# Math 210 schedule

Monday Wednesday Friday
Jan. 9

No class
Jan. 11

In Lecture:
• Overview of the course
• Two person games and the media: Why are so many news stories false?
• 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.

Homework:
A nice example of B.S.
Jan. 13

In Lecture:
• Mixed strategies in two person games
• Dominant strategies
• Optimal strategies for two person two option zero sum games
• Speakers vs. Listeners: The two-option case.

• On Bullshit (entire book)
• FAPP, Chapter 15.2
• How math can save your life, chapter 2.

Condoleeza Rice on how the government tries to shut down news stories
Jan. 16

No class, Martin Luther King holiday
Jan. 18

In Lecture:
• Speakers vs. Listeners: The two-option case, conclusions
• Extremism

Jan. 20

In Lecture:
• Extremism: Why parties out of power make those in power out to be extremists
• For two person two option zero sum games, dominant strategies exists if and only if saddlepoints do. This is not true of larger games.
• Why speaking bullshit and expecting bullshit form a saddlepoint in the absence of credibility.

Jan. 23

In Lecture:
• How can lying be a dominant political strategy? Expansion of the game theory model.
• Saddle points and dominant strategies in two person two option zero sum games.

Jan. 25

In Lecture:
• Completion of the proof that in the 2 by 2 case, saddlepoints exists if and only if dominant strategies do.
• For arbitrary zero sum games, if there is a dominant strategy there is a saddlepoint.
• Statement of the fundamental theorem of game theory.

Jan. 27

In Lecture:
• Against a fixed strategy, there is a an optimal mixed strategy which is pure
• Proof of the fundamental theorem for two by two games.

Jan. 30

In Lecture:
• Completion of the proof of the fundamental theorem for two-person two-option zero sum games

Feb. 1

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.

Feb. 3

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

Feb. 6

In Lecture:
• Dual linear programming problems
• Examples

Feb. 8

In Lecture:
• Proof of the equivalence of game theory and linear programming
• Using vertices to solve linear programming problems

Homework:
Feb. 10

In Lecture:
• First mid-term exam

Feb. 13

In Lecture:
• Applying linear programming to solve a 2 by 3 game.

Feb. 15

In Lecture:
• The 3 by 3 BS model involving only the listeners view of reality and the speaker's credibility

Feb. 17

In Lecture:
• Calculating vertices in the BS-model

Feb. 20

In Lecture:
• End of the discussion of the 3 by 3 BS model that takes into account only credibility

Feb. 22

In Lecture:
• The 3 by 3 BS model which considers only the benefit of lying
• Finding natural bases for n by m payoff matrices via the Gram Schmidt process.

Feb. 24

In Lecture:
• Proof the linear programming problems have solutions.

Feb. 27

In Lecture:
• Beginning of the proof that linear programming problems can be solved using vertices

March 1

In Lecture:
• End of the proof that linear programming problems can be solved using vertices

March 3

Video Lecture (no class meeting today):
• Partial conflict games
• Nash equilibria

• FAPP, Chapters 15.3 and 15.4

March 6

No class - spring break!
March 8

No class - spring break!
March 10

No class - spring break!
March 13

In Lecture:
• Zombie epidemic models

March 15

In Lecture:
• Zombie epidemic models, continued

March 17

In Lecture:
• Autonomous ordinary differential equations

March 20

In Lecture:
• Stability and linear stability of ordinary differential equations
• Jordan canonical forms

March 22

In Lecture:
• Applications to the zombie epidemic model

March 24

In Lecture:
• Discussion of possible term projects
• Jordan canonical forms and their exponentials
• Matrices with dependent rows have an eigenvalue equal to 0
• Finding explicit solutions of autonomous systems of ordinary differential equations

March 27

In Lecture:
• Stability conditions for equilibria
• Testing when two by two matrices have eigenvalues with negative real parts
• Eigenvectors and finding explicit solutions of differential equations.
• An updated zombie model incorporating interactions with reality

March 29

In Lecture:
• Analysis of the updated zombie model

March 31

In Lecture:
• End of discussion of zombie models
• Review for the midterm on April 3

April 3

In Lecture:
• Second Mid-term. The topics are partial conflict games and analyzing mathematical models using autonomous systems of differential equations.

April 5

In Lecture:
• Beginning of Probability theory
• Calculation of probabilities for finite sample spaces by counting and combinatorics
• Permuations and Combinations

• FAPP, Chapters 15.3 and 15.4
• FAPP, Chapters 8.1, 8.2
• How math can save your life, p. 47 - 50

April 7

In Lecture:
• The multinomial theorem
• Continuous probabilities and density functions

• FAPP, Chapters 8.1, 8.2
• How math can save your life, p. 47 - 50
• Probability and Statistics, 2nd edition, by Morris deGroot, section 1.9 Chapter 3.1-3.5.

April 10

In Lecture:
• Independent events

• FAPP, Chapters 8.1, 8.2
• How math can save your life, p. 47 - 50
• Probability and Statistics, 2nd edition, by Morris deGroot, section 1.9 Chapter 3.1-3.5.

April 12

In Lecture:
• Conditional probability
• Bayes theorem

• FAPP, Chapters 15.3 and 15.4
• FAPP, Chapters 8.1, 8.2
• How math can save your life, p. 47 - 50

April 14

In Lecture:
• Random variables
• Distribution and Density functions
• Expectation, Mean, Variance and Standard deviation

April 17

In Lecture:
• Scheduling of project presentations
• Conditional probability and prejudice
• The expectations of a sum of random variables is the sum of the expectations

• FAPP, Chapters 8.1, 8.2
• Probability and Statistics, 2nd edition, by Morris deGroot.

April 19

In Lecture:
• The variance of a sum of independent random variables is the sum of their variances
• The central limit theorem
• Examples of the central limit theorem
• Markov chains
No Video of class - technical difficulties!
April 21

In Lecture:
• The equilibrium probability distribution of a Markov chain

April 24

In Lecture:
• Project presentation: Mathematical sociology (Bartholf, Fini and Hawthorne)
• Project presentation: The evolution of cooperation (Brandt, Dura and Haidermota)

April 26

In Lecture:
• Project presentation: Expander graphs and their applications (Chan, Norleans and Sheth)
• Project presentation: Mathematics of Choice (Theory group) (Macropulos, Kennedy-Moore, Velliquette and Zou)
April 28

No class
May 1

May 3

May 5

May 8

Final class (Written projects due) in Room A6 of DRL labs, 9:00 a.m. - 11:00 a.m.
• Project presentation: Mathematics of Choice (App Group) (Fisher-Cobrie, Friedler, Henry and Morton)
• Project presentation: The page rank algorithm (Flick, Silkov, Weinstein and Zessar)
• Project presentation: How not to be wrong (Klausner, Sethudmadhavan and Sherwin)
• Project presentation: Information theory (Gumina, Delany and Luo)
May 10

No class
May 12

No class

Last updated: 4/11/17