Best way to translate "apply my knowledge to solve real world problems"
I think it can be translated as 学以致用.
学以致用 or 學以致用 is a Chinese idiom which means to study something in order to apply it. It probably comes from 《论语 子张》.
The original text is

百工居肆以成其事，君子学以致其道

by English

Workers toil and moil in the workshops to complete their job, while men of honor seek Tao by learning.

As for your sentence I want to apply my knowledge to solve real world problems, I can provide several translations for you to select from.

我想学以致用
我希望能（够）学以致用
我心怀学以致用的信念（梦想\理想）