prepositions - By which vs In Which

Sentence:

Students in the literature course will explore ways in which medieval authors represented themes of their time.

I think substituting "in which" with by which would be better for the sentence because the sentence talks about methods and ways. Why isn't "by which" a better choice?

Answer

In this case the preposition is determined by the entity to which which refers, ways. We usually employ different prepositions with different sorts of object. For instance:

Mediaeval authors represented themes of their times through established narrative conventions.
Mediaeval authors represented themes of their times by manipulating audience expectations.
Mediaeval authors represented themes of their times with stock stories and characters.
Mediaeval authors represented themes of their times through often very subtle deviations from conventional patterns.

These are tendencies rather than rules; but some of them are very strong. Method and means, for instance, almost always take by:

By this method Chretien achieves an unprecedented structural clarity.
Chaucer's deepest effects are effected by this means.

Way on the other hand almost always takes in:

Mediaeval authors represented themes of their times in many ways.
Chretien structured romantic narrative in a way for which there is no precedent in earlier analogues.

Since in this case which refers to ways, the appropriate preposition is in:

... will explore ways in which ... because authors represent themes in ways

If it were methods, by would be more appropriate:

... will explore methods by which ... because authors represent themes by methods