Friday, July 30, 2010

Structure and Randomness in the Prime Numbers (Terence Tao)

Terence Tao: Structure and Randomness in the Prime Numbers, UCLA
Slides: pdf, powerpoint

Lecture for a general audience: Terence Tao is UCLA's Collins Professor of Mathematics, and the first UCLA professor to win the prestigious Fields Medal.

Tuesday, July 27, 2010

Johann Bernoulli (1667 - 1748) anniversary

Johann Bernoulli (1667 - 1748) was born on July 27, 7^3 years ago, in Basel, Switzerland. He was Euler's "mathematical parent".

And here is the... "sophomore's dream" - neat identities due to Johann Bernoulli (1697):

Wednesday, July 21, 2010

A traffic flow simulation

This traffic flow educational project with Matlab features a gradually increasing car density starting from an initial value of 0.2. There are 250 cells. The update rule (describing the transition from time t to time t + 1): apply rule 184, after which randomly select a position - if occupied, nothing happens, while if empty, introduce a car at the selected place with probability 0.7. The image follows the first 500 time units. Notice the transition to a congested regime happening at some point (emerging shock waves). In the picture, free cells are blue, while cells occupied by "cars" are red.

Shockwave traffic jams


Traffic jams replicated on the test-track (courtesy of Mathematical Society of Traffic Flow, Japan).

Sunday, July 18, 2010

Memories


Just discovered online an old colloquium announcement from 1997 - a talk that I gave at the University of Montana, Missoula. Great city, amazing people, unforgettable nature, and a very nice campus.

Tuesday, July 13, 2010

On the ranges of discrete exponentials

Florin Caragiu and Mihai Caragiu, “On the ranges of discrete exponentials,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 42, pp. 2265-2268, 2004. doi:10.1155/S016117120431 2056

Reference link

On the Ranges of Discrete Exponentials

Sunday, July 11, 2010

A great book by J. W. S. Cassels

"An introduction to the geometry of numbers" was the main reference for my 1987 senior capstone thesis (Methods of Geometry of Numbers) at the University of Bucharest. A great book! I just found out that today is the anniversary of the author, J. W. S Cassels (born on July 11, 1922 in Durham, England). Happy birthday!!!