There are ten kinds of people in the world. Those who think in binary and those who don't.

Talks Slides for various talks.
## Course Information

Spring 2014 I will teach Algebra II. Students must have taken Algebra I
to register but it is NOT necessary that they took it from me and it
is NOT necessary that they took it Fall 2013. Click
here for more information.
Students may email with queries at any time.

## The Erdos-Selberg Controversy

Over 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.
click here for the article

## 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 and
jazmin
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.

## Math News !

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.
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.

## 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 page

Erdos Wikipedia page

Danielle (daughter)'s website

Erdos Number Project

Budapest Semesters in Mathematics

Combinatorialist
Rogue Gallery
[TOP]