[HN Gopher] Stem Formulas
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       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.
        
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       (page generated 2023-07-23 23:01 UTC)