Alëksis Arendt（ファム バオ）
introduction · 紹介
Hi! My full name is Pham Ngoc Gia Bao, though I usually go by Alëksis. Much of my current mathematical taste comes from the border between Combinatorics and Harmonic Analysis. I like the idea that certain problems in analysis can be studied by discretizing them into geometric pieces such as tubes, spheres, or rectangles. This perspective is what draws me toward Projection Theory, Incidence Geometry, and Geometric Measure Theory.
I also spend time with mathematical physics, particularly analytical mechanics and the applications of differential geometry to relativity and electrodynamics.
I have a background in mathematical olympiads, and I still enjoy the strange elegance of olympiad combinatorics. One project I am slowly building is a collection of combinatorial problems viewed through Linear Algebra, Probability, and Graph Theory. I am especially drawn to the recurring mechanisms behind IMO-style problems, where a hidden change of viewpoint can make a difficult problem suddenly become almost transparent.
This site is where I keep mathematical notes, selected writings, and small academic projects that I want to organize more carefully. I also enjoy building web interfaces and designing UI/UX as a way to make technical writing more readable and personal.
Currently, I am an undergraduate at HCMUS. My email is phambao0205@gmail.com.
recent posts · 最近の記録
all posts →Picard-Lindelöf Theorem
We discuss the Picard-Lindelöf theorem on local existence and uniqueness of solutions to first-order ODEs, building up from the completeness of C(K,E) under the supremum norm, the Banach fixed point theorem, and Grönwall's inequality.
Fatou's Lemma and applications
We discuss Fatou's lemma, a fundamental inequality that allows interchange of limits and integrals for nonnegative measurable functions, together with its classical applications to MCT, DCT and completeness of Lp space.
Linear Transformations and the Scaling of Lebesgue Measure
How the determinant controls volume distortion, and why translation invariance uniquely characterizes Lebesgue measure up to a scalar.