This is the 650th most frequent Japanese word.
科
"科" means "department," "section," "course," or "branch (of study)."
In this sentence, '科' is a component of the word '科学' (science), signifying a field of study or branch of knowledge.
私は新しい科学の本を買いました。
I bought a new science book.
Here, '科' refers to a department or branch within an academic institution, as part of '工学科' (engineering department).
この大学では最新の工学科が設けられました。
A new engineering department was established at this university.
In this usage, '科' is used in '医学科' (medical department), indicating a specialized discipline within education.