Graduate student seminar – Very large finite numbers

October 15, 2008

Today I gave a talk at the Graduate student seminar on some recent combinatorial results that produce sequences that grow very fast (in a precise sense). The talk is titled Very large finite numbers and here is the .pdf file.

It is based on two recent papers of mine that can be found on my papers page: Regressive functions on pairs, that has been submitted to the European Journal of Combinatorics, and Goodstein’s function, that appeared in Revista Colombiana de Matemáticas 41 (2)(2007), 381-391.

For a nice introduction to incompleteness and Goodstein’s theorem, see Will Sladek’s paper here.


175 -Error from Simpson's rule

October 15, 2008

I am following the nice article “Simpson’s rule is exact for quintics” by Louis A. Talman, in its computation of the error term for approximating integrals using Simpson’s rule. The article was published in the American Mathematical Monthly, vol 113 February 2006, pp. 144-155. Albertsons library is subscribed to the Monthly, so you can find the article there. You can also find it in Dr. Talman’s page. More details on Taylor’s formula can be found on section 8.9 of the book.