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
Notes
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
MathBits
From the Monthly Over 100 Years Ago
Jonathan Sondow
One More Proof of the Irrationality of √2
Amrik Singh Nimbran