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MARCH 2003

**Yuen-Gin Gung and Dr. Charles Y. Hu Award for**

Distinguished Service to Clarence F. Stephens

by Robert E. Megginson

meggin@msri.org

**Quatum Computation**

by Stan Gudder

sgudder@math.du.edu

Quantum computers may be the next revolution in the computer industry. Primitive quantum computers have already been constructed and fast quantum algorithms for factorization and data searches have been derived. Employing mathematical methods from linear algebra, this paper surveys some of the latest developments in quantum computation. This is an exciting new field that is only about ten years old. The topics covered included quantum circuits, superdense coding, quantum teleportation, Grover's search algorithm, quantum Fourier transforms, and Shor’s factorzation algorithm.

**The Crystallographic Restriction, Permutations, and Goldbach’s Conjecture**

by John Bamberg, Grant Cairns, and Devin Kilminster

john.bam@maths.uwa.edu.au, g.cairns@latrobe.edu.au, devin@maths.uwa.edu.au

We examine the connection between the crystallographic restriction, the orders of the elements of the symmetric group, and Goldbach’s conjecture. In particular, we observe that Goldbach’s conjecture, in the strong sense that every even integer greater than six can be written as the sum of two distinct odd primes, is equivalent to the following condition: for every even integer n greater than six there is an integer matrix of order pq for distinct odd primes p and q, and there is no smaller integer matrix of this order.

**Generalizing the Petr-Douglas-Neumann Theorem on n-gons**

by Stephen B. Gray

stevebg@adelphia.net

In 1908, Karel Petr published an unusual theorem about triangle constructions on n-gons. It was rediscovered twice in the early 1940s by Jesse Douglas and B. H. Neumann. The author rediscovered it again in 1961, and has recently generalized it. In both the special and general versions, the integer n can range from three upwards without limit, and the number of lines in a full illustration makes it impossible to visualize for all but very small n. The generalization also stands out because of the large number of defining parameters that can be varied independently. Its new proof needs only the most elementary methods in complex variables and matrices. Several avenues are open for even further extension of this result.

**Problems and Solutions**

**Notes**

**Can Kirkman’s Schoolgirls Walk Abreast by Forming Arithmetic Progressions?**

by Lorenz Halbeisen

halbeis@qub.ac.uk

**Newton’s Identities Once Again!**

by Ján Minác

minac@uwo.ca

**An Illuminating Counterexample**

by Michael Hardy

hardy@math.mit.edu

**A Norm Inequality for Hermitian Operators**

by Ritsuo Nakamoto

nakamoto@base.ibaraki.ac.jp

**Reviews**

**Fragments of Infinity, A Kaleidoscope of Math and Art**

by Ivars Peterson

Reviewed by William Mueller

wmueller@alum.mit.edu

**Mathematical Models in Population Biology and Epidemiology **

by Fred Brauer and Carlso Castillo-Chávez

Reviewed by Shandelle M. Henson

henson@andrews.edu

**Telegraphic Reviews**