Nihal Uppugunduri's WebsiteThe term “differential analysis” has well-known meanings in the contexts of statistics and financial accounting, but it has different (ha!) meanings in other areas like mathematical analysis. In this note, I try to understand what these meanings in math are.
For a while, I was confused about the differences between subjects like manifold calculus, differential geometry, and differential topology. This post discusses my current understanding of how these subjects are defined relative to each other.
Here, we investigate a conjecture I have, that all normal numbers are transcendental.
In this post, we summarize my previous work of the series in a more readable and concise manner. (Proofs are not included.)
In this post, we continue the discussion from the previous in the series.
A lot of discussion in education today focuses on how to make certain concepts more palatable to students and more easily understandable. However, it seems that there isn’t enough emphasis on teaching people how to learn those concepts, especially when they come from suboptimal explanations. I conceptualize this as a difference between teaching content vs teaching process, and in general I’d argue both are incredibly important for students’ future success. In this post, I elaborate further on some aspects of teaching process that I think we should incorporate more deliberately in education.
In this project, we see how much we can generalize the core properties of ACID database transactions (atomicity, etc.) to general code and computer operations. The idea is to develop a framework that can provide these generalized capabilities.
When I first got into computer science, I came into it from a math background. Back then, I would think of computer science as essentially a way to “run math physically.” While in many respects this is true and a great way to capture the essence of computer science, I’ve learned over time that there are caveats in thinking of real-world systems, like those built by code, as mathematical. I’ll discuss some of these points now.
Back in 2013 and 2014, I started what I call my “Ideas Doc,” in which I wrote down ideas for new tech products that I would want to create some day. This was geared towards an entrepreneurial purpose, of seeing what ideas I could potentially start a company on. I’ve kept that stored and have been continually updating it since, adding new thoughts and ideas while removing ones that I don’t think are as viable anymore.
In this post, we continue the discussion from the previous in the series.