AMS Feature Column
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AMS Feature Column - RSS Feeden-usHow to Grow and Prune a Classification Tree
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In what follows, we will describe the work of Breiman and his colleagues as set out in their seminal book "Classification and Regression Trees." Theirs is a very rich story, and we will concentrate on only the essential ideas...Why Do We Expect Lots of Twin Primes?
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One important question is, how are prime numbers distributed among the integers? The answer is, in a very few words, rather randomly, given certain basic statistics...The Topology of Impossible Spaces
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The purpose of this month's article is to bring once more to the public consciousness some work of Sir Roger Penrose...Mathematics and Chemistry: Partners in Understanding Our World
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Here I will give a sketch of some of the issues arising from using mathematics in fields outside of mathematics, but for this column I will use examples from the area of chemistry...Congressional Redistricting and Gerrymandering
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We'll look at some measures that have been created to constrain gerrymandering...Feeling Your Way Around in High Dimensions
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The simplest objects of interest in any dimension, which are also the basis for approximating arbitrary objects, are the convex polytopes. and in this column I'll explain how to begin to probe them...The Knots in the Quipu, and in the Friar's Belt
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In a canonical numerical quipu, each pendent (or subsidiary) displays a number: a positive integer, expressed in decimal notation...Magical Mathematics - A Tribute to Martin Gardner
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Perhaps no one has done more to make the world aware of mathematics than Martin Gardner...How to Make a 3D Print
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Mathematically speaking, the 3D print is constructed from a 1-dimensional path. This article will describe how to find that path...Stereographic Projection
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In effect, stereographic projection wraps the plane around the sphere, missing only that one point...Periods
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After a brief introduction to the combinatorics on words, which builds on some of the same ground that was discussed in a prior note, I will look at a remarkable theorem due to the mathematicians Herbert Wilf and Nathan Jacob Fine...The Polish Attack on Enigma II: Zygalski sheets
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I'll say a little bit about how the mathematics was applied to reading German messages, up until a drastic change in procedure by the Germans, and I'll say more about how the Poles recovered after this change...Fedorov's Five Parallelohedra
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We will see how some elegant ideas of Conway and Sloane, introduced in the 1990s, lead to Fedorov's determination of the five parallelohedra....Spherical Dodecahedral Space
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In this column I propose to work through this construction and to start by analyzing spherical dodecahedral space as an object in polyhedral geometry. ....Words and More Words
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Here I will take a brief look at some of the ways mathematics has looked at words in the hope of exploiting the resulting ideas....The Frobenius Problem: How I bought Chicken McNuggets with exact change
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Though the problem seems like one from discrete mathematics, we will see an unexpected interplay between the continuous and discrete worlds as we use somewhat elementary techniques from calculus to arrive at a solution...More ENIGMA
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What I want to discuss in this feature is one part of Enigma operation that has been much written about elsewhere, but which still causes some confusion. This is the way in which key presses lead to rotor motion....Galileo's Arithmetic
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The manuscripts allow us very unusual, if not unique, access to the private calculations of a great scientist; it is as if we could look over his shoulder and watch him at work...Sustainability
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Can mathematics help us understand issues of sustainability and make it possible to realize enjoyable lives for all the people who share this planet, now and far into the future?...Using Projective Geometry to Correct a Camera
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There's nothing particularly deep in this problem or the solution, but I hope that it demonstrates some of the pleasure to be found in using one's mathematical intuition...