Penn Summer COVID-19 Update
Penn Summer staff are not onsite, but we are still available Monday through Friday from 9 a.m. - 5 p.m. by phone and online in case you need support: (215) 898-7326 or Visit, the University's dedicated coronavirus COVID-19 web page, for the latest updates.
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Mathematics Academy

July 1 - July 23, 2021

Dates include move-in and move-out days (if needed).
Applications open on December 1, 2020.

Residential Commuter

Residential and commuter options (if in-person)

Non-credit program

Non-credit program


Eligibility: Current 9th-11th grade students

International students

International students welcome

Financial Aid

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:

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

The Mathematics Academy has traditionally been an on-campus, in-person experience. Because of COVID-19, the program was delivered entirely online during the summer of 2020, with great success! No decisions regarding delivery (on-campus or online) have been made yet about the summer of 2021.

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.

Get application information »


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.

See more system requirements >