# Doing Calculus on the Rationals (with the help of Nonstandard Analysis)

Nonstandard Analysis is usually used to introduce infinitesimals into the real numbers in an attempt to make arguments in analysis more intuitive. The idea is that you construct a superset which contains the reals and also some infinitesimals, prove that some statement holds of , and then use a general “transfer principle” to conclude that […]

# Games Which are Impossible to Analyze

In the last post, I mentioned the computational complexity of various games. To be explicit, we consider each “game” to actually be a sequence of games for . For example, would be checkers played on an board. The problem was then to analyze the computational complexity of the function which takes and tells you which […]

# How to Show that Games are Hard

Peg Solitaire is a pretty popular game, often found in restaurants (including Cracker Barrel, if I remember correctly). It’s also NP-complete (by which I mean determining a winning strategy given the initial set-up is an NP-complete problem). You may have also heard of computational complexity results for Minesweeper (see here, for example). There are a […]