Category Archives: Uncategorized

Incredibly awesome, but with overlength

Joel David Hamkins answering Daniel Rubin’s questions is incredible. I just had to write this post. Both are great, Joel is friendly and explains extremely well, and Daniel is direct, honest, and engaging in a funny way. And they really … Continue reading

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Prefix-free codes and ordinals

Originally posted on What Immanuel Kant teach you:
Consider the problem of representing a number in computer memory, which is idealized as a sequence of zeros and ones. The binary number system is a well-known solution to this problem —…

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Defining a natural number as a finite string of digits is circular

The length of a finite string is a natural number. If a given Turing machine halts on the empty input, then the number of steps it performs before halting is a natural number. (A Turing machine halts if it reaches … Continue reading

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Theory and practice of signed-digit representations

The integers are sometimes formally constructed as the equivalence classes of ordered pairs of natural numbers . The equivalence relation is defined via iff so that gets interpreted as . This motivates the signed-digit representation. To avoid storing two numbers … Continue reading

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A list of books for understanding the non-relativistic QM — Ajit R. Jadhav’s Weblog

I really like that this post points out that QM is vast, and that it takes a prolonged, sustained effort to learn it. I also like that it explicitly recommends chemistry books. My own first exposure to the photoelectric effect … Continue reading

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On Zeros of a Polynomial in a Finite Grid: the Alon-Furedi bound

Originally posted on Anurag's Math Blog:
My joint paper with Aditya Potukuchi, Pete L. Clark and John R. Schmitt is now up on arXiv: arXiv:1508.06020. This work started a few months back when I emailed Pete and John, pointing out an easy generalization…

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Groupoids

Originally posted on Annoying Precision:
My current top candidate for a mathematical concept that should be and is not (as far as I can tell) consistently taught at the advanced undergraduate / beginning graduate level is the notion of a…

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