This course (YMSC-Problem Solving Seminar) teaches important skills in problemsolving that are not taught in a systematic way in any other course. These skills areextremely valuable in preparing students for jobs and for graduate-level research.The teaching style will be a mixture of a lecture and a problem-solving session.Training will involve the study of problems from previous Putnam competitions, forwhich this course can be regarded as a useful preparation. An attempt will be madeto look for unifying mathematical ideas. General strategies for solving problems willalso be discussed.
AbstractThe shrinking target problem concerns the sizes of the sets of the points in a metric space whose orbits under a transformation fall into a family of shrinking subsets infinitely often. We study such problems for matrices with real coefficients which are transformations on the d-dimensional torus. We obtain a zero-one law for the Lebesgue measure of the corresponding shrinking target se...
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