The Harmony of the World
75 Years of Mathematics Magazine
Published on 30. December 2007
Book
Hardback
287 pages
978-0-88385-560-7 (ISBN)
Description
Who would expect to find in the pages of Mathematics Magazine the first full treatment of one of the more important and oft-cited twentieth-century theorems in analysis, the Stone-Weierstrass Theorem in an article by Marshall Stone himself? Where else would one look for proofs of trigonometric identities using commutative ring theory? Or one of the earliest and best expository articles on the then new Jones knot polynomials, an article that won the prestigious Chauvenet Prize? Or an amusing article purporting to show that the value of pi has been time dependent over the years? These and much more are in this collection of the best from Mathematics Magazine. Readers are inundated with new material in the many mathematical journals. Gems from past issues of Mathematics Magazine or the Monthly or the College Mathematics Journal are read with pleasure when they appear, but get pushed into the background when the next issues arrive. So from time to time it is rewarding to go back and see just what marvelous material has been published over many years, articles now to some extent forgotten. There is history of mathematics (algebraic numbers, inequalities, probability and the Lebesgue integral, quaternions, Polya's enumeration theorem, and group theory) and stories of mathematicians (Hypatia, Gauss, E. T. Bell, Hamilton, and Euler). The list of authors is star-studded: E. T. Bell, Otto Neugebauer, D. H. Lehmer, Morris Kline, Einar Hille, Richard Bellman, Judith Grabiner, Paul Erdos, B. L. van der Waerden, Paul R. Halmos, Doris Schattschneider, J. J. Burckhardt, Branko Grunbaum, and many more.
Reviews / Votes
A wonderful resource of information about the recent history of mathematics as well as some gems about how important advances in earlier mathematical history were made."" - Mary Coupland, Australian Math Teacher""In all, this is an attractive, urbane, and inviting selection of mathematics, culture, and history, seen through one important journal's lens. Editor Alexanderson is well qualified, having edited the Magazine himself in the lates 1980s."" - Paul Zorn, Mathematical Reviews
More details
Series
Language
English
Place of publication
Washington DC
United States
Dimensions
Height: 274 mm
Width: 197 mm
Thickness: 21 mm
Weight
765 gr
ISBN-13
978-0-88385-560-7 (9780883855607)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Gerald L. Alexanderson is the Valeriote Professor of Science at Santa Clara University in California and former chair of the Department of Mathematics and Computer Science. Peter Ross is a Senior Lecturer in the Department of Mathematics and Computer Science at Santa Clara University, California.
Content
Introduction; A Brief History of Mathematics Magazine; Part I. The First Fifteen Years: Perfect Numbers Zena Garrett; Rejected Papers of Three Famous Mathematicians Arnold Emch; Review of 'Men of Mathematics' G. Waldo Dunnington; Oslo under the Integral Sign G. Waldo Dunnington; Vigeland's Monument to Abel in Oslo G. Waldo Dunnington; The History of Mathematics Otto Neugebauer; Numerical Notations and Their Influence on Mathematics D. H. Lehmer; Part II. The 1940s: The Generalized Weierstrass Approximation Theorem Marshall H. Stone; Hypatia of Alexandria A. W. Richeson; Gauss and the Early Development of Algebraic Numbers E. T. Bell; Part III. The 1950s: The Harmony of the World Morris Kline; What Mathematics Has Meant to Me E. T. Bell; Mathematics and Mathematicians from Abel to Zermelo Einar Hille; Inequalities Richard Bellman; A Number System with an Irrational Base George Bergman; Part IV. The 1960s: Generalizations of Theorems about Triangles Carl B. Allendoerfer; A Radical Suggestion Roy J. Dowling; Topology and Analysis R. C. Buck; The Sequence {sin n} C. Stanley Ogilvy; Probability Theory and the Lebesgue Integral Truman Botts; On Round Pegs in Square Holes and Square Pegs in Round Holes David Singmaster; ?t : 1832-1879 Underwood Dudley; Part V. The 1970s: Trigonometric Identities Andy R. Magid; A Property of 70 Paul Erdoes; Hamilton's Discovery of Quaternions B. L. van der Waerden; Geometric Extremum Problems G. D. Chakerian and L. H. Lange; Polya's Enumeration Theorem by Example Alan Tucker; Logic from A to G Paul R. Halmos; Tiling the Plane with Congruent Pentagons Doris Schattschneider; Unstable Polyhedral Structures Michael Goldberg; Part VI. The 1980s: Leonhard Euler, 1707-1783 J. J. Burckhardt; Love Affairs and Differential Equations Steven H. Strogatz; The Evolution of Group Theory Israel Kleiner; Design of an Oscillating Sprinkler Bart Braden; The Centrality of Mathematics in the History of Western Thought Judith V. Grabiner; Geometry Strikes Again Branko Gruenbaum; Why Your Classes Are Larger than 'Average' David Hemenway; The New Polynomial Invariants of Knots and Links W. B. R. Lickorish and Kenneth C. Millett; Briefly noted; The problem section; Index; About the editors.