Interactive Computations

Use the free Wolfram *Mathematica Player* to interact with the math
behind NUMB3RS.

AMITA packs her bag for class as CHARLIE writes a list on the board-- Non-negative matrices, linear programming, symmetric matrices, etc. CHARLIE Shall we call it 'Matrix Theory with Combinatorics?' AMITA How about 'Combinatorial Applications?' We should teach together-- you explain the theory, I show the applications.

The two-dimensional space Z_{3}×Z_{3} contains nine
points: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), and (2,2). The 48 invertible 2×2 matrices over Z_{3} form the general linear group known as
GL(2,3).

LARRY (re: the board) Do you know what this is? CHARLIE A Venn Diagram Intersection indicating suspects who match the description and have a history of violence. I'm helping Don. LARRY It's also an ancient religious symbol-- you may recognize it-- (outlines the 'fish') The Vesica Piscis, symbolizing the meeting of heaven and earth.

MEGAN (re: the Venn's) I remember these from geometry-- CHARLIE Venn diagrams are illustrations used in set theory, showing relationships among groups of things. We've deepened the analysis from what you learned in school by adding dimensions.

AMITA She's strong, Larry. Somebody has to do that work, and I'm glad it's somebody like Megan. He understands, he agrees, and-- speaking of strong women-- LARRY Dr. Ramanujan, I have a proposition for you. AMITA (teasing) Better not tell Charlie... LARRY Once or twice in a lifetime there are quests that require all we have to give and more. I am embarking on such a quixotic adventure and in thinking on who should be my Sancho Panza I come up with only one name-- yours. AMITA Larry, what are you talking about? LARRY I've accepted the D Zero team's offer to search for the Higgs Boson and I require a computational partner.

This demonstration shows quantum mechanical probability density for two particles in a one-dimensional well with
infinite walls. In classical statistical mechanics, identical particles are considered indistinguishable from each other
(the Boltzmann-Gibbs case). Quantum-mechanically, an elementary particle (meaning an irreducible finite-dimensional representation of the Poincaré group) is either a boson or a
fermion, according to whether its spin (the Casimir operator of the Poincaré group) is an integer or a half-integer.

CHARLIE Gonorrhea is a reportable STD, so based on public health data I can build a Sexual Networking Model for the city of Colina. We map infections back through multiple sex partners to find the source of the disease. It works like any network-- a family tree, Facebook, nerve endings--

In visualizing this genealogy of the descendants of United States President George Washington, you can determine whether
you wish to show all relationships or only those created by patrilineal or matrilineal descent.

AUDIENCE VISION - NEURAL NETWORK A network of nerves grows out of a brain, branch by smaller branch, getting more complex as it reaches nerve endings in a hand, which waves hello. CHARLIE (cont'd) Where each connection transmits data-- ancestry, friends, a nerve impulse. We notice the effect-- for example a hand waving-- and map the connections back to the source-- An electrical pulse travels from the hand back through the neural network to a particular area of the brain. END AUDIENCE VISION

Neurons communicate with each other primarily through a distinctive electrical signal known as the action potential.