1. Course Notes

•  MATH 719 

     Homeworks     Problem set 1     Problem set 2      

•  MATH 720 

     Homeworks     Midterm     Final Exam

•  MATH 733 

     Lecture notes taught by Prof. Seppäläinen

•  MATH 734 

     Lecture notes taught by Prof. Seppäläinen

•  MATH 821 

     Lecture notes taught by Prof. Tran

      Problem set 1     Problem set 2

2. Summer Schools

• Differential Geometry in Continuum Mechanic, taught by Prof. Thiffeault

• Stochastic Modeling of Particles, taught by Prof. Thiffeault

• Calculus and convergence in metric measure spaces, taught by Prof. Ambrosio

• Isoperimetric properties of smooth and non-smooth spaces with lower curvature bounds, taught by Prof. Antonelli

• Compact Manifolds with Positive Ricci Curvature and Unbounded Nilpotent Fundamental Groups, taught by Prof. Naber

3. Quals

While preparing for my qualifying exams, I found it extremely helpful to type out my solutions to past problems. My hope is that these resources will serve as a useful guide for future students as they prepare for their exams. These solutions are based on past qualifying exams from UW-Madison, which are available on the math department’s website. If you spot any errors, I would appreciate it if you could let me know. Also, if you are not able to download this document yourself, please email me.

• Real Analysis

• Applied Math