How Euler Did Even More

Erscheinungsjahr 2015
ISBN: 978-0-88385-584-3
Verlag: Mathematical Association of America (MAA)

Buch, Englisch, 247 Seiten, Format (B × H): 177 mm x 254 mm, Gewicht: 458 g

C. Edward Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This book is the second collection of Sandifer's 'How Euler Did It' columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician in history, this volume will leave the reader marveling at Euler's clever inventiveness, which Sandifer explicates and puts in context.

Autoren/Hrsg.

Sandifer, C Edward

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

Preface; Part I. Geometry: 1. The Euler line; 2. A forgotten Fermat problem; 3. A product of secants; 4. Curves and paradox; 5. Did Euler prove Cramer's Rule?; Part II. Number Theory: 6. Factoring F5; 7. Rational trigonometry; 8. Sums (and differences) that are squares; Part III. Combinatorics: 9. St Petersburg paradox; 10. Life and death – part 1; 11. Life and death – part 2; Part IV. Analysis: 12. e, p and i: why is 'Euler' in the Euler identity; 13. Multi-zeta functions; 14. Sums of powers; 15. A theorem of Newton; 16. Estimating p; 17. Nearly a cosine series; 18. A series of trigonometric powers; 19. Gamma the function; 20. Gamma the constant; 21. Partial fractions; 22. Inexplicable functions; 23. A false logarithm series; 24. Introduction to complex variables; 25. The Moon and the differential; Part V. Applied Mathematics: 26. Density of air; 27. Bending light; 28. Saws and modeling; 29. PDEs of fluids; 30. Euler and gravity; Part VI. Euleriana: 31. Euler and the hollow earth: fact or fiction?; 32. Fallible Euler; 33. Euler and the pirates; 34. Euler as a teacher – part 1; 35. Euler as a teacher – part 2; Index; About the author.

Über Autor(innen)

Sandifer, C Edward
C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University in Danbury, Connecticut. He is Secretary of The Euler Society (www.EulerSociety.org). His first book, The Early Mathematics of Leonhard Euler, was published by the MAA in December 2006, as part of the celebrations of Euler's tercentennial in 2007. The MAA published a collection of forty 'How Euler Did It' columns in June 2007.