comma before 'both' [adverb]: escalated it, both in and out of


American Eng
This is a sentence written by me to describe some of my classes:
Introductory physics courses sparked my interest in fluid mechanics while the upper level course, Mechanics, escalated it, both in and out of the classroom.

There is quite a few commas placed in close proximity. Mechanics is the name of the upper level course.
My question is do I need a comma in front of the word both?
It sounds appropriate to have a brief pause there.
  • Pausing when reading a sentence out loud does not necessitate the presence of a comma at the site of the pause nor does the presence of a comma in the sentence necessitate that you pause at the site of the comma.
    I like commas, but I wouldn't put one between every word and its neighbour.

    See here: "I don't think that the comma is essential, pyroknife." A big ol' comma between your name and an adjective, but I wouldn't pause when reading it. Would you?