MASS Seminar    Math 497D    Fall 2013  

 Thursdays 10:10-12:05  in 113 McAllister


Date Topic Homework
8/29   Means and inequalities
  (Arithmetic, geometric and power means; inequalities
  for the means, Holder and Minkowski inequalities)
  due 9/3   pdf  
9/5   Convex sets   (Basic properties, convex hull,
  Caratheodory's theorem,   separation)
  due 9/10   pdf  
9/12   Circle rotations and distribution of the first digits of powers
  due 9/17   pdf  
9/19
and
9/26
  Isometries and geodesics in
      Euclidean plane geometry,
      Spherical geometry, and
      Hyperbolic geometry.
  due 10/1   pdf  
10/3   Student presentations: Topics from the courses.
  Speakers: Aaron Calderon, Samantha Fairchild, Max Goering,
  Steven Metallo, Radoslav Vuchkov, Liuquan Wang
   
10/10   Groups, rings, and fields: basics and examples.
  Finite fields.
   
10/17   Exterior forms and symplectic vector spaces.
  Speaker: Andrew Hanlon.
  due 10/22   pdf    
10/24   Topological entropy.   due 10/29   pdf    
10/31   Career path in academia (V.S.)
  How to apply to graduate school (Professor Svetlana Katok)
        Slides   pdf
  Graduate school experience (Kurt Vinhage)
Read
Giving a talk
by Bryna Kra
pdf
11/7   Fractals, dynamics, and dimension.
  (Cantor set, Sierpinski triangle, von Koch curve, Mandelbrot set,
  Julia sets;   self-similarity, box, and Hausdorff dimensions.)
11/14   Student presentations: Course projects.
      Juan Vargas. Sums of squares and the unit circle.
      Max Goering. Lebesgue-Radon-Nikodym Theorem.
      Minh Nguyen. A different approach to the inscribed triangle
                             problem.
11/21   Student presentations: Course projects.
      Wilson Jarrell. Quaternions.
      Leah Fredrick. Neo-Riemannian music theory.
      Mike Miller. Riemann-Roch theorem.
      Joseph Kraisler. Ideals of commutative rings.
12/5   Student presentations: Course projects.
      Xu Zheyi. The Secretary Problem.
      Conrad Scott. Birkhoff Ergodic Theorem.
      Zhiying Xu. Another proof of the q-binomial Theorem.
      Hongyuan Zhan. Sobolev spaces on the circle and an application.   
      Justin Miller. Euler's theorem on partitions.
      Charles Walker. General equilibrium in economics.