Author | Anglin, W. S. author |
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Title | The Heritage of Thales [electronic resource] / by W. S. Anglin, J. Lambek |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0803-7 |
Descript | X, 331 p. online resource |
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 Hilbertโs 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 (Peanoโs 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 Fermatโs Last Theorem -- 19 What Is a Calculation? -- 20 Recursive and Recursively Enumerable Sets -- 21 Hilbertโs 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 Gรถdelโs Theorems -- 29 Proof of Gรถdelโs Incompleteness Theorem -- 30 More about Gรถdelโs Theorems -- 31 Concrete Categories -- 32 Graphs and Categories -- 33 Functors -- 34 Natural Transformations -- 35 A Natural Transformation between Vector Spaces -- References