July 6 - July 27, 2024
- Residential move-in date: July 6
- Move-out date: July 27
Summer 2024 applications are closed. The applications for summer 2025 will open in late fall 2024. Please sign up to receive more information.
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 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.
Daily Schedule: The Summer Mathematics Academy will meet Monday - Friday, from 9:30 a.m. - 5 p.m. There will be a morning lecture period from 9:30 a.m. - 12 p.m., followed by a break for lunch, then an afternoon lecture period from 1:30 - 3:30 p.m. The day will close with recitation from 3:30 - 5 p.m., where students can review concepts with the teaching assistant and work on the problems assigned for that day. Lecture periods will be led by Penn faculty and will have significant active learning components, where students work to solve problems together in groups, with assistance from the faculty speaker, academy director, and teaching assistant. Other activities after 5 p.m. and on the weekends are organized by Penn SAS High School Programs and Summer Discovery.
Academic Content: The Summer Mathematics Academy will expose students to the diverse field of mathematics over the three-week program. The academy will begin by introducing the theory of mathematical logic and proofs, and then will cover a selection of topics in higher-level mathematics, with different Penn faculty coming in for several days to teach about each new topic. Last year, the topics covered in the academy were difference equations and recurrence relations, graph theory, linear algebra, and the preliminaries of Galois theory.
Prerequisite: One year of high school algebra II/trigonometry is required for application.
Download: 2024 Syllabus (PDF)
Program Director: Dr. Yidi Wang
Dr. Yidi Wang received a PhD in mathematics at the University of Pennsylvania. Her research specializes in algebra and algebraic geometry. She has served as an instructor and teaching assistant for math courses at various levels, including college-level courses and Math Circles for high school students. She received a Good Teaching Award during her time at Penn. Outside math, Yidi enjoys playing ping pong and Rubik’s Cubes.
