Viewing profile — peterhalburt33

Wish I had time for a longer comment, but this advice rings very true for me. Reflecting back on grad school and the transition to professional life, you have to realize that your …

As a mathematician who’s only recently started to get into computation and programming, I think the difference between my thought patterns when switching hats is so fascinating. I …

I was just about to say, I was slightly disappointed to find that this wasn’t an article about a novel technique to identify fast moving water (akin to the fact that we can identif…

Not Math books, but David Griffiths Electrodynamics and Quantum Mechanics are such a pleasure to read for their style of writing.

Wait, what? The last thing we want is more Elizabeth Holmes types…

As a mathematician who works with many engineers and computer scientists, I wanted to expand on one of the points under the “Getting a Job” section. While it is certainly true that…

It aggravates me too, however, considering that the definition of a tensor according to mathematicians is an element of the tensor product of two vector spaces (or whatever other o…

I will say IMO (and experience) in professional math that while there is perhaps more of a chance for an outsider to have an impact, Mathematics is hardly free from bias towards in…

I would also mention David Graeber’s excellent “Bullshit Jobs”

To your point, how can one measure 1% improvement in a meaningful way for abstract activities (e.g., learning)? The premise is that 1% improvement each day will yield large gains t…

The first time I attempted Rudin I gave up after the second chapter. I had been through Abbot, and still didn’t truly understand Analysis (or the style of analysts). After letting …

I’d agree, but most first year students aren’t ready to work at the level of abstraction required for a rigorous LA course (i.e., more than just matrices and Gaussian Elimination e…

The equations you quoted result from minimizing the square of the norm of the residual of Ax-b over all inputs x, so in a sense least squares is just calculus…

I’d push back slightly on the idea that a PhD isn’t an optimal route to industry careers. Due to the variety of experiences and knowledge I acquired in grad school, I became conver…

Agreed this isn’t airtight, but if you accept the premise that real numbers are specified by their sequence decimal digits: .499…+.499… has 9 as its first digit after the decimal, …

You can compute it digit by digit: .999…/2 = .45 + .045 + .0045 + …

Completely correct. Too lazy to amend my answer, but even rational numbers don’t have a unique decimal representation.

I know this might be a somewhat long and tangential answer, but I wanted to give a different viewpoint, because this is such an unintuitive fact. Firstly, let me just say, for how …

I think Intel would rather we all forget about netburst.

It really depends on which field you are talking about. I’d say it is very hard to find an area of math that’s completely new , but you will often find existing areas where novel p…

I love Terry Tao’s writing on math. One thing that strikes me about him is that, despite being an absolute technical powerhouse, he writes in a very down to earth style that connec…

Exactly. As someone who has been privileged to be naturally inclined towards the more lucrative parts of STEM, I still don’t want to see a society which rewards people like me in a…

Yeah, it’s funny how most of high school is spent focusing on the “exceptional” solvable cases of nonlinear equations (low degree polynomials, simple trig equations, exponentials) …

One of my favorite perspectives on the difficulty of formulating a general theory of PDE in light of the difficulties posed by nonlinearities is Sergiu Klainerman’s “PDE as a unifi…

Huh, somehow I also learned LA best through Griffiths QM. I almost wish Griffiths would write a Linear Algebra textbook.