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
Applications?'  We should teach
together-- you explain the theory,
I show the applications.
```

# GL(2,p) and GL(3,3) Acting on Points »

The two-dimensional space Z3×Z3 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 Z3 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.
```

# Venn Diagrams »

This Demonstration shows all 127 nonempty unions and intersections of three sets A, B, C.
```                   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
```

# The Chow-Ruskey Order 5 Venn Diagram »

There are five polygons made up of touching squares, colored red, blue, yellow, green, and gray.
```                   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.
```

# Wavefunctions of Identical Particles »

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,
```

# Genealogy Graphs from XML »

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
```

# Neural Impulses: The Action Potential in Action »

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