tailieunhanh - THE AMERICAN MATHEMATICAL MONTHLY VOLUME 118

Mathematicians love to tell each other stories. We tell them to our students too, and they eventually pass them on. One of our favorites, and one that I heard as an undergraduate, is the story that Cantor was so surprised when he discovered one of his theorems that he said “I see it, but I don’t believe it!” The suggestion was that sometimes we might have a proof, and therefore know that something is true, but nevertheless still find it hard to believe. | THE AMERICAN MATHEMATICAL MONTHLY VOLUME 118 NO. 3 MARCH 2011 Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2011 to 195 Joseph A. Gallian for Distinguished Service to Mathematics Barbara Faires Was Cantor Surprised 198 Fernando Q. Gouvea On Legendre s Work on the Law of Quadratic Reciprocity 210 Steven H. Weintraub Equimodular Polynomials and the Tritangency Theorems 217 of Euler Feuerbach and Guinand Alexander Ryba and Joseph Stern The Sharkovsky Theorem A Natural Direct Proof 229 Keith Burns and Boris Hasselblatt A First Look at Differential Algebra 245 John H. Hubbard and Benjamin E. Lundell NOTES Lines of Best Fit for the Zeros and for the Critical Points 262 of a Polynomial Grant Keady Regular Matchstick Graphs 264 Sascha Kurz and Rom Pinchasi A Recursive Scheme for Improving the Original Rate of 268 Convergence to the Euler-Mascheroni Constant Edward Chlebus PROBLEMS AND SOLUTIONS 275 REVIEWS Logical Labyrinths. By Raymond M. Smullyan 283 Christopher C. Leary An Official Publication of the Mathematical Association of America Invitation to Complex Analysis Ralph P. Boas Second Edition revised by Harold P. Boas An ideal choice for a first course in complex analysis this book can be used either as a classroom text or for independent study. Written in an informal style by a master expositor the book distills more than half a century of experience with the subject into a lucid engaging yet rigorous account. The book reveals both the power of complex analysis as a tool for applications and the intrinsic beauty of the subject as a fundamental part of pure mathematics. Written at the level of courses commonly taught in American universities to seniors and beginning graduate students the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series Cauchy s theorem residues conformal mapping and harmonic functions by including accessible discussions of many intriguing .