I find a lot of joy in communicating any subeject of mathematics, from the most elementary high school math to my own scientific research. I am currently teaching an introductory course to Ideal Theory at MIT. Below there are links to the material of some of the most recent courses I have taught.

MIT, IAP 2021: Ideal Theory and Prüfer Domains (In Progress)

MIT, 18.02: Multivariable Calculus (Fall 2020)

UC Berkeley, MATH 53: Multivariable Calculus (Summer 2018)

UC Berkeley, MATH 1B: Single Variable Calculus II (Spring 2017)

UC Berkeley, MATH 1A: Single Variable Calculus I (Fall 2016)

**Ideal Theory and Prüfer Domains**
**Massachusetts Institute of Technology (IAP 2021)**

**Hours:** Mondays/Wednesdays/Fridays 4-5pm (via Zoom)

**Textbook:** We will follow the structure of Gilmer's book "Multiplicative Ideal Theory"

- Preliminaries on Rings

- Lecture 0: Localization
- Lecture 1: Prime and Maximal Ideals
- Lecture 2: Noetherian Rings
- Lecture 3: Krull's Intersection Theorem
- Lecture 4: Integral Extensions I
- Lecture 5: Integral Extensions II (Spectral Theorems)
- Lecture 6: Valuation Domains I (Characterizations)
- Lecture 7: Valuation Domains II (Overrings and Integral Closures)
- Lecture 8: Discrete Valuation Rings
- Lecture 9: Prüfer Domains I
- Lecture 10: Prüfer Domains II
- Lecture 11: Dedekind Domains