Mathematics

Every mathematician worthy of the name has experienced… the state of lucid exaltation in which one thought succeeds another as if miraculously… this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work… — André Weil, “The Apprenticeship of a Mathematician”

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work… A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted. One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. ... Read more …

Having taught CS 021 at UVM (Introduction to Programming), I thought that creating model project would be appropriate as an example. All students spend the last two weeks of the semester working on an individual or team project of their choosing. It also happens that I’ve been doing a little self-study in complex analysis. So as a model – to demonstrate a project of suitable complexity and scope – I created a little Julia set rendering program. ... Read more …

Alas, the instructions for installing the Conjecturing package for Sage posted on Nico Van Cleemput’s Conjecturing website did not work for me right out of the box. So, in hopes of saving others a little time (or misery) here are instructions to perform a local installation of the Conjecturing package for Sage on macOS Mojave, as of 10 November 2019. Only use these if you strike out using Van Cleemput’s instructions. ... Read more …

“If you really wish to learn you must mount a machine and become acquainted with its tricks by actual trial”. – Wilbur Wright (Thank you, Jim Hefferon)

On Friday, Robert J. Lemke Oliver presented a talk at the UVM Mathematics Colloquium entitled “Prime Numbers, Randomness, and the Gambler’s Fallacy.” Abstract: “Prime numbers are often said to be ‘random’, but, given that primes are deterministic, what does that actually mean? One way in which this randomness manifests is in the last digits of primes: it turns out that each possible last digit is equally likely in a certain strong sense. ... Read more …

What happens if I try to put a formula in Markdown? Does this work? Let me see. Oh, dear. My first try did not look so good. But this looks OK… $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$ You need to put a link to MathJax JavaScript into your head. That sounds funny, doesn’t it. “Into your head.” And you need double dollar signs, not just single dollar signs. Like this… ... Read more …

UVM adds quantitative reasoning requirement for general education. Good move. Memo: Approval of a proposal for a University-wide General Education requirement in Quantitative Reasoning

Giving a presentation on Ramsey Theory today. Wish me luck!