The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. The Mathematics Academy is fully residential with no commuter or online options. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students in topics such as:

Discrete mathematics

• Combinatorics (enumerative, algebraic and geometric)
• Generating functions and partitions
• Graph theory
• Probability
• Combinational game theory

Algebra and number theory

• Linear algebra
• Prime and factorization algorithms
• Congruencies and quadratic reciprocity
• Galois theory
• Geometry of numbers

Geometry and topology

• Euclidean and non-Euclidean geometries
• Geometric transformations
• Algebraic geometry
• Point-set topology
• Knot theory

If you attend a School District of Philadelphia public or charter high school, you may be eligible to attend a Penn Summer Academy free of charge with a Penn Summer Scholarship.

Features

Lectures and discussions: Attend online sessions with mathematics faculty and experts which include lectures, recitations, group work, computer simulations, and problem sessions.

Comprehensive mathematics: Explore topics such as combinatorics, generating functions and partitions, graph theory, probability, combinational game theory, Galois theory, linear algebra, prime and factorization algorithms, congruencies and quadratic reciprocity, geometry of numbers, Euclidean and non-Euclidean geometries, geometric transformations, algebraic geometry, point-set topology, and knot theory.

Prerequisite: One year of high school Algebra II/Trigonometry is required for application.