[HN Gopher] Stem Formulas
___________________________________________________________________
Stem Formulas
Author : surprisetalk
Score : 102 points
Date : 2023-07-21 18:49 UTC (2 days ago)
(HTM) web link (stemformulas.com)
(TXT) w3m dump (stemformulas.com)
| sobriquet9 wrote:
| Some of those are just definitions. Not sure what's the
| usefulness of det(A) = |A| or c=lf, it's not like one would need
| to look that up.
| Frummy wrote:
| Clicking on the det card shows definitions for 2x2 and 3x3
| matrices, probably wouldnt fit on the card
| contravariant wrote:
| The first one just looks like a tautology but the latter might
| be helpful, even if it is a bit trivial if you think about it.
| toddm wrote:
| I'm still holding on to my CRC Standard Mathematical Tables and
| Abramowitz and Stegun for when they turn the Internet off.
| kevinlinxc wrote:
| Hi everyone, I'm the creator of this! Thanks for posting this, I
| tried to post it once and it just didn't take off so I wasn't
| sure if I should post again. I'll read all the feedback now.
| tempodox wrote:
| Is this HN's auto-capitalizer? The title should be "STEM
| Formulas".
|
| It's a nice collection, it could keep me glued for hours thinking
| about all this stuff.
| gus_massa wrote:
| Yes (probably). If you notice this kind of errors, you can send
| an email to the mods hn@ycombinator.com so they fix it manualy.
| amelius wrote:
| Nice layout, but I still prefer Wikipedia.
| kevinlinxc wrote:
| I built this because of my frustration with Wikipedia actually.
| A lot of Wikipedia pages are really rigorous, but when I visit
| I just want to know the common form of the main equation, which
| is sometimes placed a few headings down.
| emmanueloga_ wrote:
| This could be seen as an index of wikipedia formulas (each
| formula links to wikipedia, anyway).
| westurner wrote:
| Lean mathlib may already have the proofs for many of these Stem
| Formulas (in LaTeX)? These formulas as SymPy would also be
| useful.
|
| latex2sympy parses LaTeX and generates SymPy symbolic CAS Python
| code (w/ ANTLR) and is now merged in SymPy core but you must
| install ANTLR before because it's an optional dependency. Then,
| sympy.lambdify will compile a symbolic expression for use with
| TODO JAX, TensorFlow, PyTorch,.
|
| "Ask HN: Did studying proof based math topics make you a better
| programmer?" Re: lean mathlib
| https://news.ycombinator.com/item?id=36463580
|
| [Mathematics in mathlib > A mathlib overview](
| https://leanprover-community.github.io/mathlib-overview.html )
|
| From https://news.ycombinator.com/item?id=36159017 :
|
| > _sympy.utilities.lambdify.lambdify()https://github.com/sympy/sy
| mpy/blob/a76b02fcd3a8b7f79b3a88df... :
|
| >> _"""Convert a SymPy expression into a function that allows for
| fast numeric evaluation [with the CPython math module, mpmath,
| NumPy, SciPy, CuPy, JAX, TensorFlow, SymPy, numexpr,]*
|
| From https://westurner.github.io/hnlog/#comment-19084622 :
|
| > _" latex2sympy parses LaTeX math expressions and converts it
| into the equivalent SymPy form" and is now merged into SymPy
| master and callable with sympy.parsing.latex.parse_latex(). It
| requires antlr-python-runtime to be installed.
| https://github.com/augustt198/latex2sympy
| https://github.com/sympy/sympy/pull/13706_
|
| ENH: 'generate a Jupyter notebook' (nbformat .ipynb JSON)
| function from this stem formula
|
| ENH: Store/export Stem formula attributes as JSON-LD Linked Data
| and/or RDFa (RDF in HTML Attributes) .
|
| JSON-LD Playground has examples of JSON-LD, as does
| https://schema.org/CreativeWork : https://json-ld.org/playground/
| westurner wrote:
| Pending are the schema.org RDFS vocabulary MathSolver class and
| mathExpression property: https://schema.org/MathSolver and
| https://schema.org/mathExpression
|
| Dbpedia has wikipedia infobox attributes as RDF.
|
| IDK if there's an RDF interface to Wolfram?
|
| ENH: Generate search urls from formula names
| runpommel wrote:
| I think this is great, though still only about 80% there.
|
| Some helpful additions would be labeling which values are
| constants, examples of both how and where the equation is used,
| and numerical representations of the formulae.
|
| When I click on Schrodinger's eq I want to be able to click on
| the Wave function and see an example of the numerical form, ie a
| matrix of vectors with toy values.
| cpp_frog wrote:
| Cool! I've just contributed several examples. If anyone is
| interested in the sheer amount of identities that have been
| discovered, good books are (many of them gigantic references
| spanning thousands of pages). When bored, try proving some of
| those facts, examples build on top of each other. These are not
| the only examples, as there are many texts like these in other
| areas of mathematics and engineering, be it numerical analysis,
| optimization and variational analysis, statistics, abstract
| algebra, control theory, geometry and so on.
|
| _Table of Integrals, Series, and Products_ , Gradshteyn &
| Ryzhik.
|
| _Special Integrals of Gradshteyn and Ryzhik, Vols. I and II_ ,
| Moll for some proofs of the above.
|
| _Handbook of Integral Equations_ , Polyanin & Manzhirov.
