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.

## Friday, July 30, 2010

## 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):

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).*

- YT link.
- Rule 184
- Fukś and Boccara's "Generalized deterministic traffic rules" (1998)

## 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

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!!!

## Tuesday, July 6, 2010

### 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

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