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 
11/7  Fractals, dynamics, and dimension. (Cantor set, Sierpinski triangle, von Koch curve, Mandelbrot set, Julia sets; selfsimilarity, box, and Hausdorff dimensions.) 

11/14  Student presentations: Course projects. Juan Vargas. Sums of squares and the unit circle. Max Goering. LebesgueRadonNikodym Theorem. Minh Nguyen. A different approach to the inscribed triangle problem. 

11/21  Student presentations: Course projects. Wilson Jarrell. Quaternions. Leah Fredrick. NeoRiemannian music theory. Mike Miller. RiemannRoch 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 qbinomial Theorem. Hongyuan Zhan. Sobolev spaces on the circle and an application. Justin Miller. Euler's theorem on partitions. Charles Walker. General equilibrium in economics. 