Original Math Notes
All Seasons
Episode 412: Power--Explore the Math
Original Math Notes
Episode 412: Power
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 3:
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.

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).
Scene 6:
                   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.
Scene 6:
                   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.

The Chow-Ruskey Order 5 Venn Diagram »

There are five polygons made up of touching squares, colored red, blue, yellow, green, and gray.
Scene 15:
                   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.
Scene 29:
                   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--

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.
Scene 29:
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.
 
Wolfram: Creators of Mathematica, Leaders in Math & Computation
Wolfram|Alpha