User:Arided/MathForGameDesigners

The intial outline (subject to change) is as follows. This is developing in a conversation with Stefan Kreitmayer. The idea is to take the basic concepts of "games" and explore them using mathematics.


 * 1) Space (including graphs and other combinatorial models of space)
 * 2) Time (focusing on movement)
 * 3) Logic (proofs, strategy... and narrative)
 * 4) Signals, learning, language, and chaos (detecting and creating patterns)
 * 5) Information theory and Game theory (mathematical models of social interaction)
 * 6) Cybernetics and ecology (building and interacting with systems)

Some links and thoughts

 * http://en.wikipedia.org/wiki/Space_%28mathematics%29
 * http://en.wikipedia.org/wiki/Simplex
 * http://en.wikipedia.org/wiki/Simplicial_complex
 * http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.61.9708&rep=rep1&type=pdf&guid=ON (this gives me a *really* good idea... so don't worry if the paper itself seems annoyingly incomprehensible)
 * http://en.wikipedia.org/wiki/Mathematical_proof (bla bla bla)
 * http://en.wikipedia.org/wiki/Proof_%28rapper%29 (actual #1 hit on google)
 * http://en.wikipedia.org/wiki/Proof_%28play%29 (hit on broadway)
 * http://en.wikipedia.org/wiki/Information_theory
 * http://en.wikipedia.org/wiki/Game_theory
 * http://en.wikipedia.org/wiki/Games_People_Play_%28book%29
 * http://ttic.uchicago.edu/~smale/papers/math_foundation_of_learning.pdf
 * http://en.wikipedia.org/wiki/Formal_language
 * http://linkinghub.elsevier.com/retrieve/pii/0031320372900180
 * http://en.wikipedia.org/wiki/Cybernetics

Potentially interesting books:


 * http://en.wikipedia.org/wiki/Winning_Ways_for_your_Mathematical_Plays

This will all need to be sorted out and chewed over further. The idea I alluded to above is to use the first couple of weeks to develop "discretized calculus on graphs" and use it to create some simulations. It would probably be good to have some worked examples so that this stuff doesn't have to be developed from scratch by participants.

Various ideas in the list of links get quite "advanced" and may not be super useful (e.g. Smale on learning!?!?). Whereever advanced mumbo-jumbo can be cut out and replaced with anything more directly related to the basic stuff that defines "games", that would be cool.