Learn Hardcore Korean: doseogwaneseo haksaeng du myeongi gongbuhago isseoyo. - Two students are studying in the library.

-에서 is a location particle that tells you where the action takes place. In 도서관에서, it means “at the library.” Whenever you describe an action happening somewhere, use -에서 after the place noun.

Could you use 도서관에 instead of 도서관에서 here? What’s the difference between -에 and -에서?

-에 and -에서 both mark locations but in different contexts:

-에 marks static existence (I am at the library) or direction (I go to the library).
-에서 marks the place of an ongoing action (I study at the library).
Because studying is an action, we need 도서관에서.

What is 명 in 두 명, and why do we need it?

명 is a counter (or classifier) used specifically for counting people. Korean numerals alone (두, 세, 네, etc.) cannot directly count nouns—you attach a counter. So 두 명 literally means “two persons.”

Why is it 학생 두 명 and not 두 학생?

In colloquial Korean the common pattern is [noun] + [number + counter]: 학생 두 명. You can also say 두 명의 학생, which is more formal or literary (“students of two persons”), but 학생 두 명 is the direct, everyday way to say “two students.”

Why is the particle 이 attached to 명 (학생 두 명이)? What does it mark?

-이/가 is the subject marker. Here, 두 명 (the two students) is the grammatical subject of the verb 공부하고 있어요, so we use 이 (attached to 명) to indicate that.

What does 공부하고 있어요 mean? How is the form -고 있어요 built?

공부하고 있어요 means “(they) are studying.” You take the verb stem 공부하- (“to study”), add -고 to connect, and then 있다 in its polite present form 있어요, giving 공부하 + 고 + 있어요. This is the present continuous (progressive) tense in Korean, showing an action in progress.

Why isn’t there a 를 after 공부? Can you say 공부를 하고 있어요?

Yes, you can say 공부를 하고 있어요, and it’s perfectly correct. In everyday speech Koreans often drop the object marker -를 when the object is obvious or unstressed. So both forms mean the same thing; the version without -를 just sounds a bit more casual.

What level of politeness is -고 있어요? Are there other ways to express the same idea?

-고 있어요 is in the polite informal style (합쇼체). Other speech levels include:
• -고 있습니다 (polite formal)
• -고 있어 (casual/informal)
The meaning stays “is/am/are doing.”

Does Korean word order always put the place first? Could you say 학생 두 명이 도서관에서 공부하고 있어요?

Korean is relatively flexible, but the neutral order is place–subject–object–verb. Moving 학생 두 명이 before 도서관에서 is grammatically fine and may put more emphasis on “the two students,” but it won’t change the core meaning.