Advanced Problem Solving & Proof

Learn how mathematicians think, reason, and communicate, through challenging non-routine problems and careful written proof.

Advanced Problem Solving & Proof

Advanced Problem Solving & Proof is a rigorous, proof-based mathematics course designed to help students learn how mathematicians think, reason, and communicate. The course emphasizes deep problem solving, logical reasoning, and clear mathematical writing rather than speed or rote techniques.

Students work on challenging, non-routine problems across mathematics and present their solutions to the class, receiving detailed feedback on both their reasoning and their writing.

Problem solving
Logical reasoning
Proof writing
Mathematical communication
Student presentations

Every PiMath course

How classes work

Live online

Seminar-style discussion over Zoom. Every session is recorded.

12 students at most

Small enough that every student is heard and known.

Canvas course site

Schedule, recordings, annotated slides, and course notes in one place.

Feedback on every proof

Detailed comments on problem solving and proof writing.

Ready to apply?

Placement is based on readiness and interest rather than age or grade level. If you are not sure which course fits, choose “Not sure which course fits — please advise” on the application and we will help.

Open the application form Questions? Contact us

Financial aid and scholarships

Partial and full need-based scholarships are available for every course. Ask about aid on the application.

Explore other PiMath courses

Transition to Advanced Mathematics Number Theory Abstract Algebra AMC & AIME Preparation Research & Mentorship