EDIT: found one - Goodtime (thanks user)
Forest is an Android and iOS app (and web addon) that lets you track the amount of time you have spent studying.
I just it to track how much time I've spent studying from month-to-month and from subject-to-subject (through using tags). I don't know that there is an open-source alternative but if there is, that would be amazing. I am about to be finished with college for the summer and so will have time to potentially develop an app if there isn't already one.
Requirements:
- timer option
- countdown option
- tags (for specific subjects or activities)
- statistics page with weekly, monthly, and annual views
Nice Features to Have:
- study together option
- number of people currently studying