Original Math Notes
All Seasons
Season 5
Episode 516: Cover Me
Emergence of an envelope from throw trajectories at different angles
Emergence of an envelope from throw trajectories at different angles
Scene 4:
          The good news is, it's still in its
          infancy.  Supplies are limited.
          There're only a handful of suspected
          dealers.  Conditions are perfect...

          Perfect for what, Charlie?

          We don't have to wait for an
          epidemic before we act.  I've got a
          plan to stop Ice now, before it
          takes off.

          A math plan...

          Economic Modeling Theory, actually.

The Keynesian ISLM Model »

The Keynesian ISLM Model
The IS-LM model is a graphical representation of a Keynesian model of the macroeconomy. The model solves for equilibrium in both the goods market and the money market, taking certain parameters as given. The IS line represents the goods market, and the LM line represents the money market.
Scene 43:
          Let's put it on the board.

Charlie tosses the ball to Alan, writes "GAME TEMPO" under
the list they're compiling - "GYM TEMPERATURE", "OPTIMUM

                    CHARLIE (cont'd)
          Tell you another thing I'd like to
          look at, and we'll want to recruit
          Larry's expertise for this...

          Go to Larry? For basketball?

          Physics, Dad... I'll bet there's
          an optimum arc for a shot that'll
          maximize its chance of going in...

          Good point, put it up.

As Charlie turns to the board, his CELL PHONE RINGS.  He
tosses the chalk to Amita.  While Charlie takes the call,
Amita adds "SHOT ARC" to their list.

Trajectory of a Soccer Ball »

Trajectory of a Soccer Ball
This Demonstration illustrates the various factors that influence the trajectory of a soccer ball. It shows the many decisions a player would make to pinpoint a shot, especially in relation to the location of the goalie.
Scene 59:
          We don't know that, Charlie.  Guy
          finds out he's surrounded, outgunned
          and out-numbered... Could
          be more than he bargained for...

          Look, right now, we hold an
          unexpected asymmetric advantage
          over the Nash Equilibrium...
            (off Cam)
          Game Theory...

Set of Nash Equilibria in 2x2 Mixed Extended Games »

Set of Nash Equilibria in 2x2 Mixed Extended Games
Consider a bimatrix (2×2) mixed extended game. The set of Nash equilibria (red) in a particular game is determined as the intersection of the graphs of best response mappings of the blue and green players; its vertices are given at the bottom.
Scene 63:
          So let's say my economic modeling
          theory works, and we destroy the
          Hawaiian Ice market... something
          else is just going to take its
          place, right?

          Probably... Did you think you
          could fix the world?

          Well... yeah.  

Modeling Return Distributions »

Modeling Return Distributions
We use numerical maximum likelihood estimation to obtain the parameters governing probability distributions that might plausibly generate the daily, weekly, monthly, or quarterly return distributions of stocks from the Dow 30. The candidate distribution types should probably be continuous and supported on the whole real line.
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