Alëksis Arendt（Vyškovská）
zavedení
Hi! My full name is Pham Ngoc Gia Bao, though I usually go by Alëksis. I like the way mathematics is actually solved, rather than just studied. This perspective is what draws me toward Graph Theory, Extremal Combinatorics, and Geometric Measure Theory.
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.
Additionally, my favorite mathematicians are June Huh and of course, Paul Erdős. I enjoy listening to shoegaze and experimental rock, with bands representative of these genres such as Whirr and Ling Tosite Sigure. I am learning Czech and really want to go to Prague and stay there for a long time.
Currently, I am an undergraduate at HCMUS. My email is phambao0205@gmail.com.
nedávné příspěvky
all posts →Vector Spaces
A first pass through vector spaces: subspaces, direct sums, linear independence, bases, Zorn's lemma, and the existence of complements.
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.