This is an archive of expository papers I have written. I have attempted to organize them by most relevant subject area.

# Linear Algebra

A series of notes I typed up for the benefit of a student over the course of a spring linear algebra class.
Part 1: Definitions, Zorn’s Lemma
Part 2: Representation, Products, Duals
Part 3: Infinite Product/Sum Isomorphism, Riesz
Part 4: Tensor Products
Part 5: Exterior Products
Part 6: Determinants

# Numerical Analysis

Crank-Nicolson notes

A series of notes I typed up for the benefit of a student over the course of a fall numerical analysis class.
Part 1: Function Spaces
Part 2: Multi-Index, Fourier Transform
Part 3: Stability, DFT, Lax Equivalence
Part 4: Lax-Richtmyer Theorem
Part 5: Elliptical PDEs, FEM

# Real Analysis/Measure Theory

Proofs of the following:

1. Integrability of $$f$$ on $$\mathbb{R}$$ does not necessarily imply the convergence of $$f(x)$$ to $$0$$ as $$x\to\infty$$
2. If $$f$$ is integrable on $$\mathbb{R}$$, then $$F(x) = \displaystyle\int_{-\infty}^x f(t)\ dt$$ is uniformly continuous.
3. Chebyshev’s Inequality
4. $$f$$ real-valued and integrable on $$\mathbb{R}^d$$ and $$\displaystyle\int_E f(x)\ dx\geq 0$$ for every measurable $$E$$ implies $$f(x) \geq 0$$ a.e.
5. A function can be integrable yet unbounded in any interval.
PDF

# Quantum Mechanics

Bell’s Inequality discussion.