arminstraub.com

On August 18, 2009, the University of Newcastle hosted a CARMA workshop on Multidimensional Numerical Integration and Special Function Evaluation. Besides enjoying very interesting talks it's been my pleasure to present, together with James Wan, on progress of our joint work with Jon Borwein, Peter Donovan and Dirk Nuyens on expectations of random walks.

Attachment: 

randomwalkintegrals.pdf

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).

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 »

The Tulane Mathematics Department as of April 27, 2009. Unfortunately but naturally, a few people are missing.

For suitable functions f the integral

is equal to

To see why this is true, start with the last integral and write the n-th power of the inner integral as a multiple integral over variables x₁, …, x_n. Then change order of integration and evaluate read more »

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

This article has been published in Advances in Applied Mathematics (Volume 41, Issue 2, August 2008, Pages 255-264) and is available at doi:10.1016/j.aam.2007.10.001.

Errata and addenda are contained in an additional document.

Attachment: 

positivity.pdf

positivity-addendum.pdf

This is my diploma thesis, supervised by PD. dr. Ralf Gramlich, as submitted at Technische Universität Darmstadt 31 March 2008 with minor corrections.

The thesis is also available at http://arxiv.org/abs/0805.2403.

Attachment: 

diploma.pdf

These are complementary notes for a StuVo talk I gave at Technische Universität Darmstadt, 10 December 2007. While this text is supposed to be informal in nature, any corrections as well as suggestions are very welcome.

Attachment: 

nonstandard.pdf

Imagine you want to hire exactly one secretary. There is a fixed number, say, N persons available for this job and you may invite each of them for an interview. However, you have to tell each one right after the interview if you will hire her. Now, what is your strategy? read more »