Harmony of the World《数学杂志》名家获奖文章精选
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ISBN：9780883855607
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简介
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 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, Pólya 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. Eight of the articles included have received the Carl B. Allendoerfer or Lester R. Ford Awards.
目录
Introduction
A Brief History of Mathematics Magazine
Part I: The First Fifteen Years
Perfect Numbers, Zena Garrett (NT)
Rejected Papers of Three Famous Mathematicians, Arnold Emch (H)
Review of Men of Mathematics, G. Waldo Dunnington (H)
Oslo under the Integral Sign, G. Waldo Dunnington (H)
Vigeland's Monument to Abel in Oslo, G. Wlado Dunnington (H)
The History of Mathematics, Otto Neugebauer (H)
Numerical Notations and Their Influence of Mathematics, D.H. Lehmer (NT)
Part II: The 1940's
The Generalized Weierstrass Approximation Theorem, Marshall H. Stone (An)
Hypatia of Alexandria, A.W. Richeson (H)
Gauss and the Early Development of Algebraic Numbers, E.T. Bell (Al)
Part III: The 1950s
The Harmony of the World, Morris Kline (M)
What Mathematics Has Meant to Me, E.T. Bell (M)
Mathematics and Mathematicians from Abel to Zermelo, Einar Hille (H)
Inequalities, Richard Bellman, (An)
A Number System with an Irrational Base, George Bergman (NT)
Part IV: The 1960s
Generalizations of Theorems about Triangles, Carl B. Allendoerfer (G)
A Radical Suggestions, Roy J. Dowling (NT)
Topology and Analysis, R.C. Buck (An, T)
The Sequence {sin n}, C. Stanley Ogilvy (An)
Probability Theory and the Lebesgue Integral, Truman Botts (PS)
On Round Pegs in Square Holes and Square Pegs inRound Holes, David Singmaster (G)
pt: 1832, Underwood Dudley (M)
Part V: The 1970s
Trigonometric Identities, Andy R. Magid (Al)
A Property of 70, Paul Erdös (NT)
Hamilton's Discovery of Quaternions, B.L. van der Waerden (Al, H)
Geometric Extremum Problems, G.D. Chakerian and L.H. Lange (G)
Pólya's Enumeration Theorem by Example, Alan Tucker (CG)
Logic from A to G, Paul R. Halmos (L)
Tiling the Plane with Congruent Pentagons, Doris Schattschneider (G)
Unstable Pollyhedral Structures, Michael Goldberg (G)
Part VI: The 1980s
Leonhard Euler, 1707, J.J. Burckhardt (H)
Love Affairs and Differential Equations, Steven H. Strogatz (An)
The Evolution of Group Theory, Israel Kleiner (Al)
Design of an Oscillating Sprinkler, Bart Braden (AM)
The Centrality of Mathematics in the Hsitory of Western Thought, Judith V. Grabiner (M)
Geometry Strikes Again, Branko Grünbaum (G)
Why Your Classes Are Larger than "Average", David Hemenway (PS)
The New Polynomial Invariants of Knots and Links, W.B.R. Lickorish and Kenneth C. Millett (CG,T)
Briefly Noted
The Problem Section
Index
About the Editors
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