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

Associated Reading:
  • 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.
Video of class (downloadable)
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.

Associated Reading:
  • 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
Video of class (downloadable)
Jan. 16

No class, Martin Luther King holiday
Jan. 18

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

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

In Lecture:
  • Extremism: Why parties out of power make those in power out to be extremists
  • maximin, minimax and saddlepoints
  • 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.

Associated Reading:
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.

Associated Reading:
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.

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

Associated Reading:
Video of class (downloadable)
Jan. 30

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

Associated Reading:
Video of class (downloadable)
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.

Associated Reading:
Video of class (downloadable)
Feb. 3

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

Associated Reading:
Video of class (downloadable)
Feb. 6

In Lecture:
  • Dual linear programming problems
  • Examples

Associated Reading:
Video of class (downloadable)
Feb. 8

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

Associated Reading:
Homework:
Video of class (downloadable)
Feb. 10

In Lecture:
  • First mid-term exam

Associated Reading:
Feb. 13


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


Associated Reading:
Video of class (downloadable)
Feb. 15

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


Associated Reading:
Video of class (downloadable)
Feb. 17

In Lecture:
  • Calculating vertices in the BS-model


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

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


Associated Reading:
Video of class (downloadable)
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.


Associated Reading:
Video of class (downloadable)
Feb. 24

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


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

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


Associated Reading:
Video of class (downloadable)
March 1


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


Associated Reading:
Video of class (downloadable)
March 3

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


Associated Reading:
  • FAPP, Chapters 15.3 and 15.4

Video lecture (downloadable)
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

Associated Reading:
Video of class (downloadable)
March 15

In Lecture:
  • Zombie epidemic models, continued

Associated Reading:
Video of class (downloadable)
March 17

In Lecture:
  • Autonomous ordinary differential equations

Associated Reading:
Video of class (downloadable)
March 20

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

Associated Reading:
Video of class (downloadable)
March 22

In Lecture:
  • Applications to the zombie epidemic model

Associated Reading:
Video of class (downloadable)
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

Associated Reading:
Video of class (downloadable)
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

Associated Reading:
Video of class (downloadable)
March 29

In Lecture:
  • Analysis of the updated zombie model

Associated Reading:
Video of class (downloadable)
March 31

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

Associated Reading:
Video of class (downloadable)
April 3

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

Associated Reading:
April 5

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

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

Video of class (downloadable)
April 7

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

Associated Reading:
  • 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.

Video of class (downloadable)
April 10

In Lecture:
  • Independent events

Associated Reading:
  • 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.

Video of class (downloadable)
April 12

In Lecture:
  • Conditional probability
  • Bayes theorem

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

Video of class (downloadable)
April 14

In Lecture:
  • Random variables
  • Distribution and Density functions
  • Expectation, Mean, Variance and Standard deviation
br>Associated Reading:
Video of class (downloadable)
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

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

Video of class (downloadable)
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
br>Associated Reading:
No Video of class - technical difficulties!
April 21

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

Associated Reading:
Video of class (downloadable)
April 24

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

Video of class (downloadable) - to be posted
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

Reading days, no class
May 3

Reading days, no class
May 5

Reading days, no class
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
Send e-mail comments to: ted@math.upenn.edu