Math 210 schedule

Tuesday Thursday
Jan. 9

No class
Jan. 11

In Lecture:
  • Overview of the course
  • Two person games and the media: Why is lying on the rise?
  • Strategies in two person games

Associated Reading:
  • On Bullshit (entire book)
  • FAPP = For all Practical Purposes, Chapter 15.1
  • How math can save your life, chapter 2. Here is an excerpt which describes two person game zero sum game theory. The recipe for determining optimal strategies for such games is described on pages 31 - 32.
  • Pages 736-739 of Raghavan's article on zero sum two person games

Homework:
A nice example of B.S.
Video of class (downloadable)
Jan. 16

In Lecture:
  • B.S. versus lying, examples from the news.
  • Two person zero sum games, continued. Examples involving credibility and the lying benefit.

Associated Reading:
  • On Bullshit (entire book)
  • FAPP = For all Practical Purposes, Chapter 15.1
  • How math can save your life, chapter 2. Here is an excerpt which describes two person game zero sum game theory. The recipe for determining optimal strategies for such games is described on pages 31 - 32.
  • Pages 736-739 of Raghavan's article on zero sum two person games

Video of class (downloadable)
Jan. 18

In Lecture:
  • Recap of analysis of the truth versus lying game
  • Why the lying benefit is necessary to explain speakers who always lie
  • Extremism
  • Multi-option, two person zero sum games
  • Dominant strategies, maximins, minimaxes and saddlepoints
  • Why speaking bullshit and expecting bullshit form a saddlepoint in the absence of credibility.

Associated Reading:
  • On Bullshit (entire book)
  • FAPP = For all Practical Purposes, Chapter 15.1
  • How math can save your life, chapter 2. Here is an excerpt which describes two person game zero sum game theory. The recipe for determining optimal strategies for such games is described on pages 31 - 32.
  • Pages 736-739 of Raghavan's article on zero sum two person games

Homework:
Video of class (downloadable)
Jan. 23

In Lecture:
  • Proof that maximin <= minimax
  • Proof that for a two person two option zero sum game, a dominant strategy exists if and only if there is a saddlepoint. This is not true of larger games.
  • For arbitrary zero sum games, if there is a dominant strategy there is a saddlepoint.

Associated Reading:
  • On Bullshit (entire book)
  • FAPP = For all Practical Purposes, Chapter 15.1
  • How math can save your life, chapter 2. Here is an excerpt which describes two person game zero sum game theory. The recipe for determining optimal strategies for such games is described on pages 31 - 32.
  • Pages 736-739 of Raghavan's article on zero sum two person games

Homework:
Video of class (downloadable)
Jan. 25

In Lecture:
  • Proof of the recipe for finding optimal strategies in a two-person two-option zero sum game

Associated Reading:
  • On Bullshit (entire book)
  • FAPP = For all Practical Purposes, Chapter 15.1
  • How math can save your life, chapter 2. Here is an excerpt which describes two person game zero sum game theory. The recipe for determining optimal strategies for such games is described on pages 31 - 32.
  • Pages 736-739 of Raghavan's article on zero sum two person games

Video of class (downloadable)
Jan. 30

In Lecture:
  • Three by three games
  • The three planes arising from the rock paper scissors game. The lower left corner is at the point (p_1,p_2,z) = (0,0,-1). The three planes are the graphs of the functions giving the expected payoff as a function of (p_1,p_2,1-p_1-p_2) played by player 1 against the three pure strategies of player 2.
  • Linear programming problems
    Associated Reading:
    Video of class (downloadable)
  • Feb. 1

    In Lecture:
    • Linear programming problems: Real world examples.
    • Statement of how optimal game theory strategies relate to linear programming

    Associated Reading:
    Video of class (downloadable) - to be posted
    Feb. 6

    No in class meeting today. Instead, please have a look at this Video (downloadable) giving an example of how to find optimal strategies via linear programming and the use of vertices.

    Associated Reading:

    Note: Skype office hours will be at 10 p.m. tonight. Please send ted an e-mail if you could like to be part of these office hours.
    Feb. 8
  • No class: Cancelled due to the Eagles parade!
  • Feb. 13

    In Lecture
    Feb. 15

    In Lecture
    • The Rock Paper Scissors game via linear programming
    • Polynomial time problems

    Associated Reading:
    Video of class (downloadable)
    Feb. 20

    In Lecture
    Feb. 22

    In Lecture
    • End of the proof that linear programming problems have solutions.

    Associated Reading:
    Video of class (downloadable)
    Feb. 27

    In Lecture
    March 1

    In Lecture
    • First mid-term exam

    Associated Reading:
    Video of class (downloadable)
    March 13

    In Lecture
    March 15

    In Lecture:
    • End of the proof that one can solve linear programming problems using vertices
    • Zombie epidemic models

    Associated Reading:
    Video of class (downloadable)
    March 20

    In Lecture:
    • Zombie epidemic models, continued
    • Autonomous ordinary differential equations

    Associated Reading:
    Video of class (downloadable)
    March 22

    In Lecture:
    • Using matrix exponentials to find explicit solutions of autonomous systems of ordinary differential equations
    • Stability and linear stability of ordinary differential equations
    • Eigenvalues of matrices

    Associated Reading:
    Video of class (downloadable)
    March 27

    In Lecture:
    • Jordan canonical forms and their exponentials
    • Testing when two by two matrices have eigenvalues with negative real parts
    • Equilibria of the updated zombie model

    Associated Reading:
    Video of class (downloadable)
    March 29

    In Lecture:
    • Stability analysis of the updated zombie model

    Associated Reading:
    Video of class (downloadable)
    April 3

    In Lecture:
    • Completion of the analysis of the updated zombie model
    • Beginning of Probability theory
    • Calculation of probabilities for finite sample spaces by counting and combinatorics

    Associated Reading:
    Video of class (downloadable)
    April 5

    In Lecture:
    • Using maple to plot vector fields
    • Permuations and Combinations
    • Multinomial theorem
    • Sigma-algebras and the borel subsets of the real numbers
    • Probability density functions

    Associated Reading:
    Video of class (downloadable)
    April 10

    In Lecture:
    • Review for the mid-term: Autonomous differential equations, stability and linear stability, modeling.
    • Conditional probability
    • Bayes theorem
    • Updating prior estimates of probabilities using new observations

    Associated Reading:
    Video of class (downloadable)
    April 12

    In Lecture:
    • Second mid-term
    April 17

    In Lecture:
    • Indpenedent events
    • Random variables
    • Density functions and distribution functions
    • Expectations and standard deviations
    • Constructing new random variables from old ones

    Associated Reading:
    Video of class (downloadable) - to be posted
    April 19

    In Lecture:
    • Central limit theorem
    • Poisson distributions
    • Graph theory

    Associated Reading: