This page lists my non-research publications. My research publications can be found here.
I occasionally write book reviews for the Mathematical Association of America's online book review column.
| Review of An Introduction to Game-Theoretic Modelling, by Michael Mesterton-Gibbons |
| Review of The Geometry of Numbers, by C. D. Olds, Anneli Lax, and Giuliana Davidoff |
| Review of A New Kind of Science, by Stephen Wolfram |
| Review of The Math Life, by Wendy Conquest, Bob Drake, and Dan Rockmore |
If you are interested in Wolfram's book, you should look through W. Edwin Clark's massive collection of reviews, as well as commentary on earlier scientists with similar ideas.
A couple of publications aren't online. The Monthly problem deals with the following strange numerical fact. Let F_n be the n-th Fibonacci number. Then the continued fraction of (F_(n+1)/F_n)^5 does not behave the way one might expect. It starts with many 11's, as it should since it is converging to the fifth power of the golden ratio (which has all 11's in its continued fraction), but when the pattern breaks down there's a huge partial quotient, followed by a new repeating pattern. Here's an example. That does not seem to hold for any other exponents. You can download my original submission to the Monthly.
| Mathematics at Microsoft Research, Mathematical Association of American FOCUS, Feb. 2001, pp. 8-9 |
| Problem 10457, American Mathematical Monthly 102 (1995), p. 464 |
The first paper is an exposition of some basic algebraic number theory, leading up to a proof of quadratic reciprocity using cyclotomic fields. My coauthors and I intended to revise it some more, but since we haven't worked on it since 1996 we probably never will. The second paper is some sketchy lecture notes on elementary representation theory for finite groups.
The quantum groups paper is my "minor thesis". In the mathematics department at Harvard, graduate students are required to write a minor thesis, which is an expository paper on an unfamiliar topic one doesn't plan to specialize in; there is a three week time limit.
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Algebraic number theory and quadratic reciprocity (with Joshua Greene and Jonathan Hanke) |
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Outline of basic representation theory |
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Quantum groups |