Mathematics Academy

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July 1 – July 21, 2018

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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

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 >



Relevant field trips, including visits to the National Math Museum in New York City, and the National Cryptologic Museum, may also be included.

See this program’s 2016 syllabus (PDF).

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


Avi Barr

Program Director: Avi Barr
Avi Barr has worked as a part-time instructor of mathematics at the University of Pennsylvania for 34 years, where he also implemented and taught an online learning course. Avi taught high school math for 43 years, and was department chair for the last ten years.

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Penn Summer

3440 Market Street, Suite 100
Philadelphia, PA 19104-3335

(215) 898-7326

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