15 Math Programs for High School Students in Pennsylvania
- Stephen Turban
- 2 hours ago
- 12 min read
If you’re looking for ways to go beyond your regular math classes, specialized programs can give you a more challenging academic experience. Many of these opportunities allow you to explore advanced topics, connect with faculty, and get a feel for campus life while still in high school. You will build practical skills like problem-solving, research writing, collaboration, and presenting technical ideas clearly. Many of these programs also provide mentorship, networking opportunities, and structured research experiences.
Why should I do a math program in high school?
Participating in math programs can connect you with professors, graduate students, or industry professionals, helping you understand how mathematics is used beyond textbooks while expanding your network. From a college admissions perspective, selective math programs demonstrate sustained academic interest and initiative. Completing a funded and competitive program signals both ability and commitment. You also gain concrete outcomes—research papers, presentations, or collaborative projects—that you can reference in applications or interviews.
If you’re hoping to find math programs for high school students in Pennsylvania that combine academic depth with practical exposure, this list narrows your search to options that meet those standards. Below are 15 selective math programs for high school students in Pennsylvania.
Location: Virtual, hosted by Lumiere Education
Cost: Varies; Need-based financial aid offered
Acceptance Rate: Highly selective
Dates: 12-week program; Multiple cohorts in a year
Application Deadline: Varies by cohort
Eligibility: High school students with a GPA of 3.3+
The Lumiere Research Scholar Program is a research-focused opportunity designed for high school students who want to explore academic topics in depth. You work 1-on-1 with a Ph.D. mentor on an independent project in a subject area you choose. Over the course of twelve weeks, you learn how to form a research question, gather information, and develop your ideas into a full research paper. You can select from fields such as psychology, physics, economics, data science, computer science, engineering, chemistry, international relations, and several others.
Location: Carnegie Mellon University, Pittsburgh, PA
Cost/Stipend: Free
Acceptance Rate or Cohort Size: Highly selective; small statewide cohort
Dates: Five weeks during the summer
Application Deadline: February 1
Eligibility: Rising high school seniors who are residents of Pennsylvania and have completed their junior year prior to the start of the program
The Pennsylvania Governor’s School for the Sciences (PGSS) is a five-week STEM residency program hosted by Carnegie Mellon University. You will complete coursework in biology, chemistry, computer science, mathematics, and physics, alongside laboratory work. In addition to core classes, you participate in team research projects where you develop a hypothesis, design experiments, analyze data, and present your findings at the annual PGSS Scientific Symposium. You also submit a written summary of your research to the Journal of PGSS. The program does not assign grades, allowing you to explore challenging topics without the pressure of formal assessment while living in university dorms and engaging in structured social activities.
Location: Virtual
Cost: Varies depending on program type
Application Date: Multiple deadlines throughout the year for the Spring, Summer, and Fall cohorts.
Program Dates: The spring and fall cohorts run 15 weeks, while the summer cohort runs 10 weeks (June-September).
Eligibility: High school students with good academic standing (>3.67/4.0 GPA) can apply. Most accepted students are 10th/11th graders! A few tracks require prerequisites; see here.
Horizon offers trimester-long research programs for high school students across subject areas such as psychology, politics, economics, and more! Horizon is one of the few research programs for high school students that offers you the choice to engage in either quantitative or qualitative research. Once you select a particular subject track, Horizon pairs you with a professor/PhD scholar who acts as a mentor throughout your research journey. As a participant, you will be expected to develop a 20-page research paper that you can send to prestigious journals for publication as a high school student. The program also provides a letter of recommendation for each student and detailed project feedback that you can use to work on future projects. Apply here!
Location: Carnegie Mellon University, Pittsburgh, PA
Cost/Stipend: Free (travel costs not included)
Acceptance Rate or Cohort Size: Highly selective; cohort size not publicly specified
Dates: Virtual Jumpstart June 15–June 16; In-person program June 20–August 1
Application Deadline: February 1
Eligibility: U.S. citizens or permanent residents who are rising seniors and at least 16 years old by the program start date (currently in 11th grade at the time of application submission)
Carnegie Mellon University’s Summer Academy for Math and Science (SAMS) is a six-week residential pre-college program designed for students underrepresented in STEM. You will begin with a required virtual Jumpstart and then transition to a full-time academic experience that includes coursework in math, biology, chemistry, and related fields. In mathematics, you may study topics such as game theory, learning how to model and analyze strategic decision-making through both theory and application. The program culminates in a research symposium where you present your work, and it also includes a college transition course focused on academic identity and preparation. Beyond academics, you engage in sustained mentorship, structured enrichment sessions, and community-building experiences that continue virtually after the summer ends.
Location: Temple University, Philadelphia, PA
Cost/Stipend: Free
Acceptance Rate or Cohort Size: Selective; cohort size not publicly specified
Dates: Academic year program and six-week summer program (July–August)
Application Deadline: May 31
Eligibility: Current 9th or 10th grade students (8th graders may apply in the spring before entering high school); must attend a Philadelphia public district or charter high school and reside in Philadelphia; must meet at least one federal TRiO eligibility guideline (first-generation college student, meet federal income guidelines, or demonstrate academic risk)
Temple University’s Upward Bound Math & Science (UBMS) is a federally funded college-preparation program designed for students with a demonstrated interest in math- or science-related careers. You participate in year-round programming that includes academic tutoring, enrichment classes, SAT and ACT preparation, college visits, and career exploration workshops. A distinguishing feature of UBMS is the required science research project, which you complete annually and present at the end of the six-week summer session. During the academic year, you attend weekday and Saturday sessions focused on skill development, cultural enrichment, and college readiness. The program requires a sustained commitment through high school graduation and is intended for students who plan to pursue a college degree.
