[nlarew]

"here are my courses" is definitely more grammatically correct for written English but "here is my courses" sounds like something you'd say informally in conversation when you're not overthinking grammar. Maybe the goal is to sound more personable/folksy?

[hunter2_]

I'm guilty of the occasional are->'s contraction when speaking quickly, but I'd never just substitute are->is because that doesn't save a syllable.

[benmanns]

's short for "is the list of"

[gtirloni]

I'd love to read more about that. Is that a new idiom?

[emsixteen]

there's a lot

there are a lot

[hunter2_]

There's no way "there's a lot" is a contraction of "there is a list of a lot" which is what you're implying based on the way this particular thread has evolved.

Also, your example is ambiguous because "lot" is a singular noun (you wouldn't use "are" if the object is a parking lot, for example) but if you're truncating a longer phrase like "a lot of widgets" then "a lot" is modifying a plural noun (you'd definitely use "are" for that, or the informal apostrophe+s we're discussing).

[emsixteen]

Please tell me what else it's a contraction of. :)