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Hardcover ISBN:  9780883855607 
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List Price:  $115.00 $90.00 
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AMS Member Price:  $86.25 $67.50 
Hardcover ISBN:  9780883855607 
Product Code:  SPEC/56 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859667 
Product Code:  SPEC/56.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Hardcover ISBN:  9780883855607 
eBook ISBN:  9780883859667 
Product Code:  SPEC/56.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 

Book DetailsSpectrumVolume: 56; 2007; 287 pp
Who would expect to find in the pages of Mathematics Magazine the first full treatment of one of the more important and oftcited twentieth century theorems in analysis, the StoneWeierstrass 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, Pólya's enumeration theorem, and group theory) and stories of mathematicians (Hypatia, Gauss, E. T. Bell, Hamilton, and Euler). The list of authors is starstudded: E. T. Bell, Otto Neugebauer, D. H. Lehmer, Morris Kline, Einar Hille, Richard Bellman, Judith Grabiner, Paul Erdős, B. L. van der Waerden, Paul R. Halmos, Doris Schattschneider, J. J. Burckhardt, Branko Grunbaum, and many more.

Table of Contents

The First Fifteen Years [ MR 2307942 ]

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. Waldo Dunnington (H)

The History of Mathematics, Otto Neugebauer (H)

Numerical Notations and Their Influence on Mathematics, D. H. Lehmer (NT)

The 1940s [ MR 2307942 ]

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)

The 1950s [ MR 2307942 ]

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)

The 1960s [ MR 2307942 ]

Generalizations of Theorems about Triangles, Carl B. Allendoerfer (G)

A Radical Suggestion, 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 in Round Holes, David Singmaster (G)

$\pi _t$: 1832–1879, Underwood Dudley (M)

The 1970s [ MR 2307942 ]

Trigonometric Identities, Andy R. Magid (Al)

A Property of 70, Paul Erdős (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 Polyhedral Structures, Michael Goldberg (G)

The 1980s [ MR 2307942 ]

Leonhard Euler, 1707–1783, 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 History 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)


Reviews

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


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Who would expect to find in the pages of Mathematics Magazine the first full treatment of one of the more important and oftcited twentieth century theorems in analysis, the StoneWeierstrass 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, Pólya's enumeration theorem, and group theory) and stories of mathematicians (Hypatia, Gauss, E. T. Bell, Hamilton, and Euler). The list of authors is starstudded: E. T. Bell, Otto Neugebauer, D. H. Lehmer, Morris Kline, Einar Hille, Richard Bellman, Judith Grabiner, Paul Erdős, B. L. van der Waerden, Paul R. Halmos, Doris Schattschneider, J. J. Burckhardt, Branko Grunbaum, and many more.

The First Fifteen Years [ MR 2307942 ]

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. Waldo Dunnington (H)

The History of Mathematics, Otto Neugebauer (H)

Numerical Notations and Their Influence on Mathematics, D. H. Lehmer (NT)

The 1940s [ MR 2307942 ]

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)

The 1950s [ MR 2307942 ]

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)

The 1960s [ MR 2307942 ]

Generalizations of Theorems about Triangles, Carl B. Allendoerfer (G)

A Radical Suggestion, 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 in Round Holes, David Singmaster (G)

$\pi _t$: 1832–1879, Underwood Dudley (M)

The 1970s [ MR 2307942 ]

Trigonometric Identities, Andy R. Magid (Al)

A Property of 70, Paul Erdős (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 Polyhedral Structures, Michael Goldberg (G)

The 1980s [ MR 2307942 ]

Leonhard Euler, 1707–1783, 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 History 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)

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