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American Mathematical Monthly - December 2014

The Monthly finishes out 2014 in high style with 4 great articles and 6 terrific notes. Learn about the deep connections between numerical semigroups and cyclotomic polynomials in Pieter Moree's article "Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers." Bill Trench shows us that we might have missed something in his note "An Unnoticed Consequence of Szegö’s Distribution Theorem." Genevieve Walsh reviews Richard Schwartz's "Mostly Surfaces," and as usual, our Problems Section will keep you busy through the New Year. Ring in the New Year and the MAA Centennial celebration with us in the January Monthly.


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Table of Contents

Evolving Evolutoids

P. J. Giblin and J. P. Warder

Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers

Pieter Moree

A Perron Type Theorem on the Principal Eigenvalue of Nonsymmetric Elliptic Operators

Lei Ni

Absolute Convergence in Ordered Fields

Pete L. Clark and Niels J. Diepeveen


An Unnoticed Consequence of Szegö’s Distribution Theorem

William F. Trench

Coset Intersection Graphs for Groups

Jack Button, Maurice Chiodo, and Mariano Zeron-Medina Laris

Complex Descartes Circle Theorem

Sam Northshield

The Length of an Arithmetic Progression Represented by a Binary Quadratic Form

Pallab Kanti Dey and R. Thangadurai

Cosines and Cayley, Triangles and Tetrahedra

Marshall Hampton

A Note on the Spectral Theorem in the Finite-Dimensional Real Case

Felipe Acker

Problems and Solutions

Book Review

Mostly Surfaces - By Richard E. Schwartz

Reviewed by Genevieve S. Walsh

Editor’s EndNotes

Monthly Referees for 2014


From the Monthly Over 100 Years Ago

Jonathan Sondow

One More Proof of the Irrationality of √2

Amrik Singh Nimbran