I gave up the Chinese course. I found it too hard and decided to learn Italian instead.
I gave up on the Chinese course. I found it too hard and decided to learn Italian instead.
What is the difference in meaning? Are both grammatically correct and interchangeable? Is "give up on" simply the transitive form of "give up" (thus being the correct or preferable form in this context in which 'the course' is the object)?
I'm asking because I read that 'give up on' originally means to stop believing in someone or something: "I give up on Paul (after several attempts to help him). He’ll never change".
But in the example, the person simply discovers that Chinese was harder than she expected (and without keep on trying) decided to drop out of the course, so the use of 'give up on' under the meaning of to stop believing would not apply. Or maybe it would only be correct to use “I gave up on the Chinese course” if she tried taking this same course many times (quitting it and starting again) until finally giving up definitely.