|
| _Scalar, Vector, and Matrix Mathematics_ , Bernstein.
|
| _Handbook of Number Theory I and II_ , Sandor, Crstici &
| Mitrinovic.
|
| Wikipedia also has a plethora of pages with mathematical
| identities. Some of them:
|
| https://en.wikipedia.org/wiki/Vector_calculus_identities
|
| https://en.wikipedia.org/wiki/Vector_algebra_relations
|
| https://en.wikipedia.org/wiki/Exterior_calculus_identities
|
| https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spheric...
|
| https://en.wikipedia.org/wiki/List_of_formulas_in_Riemannian...
|
| https://en.wikipedia.org/wiki/List_of_set_identities_and_rel...
|
| https://en.wikipedia.org/wiki/List_of_triangle_inequalities
|
| https://en.wikipedia.org/wiki/List_of_trigonometric_identiti...
|
| ... and its several lists of integrals (including trigonometric,
| exponential, rational).
|
| https://en.wikipedia.org/wiki/Lists_of_integrals#Lists_of_in...
|
| More advanced topics:
|
| http://proximity-operator.net/
| 6gvONxR4sf7o wrote:
| Can't have a list like that without a mention of Abramowitz &
| Stegun [0], or its successor, the NIST Digital Library of
| Mathematical Functions [1]. It's about as comprehensive as it
| gets.
|
| [0] https://en.wikipedia.org/wiki/Abramowitz_and_Stegun
|
| [1] https://dlmf.nist.gov/
| SnowHill9902 wrote:
| Formulas are like magic spells. You don't get to use them without
| understanding what they mean, and more importantly what they
| assume.
| dang wrote:
| Recent and related:
|
| _Show HN: Stemformulas.com_ -
| https://news.ycombinator.com/item?id=36737925 - July 2023 (3
| comments)
|
| (reposts are fine if an article didn't get significant attention
| - this one is just interesting because it's a Show HN)
| codemonkey-zeta wrote:
| Great site! Definitely should not be paginated though. Just put
| them all on one page.
| PartiallyTyped wrote:
| The matrix formula is one of my favourites because it works for
| any ring, including the case where abcd elements are matrices
| themselves.
| contravariant wrote:
| Those formulas with i as interest rates are really tripping me
| up. I mean (1+i)^n just looks like it aught to be complex.
|
| Edit: I'm also not too happy with the explanation of Feymann's
| trick, it fails to properly explain Feynman's trick, says n! is
| the gamma function, and applies the trick to an integral which
| follows directly from the definition of the Gamma function and
| cannot be simplified without that definition.
| beebmam wrote:
| Good news! Real numbers are complex numbers!
| layer8 wrote:
| That's accidental complexity though, not essential
| complexity. ;)
| pkaye wrote:
| The "i" in (1+i)^n is the interest rate.
| kevinlinxc wrote:
| Hi, creator here. Thanks for the feedback, I've been kind of
| using this site just to store things that I find personally
| useful and in ways that I, an undergraduate student, understand
| so I'm sure there are some corners being cut like in the case
| of Feynman's trick. Do you think you could help me improve that
| page? The source code is here:
| https://github.com/stemformulas/stemformulas.github.io/blob/...
| franczesko wrote:
| Could anyone share an advice or resources where to start with
| learning to read mathematical notations?
| lmpdev wrote:
| Clean!
|
| I submitted the first formula that popped into my head from uni
| years ago: the Generalised Linear Model definition from one of
| the later stats courses
|
| This project vaguely reminds me of Gradshteyn and Ryzhik
| (https://en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik)
| rudolfwinestock wrote:
| There's an effort to provide proofs for every single integral
| in Gradshteyn & Ryzhik.
|
| http://www.math.tulane.edu/~vhm/Table.html
| westurner wrote:
| Rosetta Code: https://rosettacode.org/
|
| > _Complexity Zoo > Petting Zoo > {P, NP, PP,}, Modeling
| Computation > Deterministic Turing Machine
| https://complexityzoo.net/Petting_Zoo#Deterministic_Turing_M...
| _
|
| From https://news.ycombinator.com/item?id=31719696 :
|
| > _Fixed-point combinator > Y Combinator, Implementations in
| other languages: https://en.wikipedia.org/wiki/Fixed-
| point_combinator _
|
| > _Y-combinator in like 100
| languages:https://rosettacode.org/wiki/Y_combinator #Python_
|
| Quantum Algorithm Zoo by Microsoft Quantum:
| https://quantumalgorithmzoo.org/
|
| From https://westurner.github.io/hnlog/#comment-30784573 :
|
| > _Quantum Monte Carlo_ ,
|
| QFT and iQFT; _Inverted_ Quantum Fourier Transform:
| https://en.wikipedia.org/wiki/Quantum_Fourier_transform
|
| From "Common Lisp names all sixteen binary logic gates"
| https://news.ycombinator.com/item?id=32804463 :
|
| - Quantum_logic
|
| The matrix representations of quantum gates and operators are
| neat too;
| https://www.google.com/search?q=matrix+representations+of+qu...
| LudwigNagasena wrote:
| Looks like a worse version of ProofWiki but with a more modern
| design.
| jmrm wrote:
| Is shocking for me how after studying Telco Eng. I've used or
| learnt about 90% of them, and it's sad how most of us would never
| use them again.
___________________________________________________________________
(page generated 2023-07-23 23:01 UTC)