Sandifer has been studying Euler for decades and is one of the world s leading experts on his work. This volume 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 of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.
Sandifer has been studying Euler for decades and is one of the world s leading experts on his work. This volume 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 of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.
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.
Inhaltsangabe
* Preface * Part I: Geometry * 1. The Euler Line (January 2009) * 2. A Forgotten Fermat Problem (December 2008) * 3. A Product of Secants (May 2008) * 4. Curves and Paradox (October 2008) * 5. Did Euler Prove Cramer's Rule (November 2009 - A Guest Column by Rob Bradley) * Part II: Number Theory * 6. Factoring F5 (March 2007) * 7. Rational Trigonometry (March 2008) * 8. Sums (and Differences) that are Squares (March 2009) * Part III: Combinatorics * 9. St. Petersburg Paradox (July 2007) * 10. Life and Death - Part 1 (July 2008) * 11. Life and Death - Part 2 (August 2008) * Part IV: Analysis * 12. e, π, and i: Why is "Euler" in the Euler Identity (August 2007) * 13. Multi-zeta Functions (January 2008) * 14. Sums of Powers (June 2009) * 15. A Theorem of Newton (April 2008) * 16. Estimating π (February 2009) * 17. Nearly a Cosine Series (May 2009) * 18. A Series of Trigonometric Powers (June 2008) * 19. Gamma the Function (September 2007) * 20. Gamma the Constant (October 2007) * 21. Partial Fractions (June 2007) * 22. Inexplicable Functions (November 2007) * 23. A False Logarithm Series (December 2007) * 24. Introduction to Complex Variables (May 2007) * 25. The Moon and the Differential (October 2009 - A Guest Column by Rob Bradley) * Part V: Applied Mathematics * 26. Density of Air (July 2009) * 27. Bending Light (August 2009) * 28. Saws and Modeling (November 2008) * 29. PDEs of Fluids (September 2008) * 30. Euler and Gravity (December 2009 - A Guest Column by Dominic Klyve) * Part VI: Euleriana * 31. Euler and the Hollow Earth: Fact or Fiction? (April 2007) * 32. Fallible Euler (February 2008) * 33. Euler and the Pirates (April 2009) * 34. Euler as a Teacher - Part 1 (January 2010) * 35. Euler as a Teacher - Part 2 (February 2010) * About the Author
* Preface * Part I: Geometry * 1. The Euler Line (January 2009) * 2. A Forgotten Fermat Problem (December 2008) * 3. A Product of Secants (May 2008) * 4. Curves and Paradox (October 2008) * 5. Did Euler Prove Cramer's Rule (November 2009 - A Guest Column by Rob Bradley) * Part II: Number Theory * 6. Factoring F5 (March 2007) * 7. Rational Trigonometry (March 2008) * 8. Sums (and Differences) that are Squares (March 2009) * Part III: Combinatorics * 9. St. Petersburg Paradox (July 2007) * 10. Life and Death - Part 1 (July 2008) * 11. Life and Death - Part 2 (August 2008) * Part IV: Analysis * 12. e, π, and i: Why is "Euler" in the Euler Identity (August 2007) * 13. Multi-zeta Functions (January 2008) * 14. Sums of Powers (June 2009) * 15. A Theorem of Newton (April 2008) * 16. Estimating π (February 2009) * 17. Nearly a Cosine Series (May 2009) * 18. A Series of Trigonometric Powers (June 2008) * 19. Gamma the Function (September 2007) * 20. Gamma the Constant (October 2007) * 21. Partial Fractions (June 2007) * 22. Inexplicable Functions (November 2007) * 23. A False Logarithm Series (December 2007) * 24. Introduction to Complex Variables (May 2007) * 25. The Moon and the Differential (October 2009 - A Guest Column by Rob Bradley) * Part V: Applied Mathematics * 26. Density of Air (July 2009) * 27. Bending Light (August 2009) * 28. Saws and Modeling (November 2008) * 29. PDEs of Fluids (September 2008) * 30. Euler and Gravity (December 2009 - A Guest Column by Dominic Klyve) * Part VI: Euleriana * 31. Euler and the Hollow Earth: Fact or Fiction? (April 2007) * 32. Fallible Euler (February 2008) * 33. Euler and the Pirates (April 2009) * 34. Euler as a Teacher - Part 1 (January 2010) * 35. Euler as a Teacher - Part 2 (February 2010) * About the Author
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