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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.

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    $\begingroup$ 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. $\endgroup$ – andre314 Apr 23 '16 at 12:12
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    $\begingroup$ Animated Mathematica Functions: reference.wolfram.com/legacy/flash $\endgroup$ – Karsten 7. Apr 23 '16 at 17:11
  • $\begingroup$ @Karsten, now if only there were animations for the newer functions as well… $\endgroup$ – J. M.'s discontentment Apr 23 '16 at 17:16
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    $\begingroup$ 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. $\endgroup$ – Jens Apr 23 '16 at 22:57
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    $\begingroup$ One should know the symbols that are used the most. $\endgroup$ – Karsten 7. Apr 24 '16 at 8:57
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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.

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