Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22) (Dolciani Mathematical Expositions)

Dunham Provides A Brief Overview Of Euler's Life And Delves Into The Conceptualization And Proofs Behind His Contributions To Mathematics, Including Euler's Seminal Work Opera Omnia. Euler And Number Theory -- Euler And Logarithms -- Euler And Infinite Series -- Euler And Analytic Number Theory -- Euler And Complex Variables -- Euler And Algebra -- Euler And Geometry -- Euler And Combinatorics. Edited By William Dunham. Includes Bibliographical References And Index. Contents (ix)......Page 7 Acknowledgments (xi)......Page 8 Preface (xv)......Page 11 Biographical Sketch (xix)......Page 15 1. Euler and Number Theory (1)......Page 25 2. Euler and Logarithms (17)......Page 41 3. Euler and Infinite Series (39)......Page 62 4. Euler and Analytic Number Theory (61)......Page 84 5. Euler and Complex Variables (81)......Page 103 6. Euler and Algebra (103)......Page 125 7. Euler and Geometry (125)......Page 147 8. Euler and Combinatorics (149)......Page 171 Conclusion (171)......Page 192 Appendix Euler's Opera Omnia (175)......Page 195 Index (181)......Page 201 Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work. Of all branches of mathematics, none is so natural-nor so deceptively difficult-as the theory of numbers.