Makers of Mathematics (Dover Books on Mathematics) by Hollingdale, Stuart -- Read -- Imperial Library of Trantor

Index

Title Page Copyright age Contents Preface List Of Illustation Chapter 1: The beginnings

1. Prehistory 2. Egypt 3. Mesopotamia

Chapter 2: Early Greek mathematics

1. Introduction 2. The Greek contribution 3. The textual sources 4. Thales and Pythagoras 5. The classification of numbers 6. The discovery of incommensurability 7. Hippocrates of Chios 8. ‘Ruler and compasses’ constructions 9. The three classical problems 10. Hippias of Elis 11. Eudoxus of Cnidus 12. The Eudoxan theory of proportion 13. The method of exhaustion 14. Eudoxan astronomy

Chapter 3: Euclid and Apollonius

1. Introduction 2. Euclid: his life and works 3. The Elements of Euclid 4. The regular pentagon and the golden section 5. The Euclidean algorithm 6. Rational approximations 7. Apollonius: his life and works 8. The Conics of Apollonius

Chapter 4: Archimedes and the later Hellenistic period

1. Archimedes of Syracuse 2. Archimedes’ works 3. Quadrature of the Parabola 4. On the Sphere and Cylinder 5. On Conoids and Spheroids 6. The Archimedean spiral 7. The Method 8. Angle trisection by neusis 9. Construction of the regular heptagon 10. Numerical studies 11. The later Hellenistic age 12. Ptolemy of Alexandria 13. Diophantus of Alexandria 14. Pappus of Alexandria

Chapter 5: The long interlude

1. Introduction 2. China 3. India 4. The Muslim world 5. Leonardo of Pisa 6. An architectural note

Chapter 6: The Renaissance

1. Introduction 2. Nicolas Chuquet 3. Luca Pacioli and Michael Stifel 4. Girolamo Cardano 5. Tartaglia and the strange story of the cubic equation 6. Cardano’s published treatment of the cubic equation

Chapter 7: Descartes, Fermat and Pascal

1. Introduction 2. René Descartes 3. Descartes’s philosophical position 4. La Géométrie 5. Pierre de Fermat 6. Fermat and coordinate geometry 7. Towards the calculus 8. The theory of numbers 9. Blaise Pascal 10. Pascal’s theorem and projective geometry 11. The cycloid 12. The mathematical theory of probability

Chapter 8: Newton

1. Introduction 2. His life 3. Newton the man 4. Newton the natural philosopher 5. Analysis by infinite series 6. The fluxional calculus 7. Optical experiments and speculations 8. Geometrical researches 9. Early thoughts on mechanics and gravitation 10. Researches in numerical mathematics 11. Later years: the priority dispute

Chapter 9: Newton’s Principia

1. The writing and publication of the Principia 2. The content of the Principia 3. Book 1: The motion of bodies in ‘empty’ space 4. Book 2: The motion of bodies in resisting media 5. Book 3: The System of the World 6. The General Scholium

Chapter 10: Newton’s circle

1. Introduction 2. JohnWallis 3. Wallis’s algebraic investigations 4. Isaac Barrow 5. Barrow and Newton 6. Barrow’s geometrical lectures 7. Edmond Halley 8. Halley’s cometary studies 9. Roger Cotes 10. Editor of the Principia 11. Cotes’s mathematical researches

Chapter 11: Leibniz

1. Introduction 2. The universal genius 3. The characteristica generalis 4. The origins of the Leibnizian calculus 5. A case study of the process of mathematical invention 6. The modern notation of the calculus 7. The transmutation rule and a famous series 8. The publication of the Leibnizian calculus 9. Summing up: Newton and Leibniz

Chapter 12: Euler

1. Introduction 2. ‘Analysis incarnate’ 3. General analysis 4. Infinite series 5. Calculus and differential equations 6. The calculus of variations 7. Analytical and differential geometry 8. Topology 9. The theory of numbers 10. Physics mechanics and astronomy

Chapter 13: D’Alembert and his contemporaries

1. Introduction 2. Jean d’Alembert 3. D’Alembert’s correspondents 4. The foundations of the calculus 5. Differential equations 6. General analysis 7. Mechanics and astronomy 8. The triumph of analysis

Chapter 14: Gauss

1. Introduction 2. The Prince of Mathematicians 3. The fundamental theorem of algebra 4. The theory of numbers 5. The theory of functions and infinite series 6. Error theory and numerical analysis 7. Differential geometry 8. Non-Euclidean geometry

Chapter 15: Hamilton and Boole

1. Introduction 2. William Hamilton 3. Researches in optics and dynamics 4. The creation of quaternions 5. George Boole 6. The algebra of logic and sets 7. Matrices 8. The liberation of algebra

Chapter 16: Dedekind and Cantor

1. The arithmetization of analysis 2. Richard Dedekind 3. Dedekind’s theory of irrational numbers 4. Georg Cantor 5. Cantor’s theory of infinite sets and transfinite numbers 6. The nineteenth century and after

Chapter 17: Einstein

1. Introduction 2. A simple genius 3. The pre-relativity papers of 1905 4. The Special Theory of Relativity 5. Derivation of the transformation equations 6. Relativistic mass and energy 7. The General Theory of Relativity 8. Experimental tests of the General Theory 9. Einstein’s later researches

Appendices

1. A Eudoxan treatment of similarity 2. Euclid’s proof that the number of primes is infinite 3. Viète’s solution of Van Roomen’s problem 4. Viète’s formula for π 5. Gauss’ Euclidean construction of the 17-sided regular polygon 6. Leonardo’s generalized ‘squares’ problem 7. A case of mistaken Newtonian identity 8. Fermat’s Last Theorem proved?

References Index