Jens Harlander, Wed. October 28, 2:40-3:30 pm, MG 120.
Introduction to Computational Complexity
Complexity theory provides ways of measuring the difficulty of computational mathematics problems. Some problems are indeed impossibly difficult (your Math 108 and 143 students are right after all!). For example, there does not exist an algorithm that decides whether a polynomial (in an arbitrary number of variables) with integer coefficients has integer roots. However for many difficult problems, simple strategies work well in practice as long as one is willing to ignore a hopefully sparse set of inputs. I will discuss basic features of the theory, give you more examples of impossibly hard problems and tell you about the relevance of all of this to Internet security.