# 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

• On Bullshit (entire book)
• FAPP = For all Practical Purposes, Chapter 15.1
• How math can save your life, chapter 2.
• Pages 736-739 of Raghavan's article on zero sum two person games

Homework:
A nice example of B.S.
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.

• On Bullshit (entire book)
• FAPP = For all Practical Purposes, Chapter 15.1
• How math can save your life, chapter 2.
• Pages 736-739 of Raghavan's article on zero sum two person games

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.

• On Bullshit (entire book)
• FAPP = For all Practical Purposes, Chapter 15.1
• How math can save your life, chapter 2.
• Pages 736-739 of Raghavan's article on zero sum two person games

Homework:
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.

• On Bullshit (entire book)
• FAPP = For all Practical Purposes, Chapter 15.1
• How math can save your life, chapter 2.
• Pages 736-739 of Raghavan's article on zero sum two person games

Homework:
Jan. 25

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

• On Bullshit (entire book)
• FAPP = For all Practical Purposes, Chapter 15.1
• How math can save your life, chapter 2.
• Pages 736-739 of Raghavan's article on zero sum two person games

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
• FAPP, Chapter 15.2
• How math can save your life, chapter 2
• Pages 736-739 of Raghavan's article on zero sum two person games

• Feb. 1

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

• FAPP, Chapter 15.2
• How math can save your life, chapter 2
• Pages 736-739 of Raghavan's article on zero sum two person games
• The part of this Wikipedia article on linear programming up to the section titled "Augmented form (slack form)".

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.

• Pages 736-739 of Raghavan's article on zero sum two person games

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
• More on converting game theory problems to linear program
• Solving linear programming problems with vertices

• Pages 736-739 of Raghavan's article on zero sum two person games

Feb. 15

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

• Pages 736-739 of Raghavan's article on zero sum two person games

Feb. 20

In Lecture
• Proof that optimal strategies can be determined by linear programming
• Beginning of the proof that linear programming problems have soliutions
• Open and closed subsets of R^n

• Pages 736-739 of Raghavan's article on zero sum two person games

Feb. 22

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

• Pages 736-739 of Raghavan's article on zero sum two person games

Feb. 27

In Lecture
• Review and discussion of homework 3

• Pages 736-739 of Raghavan's article on zero sum two person games

March 1

In Lecture
• First mid-term exam

• How math can save your life, chapter 2
• These notes on linear programming problems and finding optimal strategies.
• Pages 736-739 of Raghavan's article on zero sum two person games

March 13

In Lecture
• Applications to the 3 by 3 B.S. model
• The difference between diplomacy and B.S.
• When people are neutral about B.S., it is an optimal strategy.
• Proof that one can solve linear programming problems using vertices

• These notes on linear programming problems and finding optimal strategies.
• Pages 736-739 of Raghavan's article on zero sum two person games

March 15

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

March 20

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

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

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

March 29

In Lecture:
• Stability analysis of the updated zombie model

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

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

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

April 12

In Lecture:
• Second mid-term
April 17

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