By the time the course ends,we___(learn)a lot about math.

问题描述:

By the time the course ends,we___(learn)a lot about math.

will learn
意思是:到时候结束的时候,我们将学到很多关于数学的知识。
所以现在课程还没有结束,后面用将来时。

have learned

have learned/learnt 绝对没有错.