How do I find summer projects in math?
Few professors will have any incentive to work with you. They are either busy in summer months or unwinding from otherwise intense efforts. If you have a personal connection to someone it might be different, but &quot;cold contacts&quot; probably will fail, even not getting any response.
But there are a few things you could try.
First, it may be that your current instructors could guide you if you don't put much burden on them.
Next, they might have maintained contact with their own teachers and can introduce and recommend you to a distant university professor.
Third, you can find the course requirements online for some topic of interest to you and get a copy of the textbook. Get the syllabus if available and follow it. This will give you access to readings and possibly exercises that you can do. Do a lot of them. Getting feedback on your results will be an issue, but maybe someone local can help you.
Finally, you might consider forming a study group if you can find others who are interested and work together to learn and give each other feedback. A local professor might help you arrange such a thing and even provide minimal guidance.