenstein......................................................................................... Gödel’s Theorems................................................................................ Conclusion..................................................................................................... xiii 187 187 187 193 198 202 207 207 211 215 218 223 227 227 227 232 238 243 243 246 251 257 257 260 264 267 271 271 271 276 284 290 290 295 299 310 310 316 320 324
xiv Contents A A Mathematical Chronology....................................................................... 331 В The Origin of Some Common Mathematical Symbols........................... 335 Bibliography......................................................................................................... 337 Index...................................................................................................................... 339
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| any_adam_object | 1 |
| author | Cai, Tianxin 1963- |
| author_GND | (DE-588)1122993919 |
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| building | Verbundindex |
| bvnumber | BV049082516 |
| classification_rvk | SG 500 |
| ctrlnum | (OCoLC)1401176176 (DE-599)BVBBV049082516 |
| discipline | Mathematik |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Book |
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| id | DE-604.BV049082516 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T20:00:19Z |
| institution | BVB |
| isbn | 9783031268403 3031268407 |
| language | English Chinese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034344405 |
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| physical | xv, 344 Seiten Illustrationen, Karten 24 cm |
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| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Birkhäuser |
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| spellingShingle | Cai, Tianxin 1963- A brief history of mathematics a promenade through the civilizations of our world Architektur (DE-588)4002851-3 gnd Künste (DE-588)4033422-3 gnd Mathematik (DE-588)4037944-9 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Kultur (DE-588)4125698-0 gnd |
| subject_GND | (DE-588)4002851-3 (DE-588)4033422-3 (DE-588)4037944-9 (DE-588)4055916-6 (DE-588)4125698-0 |
| title | A brief history of mathematics a promenade through the civilizations of our world |
| title_auth | A brief history of mathematics a promenade through the civilizations of our world |
| title_exact_search | A brief history of mathematics a promenade through the civilizations of our world |
| title_full | A brief history of mathematics a promenade through the civilizations of our world Tianxin Cai ; translated by Tyler Ross |
| title_fullStr | A brief history of mathematics a promenade through the civilizations of our world Tianxin Cai ; translated by Tyler Ross |
| title_full_unstemmed | A brief history of mathematics a promenade through the civilizations of our world Tianxin Cai ; translated by Tyler Ross |
| title_short | A brief history of mathematics |
| title_sort | a brief history of mathematics a promenade through the civilizations of our world |
| title_sub | a promenade through the civilizations of our world |
| topic | Architektur (DE-588)4002851-3 gnd Künste (DE-588)4033422-3 gnd Mathematik (DE-588)4037944-9 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Kultur (DE-588)4125698-0 gnd |
| topic_facet | Architektur Künste Mathematik Sozialwissenschaften Kultur |
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