Is it permissible to memorize and study academic subjects like mathematics and physics and complete their exercises in the mosque?

There is no harm in studying and reviewing educational materials in the mosque. On the contrary, it is good for you because of the reward you gain from praying in congregation and the virtues of awaiting prayer and remaining in the mosque after prayer, as stated in the Hadith: "A man's prayer in congregation is twenty-five times more rewarded than his prayer in his house and in his marketplace..." So, be keen to make the most of your presence in the mosque by reciting the Qur'an and performing supererogatory prayers to attain these virtues.