I'm of the opinion that assistant manager is a level below a manager, whereas a manager assistant is an assistant to the manager, and not necessarily just below in level to the manager. Manager assistant seems to be more close to secretary in rank.
Who told you the second one was "not correct?" I don't think "not correct" is quite the right way to say it.
I think this has to do with the word knowledge more than the word English. When talking about any kind of knowledge, I can see where a textbook teaching formal English would recommend saying:
knowledge of X
or
knowledge about X
over
X knowledge.
After all, in these expressions:
- coin knowledge
- car knowledge
- garden knowledge
words that are mostly known as nouns are being put to work as adjectives. So a textbook might say that it would be better to use, knowledge about coins, cars and gardens.
However, in reality, such nouns are pressed into use as adjectives all the time.
Fact is, the expression English knowledge can be found in published works academic studies, as evidenced by anecdotes found here, here, and here.
However, as Edwin points out in his comment, the phrase "English knowledge" is ambiguous; it can mean knowledge possessed by the English, not knowledge about English, as is the case here.
I would say that knowledge about English might be more formal, or more syntactically precise, but I'd be hesitant to call the other "incorrect."
Best Answer
It depends on what is Applied Quantitative Methods. If it's the exact name of a course, I would say:
I am a teaching assistant for the course Applied Quantitative Methods.
You can also put the course name inside quotations. Above is how I wrote it my resume.
If Applied Quantitative Methods is an area of research, it would be better to use in.
Of can also be used in some other cases like: I am a teaching assistant of Prof. Davis.