In the sentence "Knowledge is transmitted from teacher to student.", I don't know why "teacher" and "student" are used without an article "the". It's difficult for me to know this is grammatically correct or there's a typo here.
Suppose that it's correct, then what is the type(s) of the nouns "teacher" and "student", are they mass nouns (which I've never heard of)?
It’s grammatically correct. Phrases of the form from A to B often have A and B without articles, especially when the referents of A and B are general, or anyway, not specific. Some examples:
But…
Yes, it is correct. It is an example of zero article.
'Teacher' and 'student' are countable nouns, but they are being used in a general, non-specific sense to describe the roles or categories of people, not particular individuals, so you can omit the article. In a similar way to your example, you could say that knowledge passes from "person to person" or from "generation to generation".
But, your suggestion to add an article could be correct, too - that would be an example of generic reference. You can use the definite article to speak about an entire group that is not limited to a head count - for example, "the elephant is a large mammal" would refer to the species of elephants, or elephants in general.
Both grammatical terms are different tools to get the same job done.
If I say
I've never driven from coast to coast.
the intended, and understood, meaning is "from the Atlantic to the Pacific", assuming the conversation has the USA as context.
Only a non-native speaker who is learning English might say
I've never driven from the coast to the coast. unidiomatic
Why do native speakers omit the article there?
Because we're not referring to coast as the focus of an utterance about a particular coast; we're using coast as member of a dyad, a pairing, expressing the boundaries of some kind of extent, analogous to "from top to bottom" or "from dawn to dusk" or "from side to side" or "from edge to edge" or "from bow to stern".
The same goes for from sea to sea.
Here's a sentence showing both the extent-dyad and the focus-of-utterance:
I looked the statuette over from top to bottom. There was a small chip at the top and the bottom bore a maker's mark.
P.S. The teacher-student dyad can be understood as the two endpoints of a relationship, or they can be understood as roles. When referring to a role (as distinct from a particular instance of a person in that role) we omit the article.
