earthicus

14 ms·

91.
by earthicus 8y ago
The motivation for using that example in particular is, I believe, that it's computing a fixed point - which is an idea that came up several times in the course in increasingly general settings. First you do the concrete example of ne
92.
by earthicus 8y ago
Complex numbers as 'cyclic numbers' is not widely understood. What is understood is how they fit into the arithmetic 'hierarchy': how the real numbers embed into the real axis, and how the operational rules for addition
93.
by earthicus 8y ago
I think programmers reaction to the mathematics in SICP is completely hysterical - in the sense of hysteria, not comedy. For example, the author-professors who wrote HTDP, quoted at length in this article complain about using 'complex
94.
by earthicus 8y ago
The source i linked to gives a breakdown of how the public school money is spent in the second section, titled 'Where are schools spending their money?' You can see that Public schools have many legitimate expenses that private sc
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by earthicus 8y ago
Thank you!
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by earthicus 8y ago
> Access to good private education takes more money than the majority of Americans have. I went to a fairly traditional private school (cost: $8k/yr) and absolutely hated it, but still did well. Eventually my hatred turned into a co
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by earthicus 8y ago
I have to admit that i've never gotten around to sitting down and thinking through why fast fft multiplication works, so I have a question that maybe someone here could answer. Some background: If a number is a multiple of two (i.e. n=
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by earthicus 8y ago
I think Russia itself could be used as another example of your rebuttable if you look a bit further back in time. At the end of the 19th century the country was still extremely agrarian - far less developed than the other great powers. Bu
99.
by earthicus 8y ago
Being unable to solve some tough problems is entirely normal - there is only a handful of people gifted enough to go though a mathematics curriculum, getting 100% on all their assignments, working in isolation. I certainly didn't! Havi
100.
by earthicus 8y ago
The mlkit compiler [1] for Standard ML pioneered region based manual memory management, and was a primary design inspiration for Rust's memory system [2]. This research project (CakeML) has a different, and perfectly valid set of goals
101.
by earthicus 8y ago
> Port affine types and/or a separation logic (esp with a solver) to CakeML to eliminate need for garbage collector. If not CakeML, then do it on low-level languages with ability to integrate them as trusted code into CakeML program
102.
by earthicus 8y ago
Is it possible to work with geometric algebra effectively without a metric using some more complicated construction?
103.
by earthicus 8y ago
The differential forms approach also has the advantage over geometric algebra of being widely used by mathematicians and theoretical physicists, and perhaps increasingly used by physicists in general. If you're going to put in the effo
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by earthicus 8y ago
Maxwell explicitly uses the imaginary part of a quaternion as a model of vectors, just as Hamilton did: > A german letter denotes a Hamilton vector, and indicates not only its magnitude but its direction. The constituents of a vector are
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by earthicus 8y ago
This is something of a myth. Maxwell actually uses both to ease the mathematical pain for his readers - he writes the equations out coordinate by coordinate, and he also compresses them using Hamilton's (quaternion) model of vectors.
106.
by earthicus 8y ago
I really enjoyed the 'Four Algorithmic Journeys' Lecture series by Stepanov. (actually theres only 3 journeys) It is a combination of teaching your some basics of developing (generic) Algorithms, basic abstract algebra, and some (
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by earthicus 8y ago
Here's an old post by terry tao explaining why the collatz conjecture is hard, and giving a heuristic argument that it's unlikely to be solved with purely elementary techniques. The essay is surely worth reading if you want to mak
108.
by earthicus 8y ago
I think it wasn't just limited to turing! Several of the pioneers of mathematical computing showed astonishing foresight about how farreaching this new theory was. For example, here's Sydney Brenner talking about how much von Neum
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by earthicus 8y ago
I'd also like to recommend the semi-technical talks by Nima Arkani-Hamed and Leonard Susskind. They are the only reason I have the faintest hint of what is going on in theoretical physics and cosmology.
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by earthicus 8y ago
Does anybody know if there's been a keyboard with dual trackpoints, analogous to dual joysticks on game controllers? I'm almost certain this is whats required for precision mousing. A software controller might look like this: one
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by earthicus 8y ago
Here's an old mathematical perspective that treats dynamic programming as analogous to the calculus of variations. Very different from a how it's usually talked about, I think. I haven't read much of it, but perhaps the chang
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by earthicus 8y ago
Referring to properties of linear operators. Examples are finiteness, surjectivity, non-negativity, monotonicity, min/max principles, contraction properties, etc.
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by earthicus 8y ago
I suspect your professor was referring to 'qualitative' vs 'quantitative' approaches when referring to soft vs hard analysis. The baire category theorem is intimately related to these to approaches, and leads to three t
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by earthicus 8y ago
a baire category is an old-timey synonym for a baire space. It's related to topology & analysis, not algebra (like category theory). In the modern theory we can make an analogy (but it is just an analogy!) between 'categorie
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by earthicus 8y ago
Well i think it just depends on how 'significant' you need the phd to be. As an example of what I mean, consider the first issue of this years Annals of mathematics [1] and note that there is not a single grad student on any of t
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by earthicus 8y ago
You don't need nonstandard analysis to make differentials concrete - Cauchy showed us how to model them with ordinary variables, and this method is taught in standard undergrad textbooks like Stewart. The issue i was bringing up is tha
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by earthicus 8y ago
I specifically made that claim of mathematics and theoretical physics, and requested first hand accounts of how it worked in CS.
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by earthicus 8y ago
Is that really how research in CS works? Certainly we hear about grad students doing lots of the work in laboratory sciences like biology, but in more analytic subjects like mathematics or theoretical physics its not true at all. Grad stude
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by earthicus 8y ago
In Euler's time they still didn't have a correct understanding of higher order differentials, so the work from this time period has genuine errors that you would need to be aware of. Might I suggest an alternative? There's a
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by earthicus 8y ago
If a coordinates are given, then they will be given with respect to a basis. However, it's entirely possible to do things more abstractly without introducing coordinates and bases to begin with, for example: https://en.wikip

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