July 1 - July 23, 2021
Applications for 2021 programs are now closed. Applications for 2022 summer programs open on December 1, 2021.
Courses offered online
Eligibility: Current 9th-11th grade students
International students welcome
Financial aid for select Philadelphia students
The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students in topics such as:
- Combinatorics (enumerative, algebraic and geometric)
- Generating functions and partitions
- Graph theory
- 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
To keep our students safe as the COVID-19 pandemic continues, Penn Arts and Sciences staff is dedicated to making our high-quality programs available this summer—completely online.
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.
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.
One year of high school Algebra II/Trigonometry is required for application.
Penn Summer online system requirements
We recommend that all operating systems, browsers, Flash, and other software be up to date before the start of each online class. Most courses use Canvas for assignments, discussion, and watching video, and synchronous sessions can happen in a variety of platforms. Students will receive all important information before the beginning of class.