Hello Sir,
I hope this will help you...
1. Mr. Dan joined a research group that I also belonged to.
Explanation: Mr. Dan join a research group led by another professor, I am also in this group.
Mr. Dan joined a research group lead by one of my mates and I was also a part of that team.
or
I have been involved in a research group which was joined by Mr. DAN.
or
Mr. DAN joined a research group, of which I was also a team member.
As his professor in my Linear Algebra and Advanced Calculus course, I have had the chance to observe his outstanding characteristics
I have taught him few core mathematical courses like Linear Algebra, Advanced Calculus etc. I am sure, I am eligible to judge his characteristics as I could observe his outstanding behavior in my classes throughout semester.
This is my suggestion, they might not be as per your requirement, but I am happy to help you.
Yet I request you to wait for seniors to response. I am not from a literature background, so please wait for others to comment.
Regards,