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We will not require any background not lined within the core courses. That is, we will attempt to clarify the algebraic topology so that students with a background in evaluation can observe, and clarify the analysis in order that college students with a background in algebraic topology can comply with. In the third half, we’ll see the method to use ergodic concept to count issues, for example closed geodesics on a manifold of unfavorable curvature. In order to do this, we will show that the geodesic flow is ergodic, and we will introduce dynamical ζ-functions and the Ruelle switch operator.
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