Teaching

Current Courses

• 387: Monte Carlo Methods and Applications (Fall, 2024)
• 455: Intermediate Real Analysis (Fall, 2024)

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, Fall 2024.
• 420: Continuous Time Finance. Spring 2022, Spring 2023, Spring 2024.
• 455: Intermediate Real Analysis. Fall 2024.
• 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.

• Multi-variable Calculus
  • Brief lecture notes (from Fall 2015).
  • Class website for problems and references.
  • LaTeX source.
• Undergraduate PDE
  • Lecture notes wiki
  • Class website for problems and references. I have typed solutions to all problems, which I can share with other instructors who are interested.
  • Source code. (These notes are hosted using ikiWiki.)
• Stochastic Calculus for Finance
  • Brief lecture notes (from Fall 2017).
  • Class website for problems and references.
  • LaTeX source.

Student Projects

Ph.D. Thesis

• Son Van, Investigations of the Dynamics of Models of Heat Transfer and Clustering, 2021.
• Yuanyuan Feng, Dissipation Enhancement by Mixing, 2019.
• Samuel Cohn, On the Homogenization of Diffusions in Periodic Comb-like Structures, 2018.

Masters Thesis / Projects

• Alexander Wang, Discrete vs Continuous Cheeger Constants (2024).
• Erica Wang, Generating low discrepancy samples, and an application to image stippling (2024).
• Haveesh Viswanatha, Phase transitions in the Ising Model (2024).
• 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 one-dimensional autonomous flow-free 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:

  • Lecture notes by Eugene Choi (2013/14)
  • Lecture notes by Adam Gutter (2014/15)
  • The LaTeX source for both notes
  • Class website for problems and reference.

• Stochastic Calculus:

  • Lecture notes wiki by Ryan Murray, Jimmy Murphy and others.
  • Class website for problems and references.