A Natural Proof of the Dominated Convergence Theorem
Egorov's Theorem provides a more natural proof of the celebrated Dominated Convergence Theorem than the traditional clean proof via Fatou's Lemma.
Zhijie Chen's Blog
An Interesting Exercise in Measure Theory
The solution to Exercise 2A, Problem 8 and 9, in Measure, Integration & Real Analysis.
Information Theory Behind the Kullback-Leibler Divergence
Why do we use the Kullback-Leibler (KL) divergence as a measure of distance between probability distributions? Why do we use the cross-entropy loss function in supervised machine learning?
The Axiom of Choice: Equivalent Formulations and Surprising Consequences
What is the mysterious axiom of choice? Why the hell do we need it even just to show that every infinite set has a countable subset? Why does every vector space have a basis? ...
Least Squares and Its Applications Beyond Linear Equations
The best approximate solution to a system of linear equations, and applications beyond linear equations.
An Upper Bound of the Complexity of Maximum Flow
This post is part of a series of algorithm notes originally intended only for myself.
Minimum Spanning Trees of Subgraphs
This post is part of a series of algorithm notes originally intended only for myself.
The Perplexing Determinant: the Power of Abstraction
The awkward introduction and definition of determinants often puzzle beginners, including me. However, as the level of abstraction increases, its motivation becomes clearer and the underlying elegance emerges.