Nihal Uppugunduri's WebsiteMany software engineers who have been in the industry seem to view asymptotic analysis (“big-O”) as not as effective or relevant to their work. Yet it is still fundamentally emphasized in academic computer science programs, forming a major part of standard algorithms and data structures courses. Is there still some value in asymptotic analysis, or is it better to evolve away from it going forward?
Ostensibly, at the end of the day, math should be just about what can be proven right from wrong. Thus, we may reason that we shouldn’t care about someone’s credentials in order to cite them — we can just read their proof and check the validity of their words ourselves.
But despite this, I have often found myself evaluating the authoritativeness of authors through things like credentials when trying to pick resources to learn from. Why do I end up doing this? Are there in fact aspects of doing math for which credentials become important? For these aspects, can we devise new methods to reduce dependence on credentials, or even eliminate it, in favor of judging just based on content?
The 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.