Program dates: July 11 – July 25, 2026

• Move-in: July 11
• Orientation: July 12
• Move-out: July 25

Application dates are available on the Application Information page.

The Mathematics Academy is an immersive two-week residential program designed for high school students with a strong interest and aptitude in mathematics. Led by Penn faculty and graduate teaching assistants, the program introduces participants to advanced mathematical concepts typically encountered in undergraduate study, through interactive lectures, collaborative problem-solving, and guided discovery. Students will explore the beauty and logic of mathematics as both a creative art and an analytical discipline.

Over the course of the program, participants will engage in four focused deep dives, each led by a Penn professor, into potential advanced topics such as non-Euclidean geometry and topology, graph theory, game theory and combinatorics, and mathematical logic. Proof writing will serve as the unifying foundation throughout the program, strengthening students’ ability to think abstractly, construct rigorous arguments, and communicate their reasoning with clarity and precision.

The academy fosters both intellectual challenges and community. Students will work closely with instructors and peers to tackle complex problems, present solutions, and experience the collaborative process of mathematical discovery. Emphasis is placed on developing conceptual understanding, analytical depth, and transferable skills such as teamwork, communication, and resilience in problem-solving.

Features

• Faculty-led exploration: Engage directly with Penn professors and graduate students who bring university-level mathematics to life through approachable, interactive instruction
• Four advanced topics: Experience deep dives into topics that reveal the breadth and creativity of modern mathematics
• Proof writing and problem solving: Develop the tools of a mathematician by learning to construct precise, logical proofs and apply creative reasoning to complex problems
• Collaborative learning: Work closely with peers in small groups, sharing ideas and strategies to uncover sophisticated solutions and discover the joy of mathematical collaboration
• Mathematics in action: See how mathematical reasoning underpins fields from computer science to economics and explores connections between pure theory and real-world applications

Learning outcomes

By the end of the program, students will:

• Develop a deeper understanding of fundamental and advanced mathematical concepts across four fields of study
• Construct and communicate mathematical proofs with clarity and rigor
• Apply creative and logical reasoning to solve abstract and real-world problems
• Experience the collaborative nature of mathematical inquiry through group work and discussion
• Gain confidence in exploring mathematical ideas beyond the high school curriculum

Program structure

Each weekday features two main instructional sessions:

• Morning session (9:30 a.m. - 12 p.m.), professor-led deep dive in one advanced topic
• Lunch and break (12 - 1:30 p.m.)
• Afternoon session (1:30 - 3:30 p.m.), second faculty-led deep dive topic
• TA-led problem session (4 - 5 p.m.), small-group review, collaborative problem solving, and enrichment activities

Prerequisites

Students must have successfully completed precalculus prior to the start of the program. Applicants should be prepared and eager to engage with mathematical concepts that go beyond the standard high school curriculum.

Technology statement

Students are required to bring their laptops or tablets to the program for in-class work and must have administrative access to make changes to the computer system and install applications.