How to organize math study groups online for long-distance collaboration? For example, how to organize a study group to:
Effectively go through a textbook,
Taking notes (not necessarily collaboratively),
Organizing time, exercises,
Publishing solutions to exercises and reviewing these solutions?
From my experience running computational research projects between people in my research group (in the UK) and with our collaborators in Singapore we tend to use a few tools.
Sharelatex.com / Dropbox with Latex files: Writing notes for maths is easiest in latex. I'm not sure if you already use it but if not its a mark up language which allows you to easily add mathematical and scientific notation. It is almost exclusively used in the research community and there are a ton of tutorials online. Notes and updates are well presented and easy for others to go through.
Slack: As we are working in collaboration, or in your case studying together, it can be really useful to have a chat space dedicated to the study group. Facebook chat / groups and whatsapp messages proved to be a nightmare for me before and slack is easy to use and free! You can also use the calendar integrations etc.
Speaking Together: Even though we are often based on different continents a voice conversation is infinitely better than just text. Of course this depends on the size of the group but I tend to call my collaborators on a regular basis and they call one another too.
I realise this isn't exactly a study group setting but I think its similar enough?