Difference between 공부하다 and 공부한다?
공부한다 is the plain form present tense of saying I am studying. 공부하다 Is the dictionary form of sorts. Any time you have a verb in plain form in the present tense. Remove the 다 and add ㄴ to the final syllable if it ends in a vowel, and 는 after the last syllable if it ends in a consonant, then re-add the 다
공부하다 = to study (no one uses this original form in actual conversation, you have to modify it a bit per tense)
공부한다 = present tense form of "to study"
Q1: 뭐 하니? (What are you doing?) A:1 나는 수학을 공부한다 = I study mathematics 수학=mathmatics 나는 = I
Q2: 전공이 뭐니? (What is your major?) 전공=major (in a college, university or graduate school) A2: 나는 사회학을 공부한다 = = I study Sociology = My major is Sociology 사회학=Sociology