The Heritage of Thales / by W. S. Anglin, J. Lambek
(Undergraduate Texts in Mathematics, Readings in Mathematics)
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1995 |
| 本文言語 | 英語 |
| 大きさ | X, 331 p : online resource |
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| 内容注記 | 0 Introduction 0 Introduction I: History and Philosophy of Mathematics 1 Egyptian Mathematics 2 Scales of Notation 3 Prime Numbers 4 Sumerian-Babylonian Mathematics 5 More about Mesopotamian Mathematics 6 The Dawn of Greek Mathematics 7 Pythagoras and His School 8 Perfect Numbers 9 Regular Polyhedra 10 The Crisis of Incommensurables 11 From Heraclitus to Democritus 12 Mathematics in Athens 13 Plato and Aristotle on Mathematics 14 Constructions with Ruler and Compass 15 The Impossibility of Solving the Classical Problems 16 Euclid 17 Non-Euclidean Geometry and Hilbert’s Axioms 18 Alexandria from 300 BC to 200 BC 19 Archimedes 20 Alexandria from 200 BC to 500 AD 21 Mathematics in China and India 22 Mathematics in Islamic Countries 23 New Beginnings in Europe 24 Mathematics in the Renaissance 25 The Cubic and Quartic Equations 26 Renaissance Mathematics Continued 27 The Seventeenth Century in France 28 The Seventeenth Century Continued 29 Leibniz 30 The Eighteenth Century 31 The Law of Quadratic Reciprocity II: Foundations of Mathematics 1 The Number System 2 Natural Numbers (Peano’s Approach) 3 The Integers 4 The Rationals 5 The Real Numbers 6 Complex Numbers 7 The Fundamental Theorem of Algebra 8 Quaternions 9 Quaternions Applied to Number Theory 10 Quaternions Applied to Physics 11 Quaternions in Quantum Mechanics 12 Cardinal Numbers 13 Cardinal Arithmetic 14 Continued Fractions 15 The Fundamental Theorem of Arithmetic 16 Linear Diophantine Equations 17 Quadratic Surds 18 Pythagorean Triangles and Fermat’s Last Theorem 19 What Is a Calculation? 20 Recursive and Recursively Enumerable Sets 21 Hilbert’s Tenth Problem 22 Lambda Calculus 23 Logic from Aristotle to Russell 24 Intuitionistic Propositional Calculus 25 How to Interpret Intuitionistic Logic 26 Intuitionistic Predicate Calculus 27 Intuitionistic Type Theory 28 Gödel’s Theorems 29 Proof of Gödel’s Incompleteness Theorem 30 More about Gödel’s Theorems 31 Concrete Categories 32 Graphs and Categories 33 Functors 34 Natural Transformations 35 A Natural Transformation between Vector Spaces References |
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| 一般注記 | This is intended as a textbook on the history, philosophy and foundations of mathematics, primarily for students specializing in mathematics, but we also wish to welcome interested students from the sciences, humanities and education. We have attempted to give approximately equal treatment to the three subjects: history, philosophy and mathematics. History We must emphasize that this is not a scholarly account of the history of mathematics, but rather an attempt to teach some good mathematics in a historical context. Since neither of the authors is a professional historian, we have made liberal use of secondary sources. We have tried to give ref cited facts and opinions. However, considering that this text erences for developed by repeated revisions from lecture notes of two courses given by one of us over a 25 year period, some attributions may have been lost. We could not resist retelling some amusing anecdotes, even when we suspect that they have no proven historical basis. As to the mathematicians listed in our account, we admit to being colour and gender blind; we have not attempted a balanced distribution of the mathematicians listed to meet today's standards of political correctness. Philosophy Both authors having wide philosophical interests, this text contains perhaps more philosophical asides than other books on the history of mathematics. For example, we discuss the relevance to mathematics of the pre-Socratic philosophers and of Plato, Aristotle, Leibniz and Russell. We also have vi Preface presented some original insights |
| 著者標目 | *Anglin, W. S. author Lambek, J. author SpringerLink (Online service) |
| 件 名 | LCSH:History LCSH:Mathematics LCSH:Mathematics -- Study and teaching 全ての件名で検索 FREE:History FREE:History of Science FREE:History of Mathematical Sciences FREE:Mathematics, general FREE:Mathematics Education |
| 分 類 | DC23:509 |
| 巻冊次 | ISBN:9781461208037 
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| ISBN | 9781461208037 |
| URL | http://dx.doi.org/10.1007/978-1-4612-0803-7 |
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