# Articles

## Probability

Eight Ways to Derive the Characteristic Function of the Normal Distribution

A Simple Probabilistic Proof of a Wallis-type Formula for the Gamma Function

The Strong Law of Large Numbers without Recycling

A Relatively Simple and Elementary Proof of the Baum—Katz Theorem

A Rigorous Treatment of a Fundamental Result in Self-similar Traffic Modeling

An Elementary Exposition on the Proof of the Hartman—Wintner Law of Iterated Logarithm

Exchangeability and Moment Problems

Simple Proofs of the Kolmogorov Extension Theorem and Prokhorovs' Theorem

## Real Analysis

An Intuitive Proof of the Hahn—Kolmogorov Theorem

A Proof of Hölder's Inequality using the Layer Cake Representation

Proving Integral Convergence Theorems by Viewing Integrals as Areas

Comparison of the Powers of Convergence Theorems for Integrals

## Set Theory

Borel's Proof of the Heine—Borel Theorem

Perturbing All Points in R^d into a General Position

A Note on the Axiom of Choice

## Topology

Characterization of Continuous Maps in terms of Preservation of Connected Sets

An Application of Complete Metric Space Theory: the Picard—Lindelöf Theorem

Filters in General Topology

Countable Products of Finite Spaces

An Application of Ascoli's Theorem: the Cauchy—Peano Existence Theorem

## Algebra

A Short and Self-contained Proof of the Insolvability of the Quintic by Radicals

An Overkill Proof of Wilson's Theorem using a Sylow Theorem

A Linear-algebraic Overkill Proof that Finite Fields are not Algebraically Closed

## LaTeX

I gave a 3-hour introductory lecture on LaTeX for KAIST students in Korean on May 16th, 2021. Click here for the video recording of the lecture. Please download intro_to_latex_210516 before attending the lecture. You can find answers to the exercises in after_lecture.