The Cylinder and the Moebius strip are a nice paradigm because the classical algebraic topology elements are the same for it: they are both homotopic to the circle, their cohomologies agree, their fundamental groups agree. Their metric properties like diameter or systoles agree (if implemented properly of course). Their main …
The work of John von Neumann and Oskar Morgensten from 1944 is usually considered the start of mathematical game theory. It builds on earlier work, especially of von Neumann in particular the elegant mini-max theorem of Neumann: let be the space of probability vectors in $mathbb R^m$ and let f(x,y) …
AXIOMS: Most basic mathematical structures are heavenly in the sense that they would be discussed in any part of the universe. In algebra these would be groups or rings. In topology these would be topological spaces or metric spaces, in probability theory it would be sigma algebras and stochastic processes. …
