The word is quickly. You make boats fast to docks, or you fast to
lose weight, or for religious reasons.
<OT>
Summarizing from OED:
There are four major noun forms of 'fast' (e.g., absetinence from
food), and two major verb forms, but none of those are relevant to this
discussion because in "learn it fast", fast cannot grammatically be a
noun or verb.
In the context, fast could be an adjective or adverb.
fast, a.:
I. firmly fixed in place; not easily turned aside; fixed on the shore
(of a vessel); fixed in sleep; permanent colour; resistant to stain-
removing or toxic agent (biology); constipated; close shut, bolted, locked
(door, window); gripping, tenacious (fast hold); some specialized uses
II. rapid.
quick, swift motion; indicating a time more advanced than true time
(clock); needing only brief exposure (film); some physics uses such
as fast breeder reactor; adapted to or productive of quick movement
(e.g., billiard cushions, hard dry cricket grounds); living too
extravegantly, devoted to pleasure
III. various combinations like fastback, fast buck, fast lane
fast as an adverb has very similar senses to the adjective form.
Sense specifically listed include "Quickly, rapidly, swiftly";
"in quick succession; one close upon another"; "readily, with alacrity".
As the sentance being nitted was describing a second action,
the "quick succession" sense is not ruled out, and the "with alacrity"
meaning applies as well, in addition to the "quickly, rapidly, swiftly"
meanings.
If the phrase had been "make it fast" then adjective or adverb could
both have been possibilities, but for "learn it fast", adverb is
the only real choice: "make" is a verb of intentional creation
of state and an adjective can describe a state (e.g., "make it round"),
but for "learn" an auxillary denoting mode (that is, an adverb) makes
more sense -- and... OED clearly shows "quickly" as one of the
adverbal meanings.
I would certainly agree that "quickly" would likely be a better
word than "fast" for the -probable- meaning, but "quickly" is within
the adverbal meaning, and for those other two senses I noted above, "fast"
is the appropriate word.
In summary, your nit is wrong in implying that "fast" was definitely
being used incorrectly.
</OT>