Gerald L. Alexanderson e Peter Ross
Mathematical Association of America | 2007 | 302 páginas | rar - pdf |3,8 Mb
link (password : matav)
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.
Contents
The name of each article is followed by a notation indicating the field of mathematics from which it comes: (Al) algebra, (AM) applied mathematics, (An) analysis, (CG) combinatorics and graph theory, (G) geometry, (H) history, (L) logic, (M) miscellaneous, (NT) number theory, (PS) probability/statistics, and (T) topology.
Introduction . .vii
A Brief History of Mathematics Magazine . . xi
Part I: The First Fifteen Years .. .1
Perfect Numbers, Zena Garrett (NT) .. .3
Rejected Papers of Three Famous Mathematicians, Arnold Emch (H) . 5
Review of Men of Mathematics, G. Waldo Dunnington (H) .. 9
Oslo under the Integral Sign, G. Waldo Dunnington (H) . 11
Vigeland’s Monument to Abel in Oslo, G. Waldo Dunnington (H) . .19
The History of Mathematics, Otto Neugebauer (H) . .. .23
Numerical Notations and Their Influence on Mathematics, D. H. Lehmer (NT) . .29
Part II: The 1940s .33
The Generalized Weierstrass Approximation Theorem, Marshall H. Stone (An) . . .35
Hypatia of Alexandria, A. W. Richeson (H) .. . 45
Gauss and the Early Development of Algebraic Numbers, E. T. Bell (Al) . . 51
Part III: The 1950s . . 69
The Harmony of the World, Morris Kline (M) .. 71
What Mathematics Has Meant to Me, E. T. Bell (M) .. .79
Mathematics and Mathematicians from Abel to Zermelo, Einar Hille (H) . 81
Inequalities, Richard Bellman (An) . . 95
A Number System with an Irrational Base, George Bergman (NT) . 99
Part IV: The 1960s .107
Generalizations of Theorems about Triangles, Carl B. Allendoerfer (G) . .109
A Radical Suggestion, Roy J. Dowling (NT) . .115
Topology and Analysis, R. C. Buck (An, T). 117
The Sequence fsin ng, C. Stanley Ogilvy (An) . .. . 121
Probability Theory and the Lebesgue Integral, Truman Botts (PS) . . . 123
On Round Pegs in Square Holes and Square Pegs in Round Holes, David Singmaster (G) . . 129
t : 1832–1879, Underwood Dudley (M) . . . . 133
Part V: The 1970s . . 135
Trigonometric Identities, Andy R. Magid (Al) . . .137
A Property of 70, Paul Erdos (NT) . . . .139
Hamilton’s Discovery of Quaternions, B. L. van der Waerden (Al, H) . . 143
Geometric Extremum Problems, G. D. Chakerian and L. H. Lange (G . .151
Polya’s Enumeration Theorem by Example, Alan Tucker (CG) . 161
Logic from A to G, Paul R. Halmos (L) . . . . 169
Tiling the Plane with Congruent Pentagons, Doris Schattschneider (G) .. . 175
Unstable Polyhedral Structures, Michael Goldberg (G) . . 191
Part VI: The 1980s . .197
Leonhard Euler, 1707–1783, J. J. Burckhardt (H) . . .199
Love Affairs and Differential Equations, Steven H. Strogatz (An) . 211
The Evolution of Group Theory, Israel Kleiner (Al) . . . 213
Design of an Oscillating Sprinkler, Bart Braden (AM) . . . 229
The Centrality of Mathematics in the History of Western Thought, Judith V. Grabiner (M) . ..237
Geometry Strikes Again, Branko Gr¨unbaum (G) .. 247
Why Your Classes Are Larger than “Average”, David Hemenway (PS) . 255
The New Polynomial Invariants of Knots and Links, W. B. R. Lickorish and Kenneth C. Millett (CG, T) . 257
Briefly Noted .. 273
The Problem Section . . . 279
Index . . . .281
About the Editors . . . 287
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