Resources and opportunities for students
There is so much to say about how students can get involved in the world of mathematics. Hopefully these few things are helpful. When it comes to programs, I will focus on those that I have a past or present personal connection with.
For everyone
On how to write mathematics well.
Practical suggestions for mathematical writing, by Bjorn Poonen. [pdf]
Writing Math Well, by Francis Su. [web]
For undergraduates
The Budapest Semesters in Mathematics program, which is an option for focusing on mathematics while studying abroad for a semester or a summer. There is also a Budapest Semesters in Mathematics Education program.
NSF-sponsored REUs are a great opportunity to engaged in stipend-funded summer research. There are many REU sites all over the US, having to do with all sorts of research topics.
For Pitt undergraduates
I sponsor the Magical Math enrichment program for older elementary school students, which is part of the STEAM Saturdays program of Pitt's Hill District Community Engagement Center. If you are interested in this program, please be in touch with me.
Each spring, the Mathematics Department advertises opportunities to apply to be a Painter Fellow to its undergraduates. The Painter Fellowship matches Pitt undergraduates with a faculty mentor who guides them through 8 weeks of guided mathematical exploration and/or creative work. I have enjoyed mentoring Painter Fellows during past summers.
Pitt's Office of Undergraduate Research, Scholarship, and Creative Activity sponsors Summer Undergraduate Research Awards (SURAs). Similarly to the Painter Fellowships, these awards supply a stipend with no conditions other than to do research work for the summer under the mentorship of a faculty member.
During many but not all semesters, I run a single Directed Study on a single topic for a group of undergraduates. Feel free to contact me if you have interest in this.
For high school students
PROMYS is a 6-week summer program in mathematics for strongly motivated high school students.
Main page.