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

                    DAVID
          Perfect for what, Charlie?

                    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.

                    LIZ
          A math plan...

                    CHARLIE
          Economic Modeling Theory, actually.

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:
                    CHARLIE
          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...

                    ALAN
          Go to Larry? For basketball?

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

                    AMITA
          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 »

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:
                    DON
          We don't know that, Charlie.  Guy
          finds out he's surrounded, outgunned
          and out-numbered... Could
          be more than he bargained for...

                    CHARLIE
          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 »

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:
                    CHARLIE
          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?

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

                    CHARLIE
          Well... yeah.  

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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