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.

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):

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.

Lothar Collatz anniversary

Lothar Collatz, who proposed (in 1937) the celebrated "3n+1 problem", was born 100 years ago in Arnsberg, Germany.

Mac Tutor Biography

Lothar Collatz at MGP