Thursday,   September 11,    at 2:00 P.M.  in BR306

SPEAKER:    Jeff Norden

TITLE:    Fun with Fixed Points

Free refreshments at 1:20 in the Bruner second floor faculty lounge.

Given a function f from a set to itself, a fixed point of f is just what you should expect: a point that doesn't move. To be more precise, it is a point x such that f(x)=x

Fixed points occur in many different settings. I'll discuss some of the ones that I find interesting.

Here is an easy but fun problem that you can certainly work out yourself. Let X be a finite set and let f be a function from X to itself which is chosen randomly from all such functions. Show that the probability that f has at least one fixed point is more than 63.2% (i.e., 79 out of 125).

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