Asymptotic Methods for Combinatorics and Probability (Spring '07)
Organizer:
Ross M. Richardson.
Location: AP&M 6436
Time: M,W, 2pm.
Announce:
We will be following (roughly) the Odlyzko book. Thus, by monday
we expect everyone to have read up to “Sums of Positive Terms”. Additionally,
you should look at the notation section of chapter 8 in “Concrete Mathematics”.
Finally, you should review basic complex analysis for the following:
Cauchy Integral Formula, Liouville's Theorem, Maximum Modulus Principle,
analytic and meromorphic funcions.
Schedule:
- 5/30/07: BGFs,PGFs,Convergence in Distribution--Ross M. Richardson
- 5/23/07: Steve Butler
- 5/16/07: Mellin Transforms and Rice's Method--Paul Horn
- 5/14/07: More Tauberian Theorems--Paul Horn
- 5/9/07: Tauberian Theorems and Applications--Federica Garin
- 5/7/07: Laplace Methods--Federica Garin
- 5/2/07: The Saddle Point Method--Chris Chang
- 4/30/07: The Saddle Point Method (p.77-88 de Bruijn)--Chris Chang
- 4/25/07: Analytic Generating Functions/Coefficient Extraction 2--Ross Richardson
- 4/23/07: Analytic Generating Functions/Coefficient Extraction 1--Ross Richardson
- 4/18/07: Generating Functions 2--Steve Butler
- 4/16/07: Generating Functions 1--Steve Butler
- 4/11/07: Summation Methods--Paul Horn.
- 4/9/07: Summation Methods--Paul Horn.
To Do:
Multiple Singularities (Flajolet 250), Longest Run in Words (Flajolet 287), Polylogarithms (Flajolet 390), Tree Recurances (Flajolet 409), Compare Bender and Darboux's method to Tauberian Theorems (Flajolet 415), Saddle Point Examples, perhaps Integer Partitions (Flajolet 504),
multivariate asymptotics and limit distributions (Flajolet 541).
Reading and Links:
