Queries about either course should be emailed directly to me. These files will be updated as more information becomes available.
The Erdos-Selberg Controversy
Some 60 years ago a controversy erupted between Paul Erdos and Atle Selberg over the elementary proof of the Prime Number Theorem. Ernst Straus -- then a young mathematician at the scene -- wrote a description of the events. These have been published in Math Intelligencer, along with commentary by Ron Graham and myself, and a mathematical postscript by Carl Pomerance.The Probabilistic Method -- Third Edition!
Check out a sample material and table of contents of this book with Noga Alon.Click here for the frontcover front cover with a great picture of Uncle Paul
Click here for a richgetricher new Probabilistic Lens on Preferential Attachment
Click here for a phasetransition new chapter on the Erdos-Renyi Phase Transition, with particular emphasis on the Critical Window.
Click for more, available from archives here Click here Hannah1 Hannah2 Hannah3 Hannah4 for our most beautiful and most attentive reader. She's a fox! And, in strong competition: johanna SPECIAL OFFER: Yes, your child (grandchild, niece, nephew, sibling) can have an Erdos Number of 1+\sqrt{-1}! Just send a photo of him/her absorbed in reading/playing/teething our book and I'll post it!
Photos
Photo by MA
Click for family photos, or a photo of Paul Erdos.
News Flashes!
Alantha Newman and Aleksandar Nikolov have solved the Beck Three Permutaion Problem. I had offered a prize of 100 USD for its resolution. Here are Alantha and Sasha with the prize jpg and here is the arugment (in draft form!) itself pdf They found three permutations of 1,...,n=3^t so that for any coloring of 1,...,n with +1,-1 in one of the permutations there will be a prefix whose sum has absolute value at least ct. The conjecture had been that there was an absolute constant K so that for any three permutations of any size n there would be such a coloring where in each permutation all prefixes would have sum in [-K,+K], and so the conjecture was disproved.
Robin Moser, a student of Emo Welzl (ETH), has given an algorithmic implementation of the Lovasz Local Lemma. A rough explanation:
postscript LaTeX pdf Click for Moser's paper with Gabor Tardos .
Nikhil Bansal (at TU Eindhoven (Holland)) has given an algorithmic
implementation of my result that given any n sets on n points there
is a 2-coloring with all discrepencies less than 6 \sqrt{n}. I had
long conjectured that no algorithm would exist.
Semidefinite Programming is a key ingredient. His preprint,
Constructive Algorithms for Discrepancy Minimization, is available on arXiv.
Click for
Bansal's paper .
or here
postscript
LaTeX
pdf
for my own rough explanation. Even more recently Shachar Lovett and Raghu Meka
ArXiV link .
have come up with another argument, using a restricted Brownian Motion.
Cornell Probability School 2012
[Note: Any further information will be added at this location.] I will be giving two lectures at the Cornell Probability School this July 16,18, 2012. (days still tentative). Much of the material is captured in the News Flashes above. The Moser-Tardos implementation of the Lovasz Local Lemmapostscript LaTeX pdf Click for the Moser-Tardos paper
My own "six standard deviation" result as done by Bansal
Click for
Bansal's paper .
or
postscript
LaTeX
pdf
for my own rough explanation. Even more recently Shachar Lovett and Raghu Meka
ArXiV link .
The original proofs provide a good contrast and can be found in "The Probabilistic Method" by Noga Alon and myself. The Lovasz Local Lemma in Chapter 5 (numbering in the 3rd Edition, pretty much the same in previous editions) and Six Standard Deviations in Section 13.2.
High School MathCamps
This is a topic dear to my heart. I am former chair of an AMS committee that gives grants to High School Math Camps. Click for camp information or for information about donations to a worthy cause!Some Links
My Wikipedia pageErdos Wikipedia page
Danielle (daughter)'s website
Erdos Number Project
Budapest Semesters in Mathematics
Combinatorialist Rogue Gallery
[TOP]