meaning - Differences between Amount, Count, Number and Quantity

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My programming peers suggest to use the term count with discrete things: count of words, count of sentences and so on. Then again my instructor suggest me to use the term "number" for the discrete things in a thesis. I have used the word "amount" but my instructor says that is only for continuous measures.

Please, clarify the different usages. It may be that programming jargon misuses the words. How and when to use the words in official language?

Examples about the usages with count, number and amount -- wrong or right?

I have 7 liters of juice. This amount is too much to drink alone.

I have 17 sparse polynomials. This count is irrelavant. (how my programming would say)

I have 17 sparse polynomials. This number is irrelavant. (Used amount but guided to number)