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I am aware that there are common yet very powerful operations like Map, Thread, Apply, MapThread, Transpose,Inner and Outer.

However, I am very much interested in knowing from the experienced programmers on this forum about what are some of the other core functions and operations that they find powerful and interesting over the years, and they would suggest to an aspiring Mathematica programmer to try to get familiar with so as to expand their arsenal/toolkit.

m_goldberg
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Ali Hashmi
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    I think that your approach is the good one. There is a big problem with Mathematica nowodays for newcomers : The multiplicity of operations, intended to make mathematica a natural langage tool (the multiplicity is a good thing, but for other reason) will submerse beginners (lot of to say on the subject).There should be a restricted vocabulary set for beginners. – andre314 Apr 23 '16 at 12:12
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    Animated Mathematica Functions: http://reference.wolfram.com/legacy/flash/ – Karsten7 Apr 23 '16 at 17:11
  • @Karsten, now if only there were animations for the newer functions as well… – J. M.'s missing motivation Apr 23 '16 at 17:16
  • I have tried to filter all build-in symbols from Mathematica 5.1 ( Names["System``*"] gives 1984 symbols). I have rejected all symbols having no usage message and whose name matches "*$*" "*Box*" "*Packet*" "Button*" "*Cell*" . There are still 1395 symbols !. Any idea to go further drastically ? – andre314 Apr 23 '16 at 20:12
  • There are 4664 symbols based on EntityValue["WolframLanguageSymbol", "EntityCount"]. One can use EntityList["WolframLanguageSymbol"] to get them all as a list. – Karsten7 Apr 23 '16 at 20:25
  • @Karsten When I says "go further", I mean reducing the set, not augmenting, and after that adding a few of the many functions that have appeared after Mathematica 5 :Manipulate (or DynamicI don't know), Association .... – andre314 Apr 23 '16 at 20:30
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    It would be helpful to readers if the target audience is narrowed down from generic "programmer" - e.g., are you coming from Matlab or R or do you mainly do image processing, or linguistics, or interactive demos, or 3D modeling, or numerical differential equations (just some random directions that come to mind)? It's hard to fit a catch-all answer into the format of this site. – Jens Apr 23 '16 at 22:57
  • well my question was intended for general operations and functional constructs that can be employed in functional programming, not necessarily specific for any theme. However, if you are interested in knowing about my interests, they pretty much lie in image processing. – Ali Hashmi Apr 23 '16 at 23:26
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    One should know the symbols that are used the most. – Karsten7 Apr 24 '16 at 08:57
  • thanks ! this is closest to the answer i was looking for – Ali Hashmi Apr 24 '16 at 09:18
  • Strange. I left a comment here after the question was asked, and don't remember deleting it, however it is no longer here. – Leonid Shifrin Apr 24 '16 at 22:41

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I think one of the most important core functions is ReplaceAll(/.).

I find it useful as some functions output results as rules and then you can use replaceall directly with the results.

https://reference.wolfram.com/language/ref/ReplaceAll.html.

Squigglyteeth
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