peterhalburt33

7 ms·

1.
by peterhalburt33 4y ago
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 role changes every couple of years and that the things that
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by peterhalburt33 4y ago
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 was so accustomed to hearing that mathematics is nothing if
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by peterhalburt33 4y ago
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 identify the temperature water by the sound it makes when it is pou
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by peterhalburt33 4y ago
Not Math books, but David Griffiths Electrodynamics and Quantum Mechanics are such a pleasure to read for their style of writing.
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by peterhalburt33 4y ago
Wait, what? The last thing we want is more Elizabeth Holmes types…
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by peterhalburt33 4y ago
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 a mathematics education provides a great background for und
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by peterhalburt33 4y ago
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 objects you can tensor together), and according to physicists
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by peterhalburt33 4y ago
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 insiders: it can manifest itself as subtly as using notation a
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by peterhalburt33 4y ago
I would also mention David Graeber’s excellent “Bullshit Jobs”
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by peterhalburt33 4y ago
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 through the power of compounding, but if you aren’t sure you
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by peterhalburt33 4y ago
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 it sit for a few months, I picked Rudin back up and it insta
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by peterhalburt33 4y ago
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 etc.)
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by peterhalburt33 4y ago
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…
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by peterhalburt33 4y ago
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 conversant in a few different fields, which allowed me to cross di
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by peterhalburt33 4y ago
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, 9 as its second and so on - the only other number that has t
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by peterhalburt33 4y ago
You can compute it digit by digit: .999…/2 = .45 + .045 + .0045 + …
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by peterhalburt33 4y ago
Completely correct. Too lazy to amend my answer, but even rational numbers don’t have a unique decimal representation.
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by peterhalburt33 4y ago
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 much time we spend learning about the number line and calcul
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by peterhalburt33 4y ago
I think Intel would rather we all forget about netburst.
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by peterhalburt33 4y ago
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 perspectives are driving math forward. Geometric algebra may
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by peterhalburt33 4y ago
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 connects disparate areas of math - e.g. his article on “what is a
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by peterhalburt33 4y ago
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 vastly outsized way, while being indifferent or punitive to
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by peterhalburt33 5y ago
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) that one can come out with the skewed idea that solvability
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by peterhalburt33 5y ago
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 unified subject” https://web.math.princeton.edu/~
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by peterhalburt33 5y ago
Huh, somehow I also learned LA best through Griffiths QM. I almost wish Griffiths would write a Linear Algebra textbook.
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by peterhalburt33 5y ago
It really depends on what you’d like to learn LA for, and how comfortable you are with abstraction: LA can span from concrete multiplication of matrices and vectors all the way to very abstract (e.g. vector spaces over general fields or eve
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by peterhalburt33 5y ago
I would also add that one fundamental aspect of linear algebra (that no one ever taught me in a class) is that non-linear problems are almost never analytically solvable (e.g. e^x= y is easily solved through logarithms, but even solving xe^
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by peterhalburt33 5y ago
Teaching only statistics and no calculus is how you end up with people such as Tai reinventing high-school calculus and attempting to use statistical methods to validate their “method”. https://math.berkeley.edu/~ehallman&#x
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by peterhalburt33 5y ago
They will always be the Unreal Tournament company to me. Unreal and Return to Na Pali are still two of my favorite games to this day. Honestly wish someone would make games like those again.
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by peterhalburt33 5y ago
I’d be hard pressed to recommend D&F to a self study audience. Perhaps it’s just me, but the endless enumeration of examples and counterexamples at the beginnings of most chapters seemed to destroy my intuition rather than reinforce it.

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