All Posts
Here’s a list of all of the content ever posted on this website, organised by date posted. Maybe I’ll improve the organisation some time in the distant future.
Important Websites Written: 8/30/2022 Modified: 4/7/2024 |
A collection of interesting links, webpages, and materials that I've found on the internet. Some of these are funny, some are absurd, but some are also very beautiful relics of people's lives. |
Cool People Written: 8/30/2022 Modified: 4/7/2024 |
A list of people that have been important to my development as a mathematician, whether intentional, conscious, both, or neither. I wouldn't be where I am today without them. |
Spring 2021 Analysis Qual Solutions Written: 3/6/2024 Modified: 3/6/2024 |
Some (hopefully) correct solutions for the Spring 2021 analysis qual at UCLA. |
Thoughts on teaching PIC 10A Written: 12/21/2023 Modified: 12/21/2023 |
A collection of some things that I've been reflecting on. As a new TA, a long-time tutor, and a student, I feel like this has been...enlightening, for better or for worse. |
Fractal Explorer Written: 10/11/2023 Modified: 10/11/2023 |
A coding project that procedurally generates and animates Newton fractals. |
An Integral Trick from the Sewers of New York Written: 9/20/2023 Modified: 9/20/2023 |
A frustratingly dirty integral trick that plays an integral role in computing a contour integral. |
A Cute Solution to a Cute Problem Written: 8/30/2023 Modified: 8/30/2023 |
A simple problem posed in an undergraduate analysis class that once evaded a simple solution. My mind's eye has been opened to new possibilities. |
Qual Attempt #4 Written: 8/30/2023 Modified: 8/30/2023 |
A set of solutions to UCLA's fall 2022 analysis qual, which was crunched out over roughly a day with a lot of help. |
Revisiting Qual Attempt #1 Written: 7/28/2023 Modified: 7/28/2023 |
I go back and revisit most of the problems I failed to solve during my first attempt at the qualifying exam. I was able to solve all but one of them. |
A Cute Problem in Undergrad Analysis Written: 7/14/2023 Modified: 7/14/2023 |
A simple problem posed in an undergraduate analysis class that evades a simple solution (indicating my lack of brain). |
Qual Attempt #1 Written: 7/14/2023 Modified: 7/14/2023 |
A moderately pathetic first attempt at UCLA's analysis qualifying exam from Fall 2011. |
A Quick Summer Update Written: 6/27/2023 Modified: 6/27/2023 |
Planned updates to the website going forward, with a handful of thoughts about graudating. |
Improvements on Lower Bounds of Sphere Packing Densities in High Dimensions Written: 2/20/2023 Modified: 2/20/2023 |
A discussion on a modest asymptotic improvement on the lower bound of sphere packing densities in high dimensions largely based on Venkatesh's work. |
Constructing Measures Written: 9/30/2022 Modified: 9/30/2022 |
An overview of premeasures and outer measures; the construction of the Lebesgue outer measure. Carathéodory's method for constructing measures and taking the completion of a measure. |
Some Things I Learned at a Restaurant Written: 9/30/2022 Modified: 9/30/2022 |
A recollection of stories, lessons, memories, and mistakes I gathered during my yearlong employment in the food industry. |
Measures and Their Properties Written: 9/7/2022 Modified: 9/9/2022 |
An overview of measures and some of their basic properties. A look at \(\sigma\)-finite and complete measures. |
Measures Written: 9/6/2022 Modified: 9/7/2022 |
An overview of measures and measure spaces, the fundamental structure that's studied in measure theory. |
\(\sigma\)-Algebras Written: 9/6/2022 Modified: 9/6/2022 |
A discussion of \(\sigma\)-algebras and their properties, examples of them, as well as product \(\sigma\)-algebras. |
Overview of Measure Theory Written: 9/6/2022 Modified: 9/6/2022 |
A discussion of which questions motivated measure theory, as well as a broad overview of what this set of notes will aim to cover and address. |
Musical Terminology Written: 9/5/2022 Modified: 9/5/2022 |
A very short introduction on musical terminology that I think is essential to describing and talking about music. |
Overtime (KNOWER) Written: 9/3/2022 Modified: 9/3/2022 |
A dive into how the chord progressions and rhythms of this song work together to build a unique mix of nervous energy masked behind projected confidence. |
3D ASCII Renderer Written: 8/30/2022 Modified: 8/30/2022 |
A coding project I started that renders 3D objects in a terminal. This post describes some of the math and design choiced behind it. |
More About This Website Written: 8/30/2022 Modified: 8/30/2022 |
Some technical details about how this website was constructed and how it is maintained, for the nerds that are interested. |