Here are a collection of notes I’ve written over the years. Many are incomplete, and will maybe eventually be finished or rewritten entirely. They are of varying quality, as I’ve grown both as a mathematician and a writer. I’ve drawn heavily from different lectures/texts over the years. If you have any issues with anything you see, please contact me and I will take it down/change it.

Probability/Statistics

Probability Theory

A summary of different probability concepts. See MA/STAT 416 at Purdue for more information.

Statistical Theory

Notes on statistical theory. See MA 417 at Purdue for more information.

Mean/Variance of Binomial and Negative Binomial Random Variables

A reference for the proof of the mean/variance of binomial and negative binomial random variables.

Markov Chains and Mixing Times

Some brief notes on Markov Chains and Mixing Times. Preliminary work for my REU paper.

Real Analysis/Calculus

Real Analysis and Measure Theory

Notes from my measure theory course at Purdue in 2019.

Fourier PDE Notes

Notes on Fourier applications to PDEs lectures.

Ryll-Nardzewski Notes

Notes on Ryll-Nardzewski's fixed point theorem an applications.

Functional Analysis Problems

Solutions to various functional analysis problems (I do not guarantee the completeness of any solution).

Dynamics

A Survey of the Livschitz Theorem

Notes on Livschitz's theorem.

Dynamics Problems

Solutions to various dynamical systems problems (I do not guarantee the completeness of any solution).

Algebra

Commutative Algebra

Notes from the commutative algebra course at Purdue university.

Pell's Equation

A report I wrote on Pell's Equation.