Teaching
Current Courses
Course Websites
These are websites from all courses I have taught at CMU.
The homework, exams and syllabus should be accessible to anyone.
Solutions, however, are restricted to CMU faculty.
 268: Multidimensional Calculus.
Fall
2015,
Spring
2018,
Spring
2020.
 269: Vector Analysis.
Spring
2012,
Spring
2017,
Spring
2019.
 272: Introduction to PDE’s.
Fall
2015.
 341: Linear algebra.
Fall
2009,
Spring
2011.
 370: Discrete Time Finance.
Fall
2020,
Fall
2021.
 372: PDE’s and Fourier Analysis.
Spring
2012,
Spring
2013,
Spring
2014.
 387: Monte Carlo Methods and Applications.
Fall
2023.
 420: Continuous Time Finance.
Spring
2022,
Spring
2023.
 720: Measure Theory.
Fall
2012,
Fall
2013,
Fall
2014,
Fall
2020,
Fall
2022.
 880: Stochastic Calculus.
Fall
2010,
Fall
2011,
Fall
2012,
Fall
2013.
 881: Advanced Stochastic Calculus II.
Spring
2010.
 944: Stochastic Calculus for Finance 1.
Spring
2017,
Fall
2017,
Spring
2019,
Spring
2020,
Fall
2021,
Fall
2022.
 Fluids working group.
Fall
2012,
Fall
2016.
 SPDE working group.
Spring
2018.
 Markov Process / Mixing working group.
Spring
2023.
Lecture Notes
All these notes are free and open source. You may modify and or use them for your own purposes, as long as you follow the licence terms.
 Multivariable Calculus
 Undergraduate PDE
 Stochastic Calculus for Finance
Student Projects
Ph.D. Thesis
Masters Thesis / Projects
 Ethan Lu, A probabilistic analysis of enhanced dissipation (2022), which led to this joint paper.
 Hongyi Zhou,
The mixing time of cellular flows with small molecular diffusivity (2022) which led to this joint paper.
 James T. Murphy III,
Resolving the onedimensional autonomous flowfree explosion problem (2014)
which was published
in SIURO.
Student Lecture Notes
These lecture notes have been written entirely by students while taking courses taught by me.
My only contribution is teaching the course and setting up the websites to host them.
You are free to edit, modify and redistribute these notes (under the terms stated in the respective licenses).

Measure Theory:

Stochastic Calculus: