It's not really right, but it is something that native English speakers often say.
It's so common to hear native speakers say 'amount of people' or 'amount of times' that we barely notice it. Most people probably don't even realise that 'amount' should only be used for uncountable nouns.
An even worse "mistake" is when people say 'less' rather than 'fewer' for countable nouns. This is also becoming increasingly common.
Sometimes you learners of English have a better grasp of the grammar of the language than native speakers do.
Perhaps it should say "...a huge number of courses", but it'll be interesting to see if I'm missing something related to the countable vs. uncountable -rules pertaining to this example. There are people here who have far better knowledge of English grammar rules and -exceptions.
I would wager that you can find some incorrect usage of "amount" in e.g. many news articles written by native English-speakers, as this is one of those things that is easy to make mistakes with.
Some "pairs" for comparison:
Mail (uncountable) - Letters (countable)
Marijuana (uncountable) - Marijuana plants (countable)
Snow (uncountable) - Snowballs (countable)
Data (uncountable) - Documents (countable)