Starting from my inbox, I discovered that
The Art of Computer Programming, Volume 4, Fascicle 4 : Generating All Trees–History of Combinatorial Generation
is available for sale now. Here is a totally no-commission-involved link to the item on Amazon.com. The previous three fascicles are of course also available.
“Computers and the Future of Mathematical Proofs”
Thomas Hales, Mellon Professor
U. of Pittsburgh, Dept. of Mathematics
Friday, February 24, 3:30 pm
2500 W. W. Posvar Hall
Presented by Pitt’s Ctr. for Philosophy of Science ANNUAL LECTURE SERIES
Abstract: It is relatively common for the mathematical proof of a single theorem to run hundreds or even thousands of pages. It has also become common for mathematical proofs to rely on computer-assisted calculations. An editor of one of the most prestigious mathematical journals has recently declared that it has become impossible to find peers who are willing to review computer code. As a result, the journal has started to publish theorems without any meaningful review of the underlying computer code. What do these developments mean for computers and the future of mathematical proofs?
A Geometric Perspective on Learning Theory and Algorithms
Professor Partha Niyogi, University of Chicago
Tuesday, February 28, 2006
3:30 -4:30 pm
5409 Wean Hall
Abstract:
Increasingly, we face machine learning problems in very high dimensional spaces. We proceed with the intuition that although natural data lives in very high dimensions, they have relatively few degrees of freedom. One way to formalize this intuition is to model the data as lying on or near a low dimensional manifold embedded in the high dimensional space. This point of view leads to a new class of algorithms that are “manifold motivated” and a new set of theoretical questions that surround their analysis. A central construction in these algorithms is a graph or simplicial complex that is data-derived and we will relate the geometry of these to the geometry of the underlying manifold. Applications to embedding, clustering, classification, and semi-supervised learning will be considered.
