tailieunhanh - THE AMERICAN MATHEMATICAL MONTHLY VOLUME 118, NO. 1

The Eisenstein irreducibility critierion is part of the training of every mathematician. I first learned the criterion as an undergraduate and, like many before me, was struck by its power and simplicity. This article will describe the unexpectedly rich history of the discovery of the Eisenstein criterion and in particular the role played by Theodor Sch¨onemann. | THE AMERICAN MATHEMATICAL MONTHLY VOLUME 118 NO. 1 JANUARY 2011 Why Eisenstein Proved the Eisenstein Criterion and Why 3 Schonemann Discovered It First David A. Cox How Small Can a Polynomial Be Near Infinity 22 Jennifer M. Johnson and Janos Kollar Arnol d the Jacobi Identity and Orthocenters 41 Nikolai V. Ivanov NOTES Two Extensions of Results of Archimedes 66 Nicholas Pippenger On Polynomial Rings with a Goldbach Property 71 Paul Pollack Measurable Functions with a Given Set of Integrability 77 Exponents Alfonso Villani Operator Reverse Monotonicity of the Inverse 82 Alexis Akira Toda PROBLEMS AND SOLUTIONS 84 REVIEWS What s Math Got To Do With It By Jo Boaler 92 Virginia McShane Warfield An Official Publication of the Mathematical Association of America Cambridge Fantastic Titles from Cambridge FORTHCOMING. How to Fold It The Mathematics of Linkages Origami and Polyhedra Joseph O Rourke Hb 978-0-521-76735-4 176 pp. Pb 978-0-521-14547-3 Networks Crowds and Markets Reasoning About a Highly Connected World David Easley and Jon Kleinberg Hb 978-0-521-19533-1 744 pp. Elementary Differential Geometry Christian Bar Hb 978-0-521-89671-9 330 pp. Pb 978-0-521-72149-3 Prices subject to change. NIST Handbook of Mathematical Functions Edited by Frank w. J. Olver Daniel w. Lozier Ronald F. Boisvert and Charles w. Clark 1 Hb 1 CD-ROM 978-0-521-19225-5 1 Pb 1 CD-ROM 978-0-521-14063-8 968 pp. Kurt Godel Essays for his Centennial Edited by Solomon Feferman Charles Parsons and Stephen G. Simpson Lecture Notes in Logic Hb 978-0-521-11514-8 384 pp. NEW IN PAPERBACK Essentials of Statistical Inference G. A. Young and R. L. Smith Cambridge Series in Statistical and Probabilistic Mathematics Pb 978-0-521-54866-3 236 pp. BRAND NEW SERIES Creative Mathematics A Gateway to Research Alan F. Beardon AIMS Library of Mathematical Sciences Pb 978-0-521-13059-2 120 pp. Understanding Fluid Flow Grae Worster AIMS Library of Mathematical