Mathematics

This Sage package accompanies the paper Special values of generalized log-sine integrals.

Besides the package you find a notebook which shows basic usage. If you don't have access to Sage you can still look at the attached pdf file logsine-sage-usage.pdf which illustrates the package in use.

Note that the package is preliminary and has several rough edges—please report any issues to math@arminstraub.com. Integration into the core of Sage is a hoped for possibility. read more »

Attachment: 

logsine.sage

logsine-sage-usage.sws

logsine-sage-usage.pdf

This Mathematica package accompanies the paper Special values of generalized log-sine integrals. Besides the package you find a notebook which shows basic usage. If you don't have access to Mathematica you can still look at the attached pdf file logsine-usage.pdf which illustrates the package in use.

Note that the package is preliminary and hasn't received final touches yet—please report any issues to math@arminstraub.com. read more »

Attachment: 

logsine.m

logsine-usage.nb

logsine-usage.pdf

Let's assume you wish to have children—moreover, you want just as many girls as boys. In fact, you are so very much determined that you set out to not stop getting kids until the number of girls matches precisely the number of boys. How big a family will that make you, on average? read more »

PSLQ is an algorithm to find integer relations between a set of real numbers. Last summer I had written an introduction to PSLQ, how it works, and how it can and has been used. This introduction, which can be downloaded below, should be easily understandable by an advanced undergraduate student.

The PSLQ algorithm is one of the basic tools of experimental mathematics. A very basic and naive implementation for Mathematica is attached to this post. The file pslq-usage.nb contains instructions and examples. read more »

Attachment: 

pslq.pdf

pslq.m

pslq-usage.nb

Recently, I got myself a Nook because it seems perfect for reading while traveling when you (literally, with the current baggage restrictions) can't afford to have several rather voluminous books with you. While hoping that this Nook will lower hurdles for picking up some non-mathematical reading again, another big hope was that I would be able to read mathematical papers (and possibly books) on it so as to spare the rain forest and me. read more »

Attachment: 

cenbin-nook.pdf

ramanujantau-nook.pdf

I very much enjoy reading the "What Is…?" column in the Notices of the AMS. Unfortunately, there seemed to be no index to this column. I have therefore created this one in the hope that it'll be helpful to others as well.

1. What is…an amoeba? — Oleg Viro, September 2002
2. What is…the monster? — Richard Borcherds, October 2002

Ming-Hua Lin from the University of Regina sent me the following problem:

Problem: Let p ≥ 2 be an integer, and define

Show that . read more »

Today, I have been playing a little bit with Apollonian circle packings. Here is the code I wrote in Mathematica to visualize such packings (see below for an example). read more »

Attachment: 

apolloniancirclepackings.nb

Recently, I have been doing experiments involving q-binomial coefficients in Mathematica. Starting with version 7, Mathematica is prepared for some q-business; in particular, there exists a function named QBinomial giving the q-analog of Binomial. However, this implementation turned out to not be fast enough for my needs. Here is an alternative approach which is not only way faster but provides a full factorization. read more »