Location: Carnegie Mellon University (practice leadership), Pittsburgh, PA; ARML competition held at Penn State University, University Park, PA
Cost/Stipend: Free; travel to some non-ARML competitions may not be entirely covered
Acceptance Rate or Cohort Size: Open for practice; 15 students selected for ARML team
Dates: Academic year practices; ARML in early June
Application Deadline: Rolling for practice; team selected in late April
Eligibility: Grades 6–12 in Western PA; background in algebra and geometry recommended
Western Pennsylvania ARML is a competitive math team for middle and high school students in the Pittsburgh area who want exposure to advanced problem-solving beyond the standard curriculum. You will attend weekly practices that include short lessons, collaborative problem-solving sessions, and full-group solution discussions led by Carnegie Mellon graduate and undergraduate students with strong competition backgrounds. Over the year, you can compete in contests such as ARML, the Harvard/MIT Mathematics Tournament (HMMT), and the Princeton University Mathematics Competition (PUMaC), with team selection based on performance in qualifying events. Practices are divided into Junior Varsity and Varsity levels, depending on your experience and competition background. If selected for ARML, you travel to Penn State University to compete in a multi-round, day-long national team competition focused on speed, accuracy, and collaborative strategy.
Location: University of Pittsburgh at Greensburg, Greensburg, PA
Cost/Stipend: Free
Acceptance Rate or Cohort Size: A limited number of students are selected
Dates: Summer (multi-day residential program; specific dates vary).
Application Deadline: By school nomination; timeline coordinated through participating schools
Eligibility: Middle school students entering 9th grade; must be recommended by a principal, guidance counselor, and/or science or math teacher
The Summer Science and Math Experience (SSME) at the University of Pittsburgh at Greensburg is a residential STEM program designed for students entering 9th grade. You explore biology, chemistry, math, and related STEM fields through inquiry-based, hands-on learning in small cohorts. Throughout the program, you work closely with Pitt-Greensburg faculty and participate in workshops, lab activities, and research-based sessions. You also take part in off-campus experiences, including a field trip to the Tour-Ed coal mine. While living in campus residence halls, you engage in structured evening activities and receive mentorship from faculty and program staff.
Location: University of Pennsylvania, Philadelphia, PA
Cost/Stipend: $6,700 tuition for the two-week residential program; $100 nonrefundable application fee; $1,500 nonrefundable enrollment deposit applied toward tuition. Limited scholarships available for select Philadelphia public and charter school students.
Acceptance Rate or Cohort Size: Selective; cohort size not publicly specified.
Dates: July 11 – July 25 (Move-in July 11; Move-out July 25).
Application Deadline: Rolling admissions until capacity is reached.
Eligibility: Current 9th–11th grade students who have completed precalculus before the program; minimum 3.5 GPA recommended. International students welcome (tourist or B-2 visa required). See full eligibility criteria here.
The University of Pennsylvania Mathematics Academy is a two-week residential program for high school students with a strong interest and aptitude for mathematics. You participate in professor-led deep dives into four advanced topics, including non-Euclidean geometry and topology, graph theory, game theory, and combinatorics, or mathematical logic. Proof writing forms the foundation of the program, and you strengthen your ability to construct rigorous arguments and communicate your reasoning clearly. Each weekday includes faculty lectures, small-group problem sessions led by graduate teaching assistants, and collaborative discussions. Through sustained engagement with abstract concepts and peer collaboration, you experience mathematics beyond the high school curriculum while living on campus.
Location: University of Pennsylvania, Philadelphia, PA (hybrid: virtual + in-person on campus).
Cost/Stipend: Tuition varies by participation: virtual or in-person; residential fee for Penn dorms is $6,295 (housing and most meals included)
Acceptance Rate or Cohort Size: Selective; cohort size not publicly specified
Dates: June 24 – July 24
Application Deadline: Not publicly specified; see application page for current cycle details
Eligibility: High school students who have completed grade 9 by the start of the program; a strong understanding of Algebra I is required
The Program in Algorithmic and Combinatorial Thinking (PACT) is a five-week intensive course focused on theoretical computer science rather than programming. You will study discrete mathematics, proof techniques, combinatorics, probability, graph theory, and the foundations of algorithms through rigorous, proof-based instruction. Each day typically includes a multi-hour lecture followed by independent or collaborative work on challenging problem sets that increase in difficulty over time. Guest lecturers introduce additional topics, including cryptography, computational geometry, and complexity theory. If you continue into the year-round component or advanced groups, you may explore subjects like randomized algorithms, approximation algorithms, and NP-completeness, often engaging with undergraduate- or graduate-level material.
Location: University of Pennsylvania, Philadelphia, PA
Cost/Stipend: Tuition-free for eligible City of Philadelphia public and charter school students (one course in fall and one in spring); $100 application fee (automatically waived for eligible Philadelphia public/charter school students)
Acceptance Rate or Cohort Size: Selective; enrollment is limited
Dates: Fall semester (August 25 – December 17); Spring semester (January – May)
Application Deadline: Fall entry deadline August 1 (application opens April 1); spring applications typically close earlier in the academic year
Eligibility: Current 11th-grade students attending a local high school within commuting distance (approximately up to one hour); minimum 3.5 unweighted GPA. See full eligibility criteria here.
The Young Scholars High School Program allows you to enroll in undergraduate courses at the University of Pennsylvania during the fall and spring semesters. You will take one Penn course per semester alongside college students and will be evaluated under the same academic standards as undergraduates. Course options span disciplines such as mathematics, economics, philosophy, English, anthropology, and sociology, depending on availability. Classes meet multiple times per week and may include exams, research papers, and required readings. Upon completing the course successfully, you earn one Penn course unit (equivalent to four college credit hours), which may be transferable at the discretion of your future institution.
Location: Bryn Mawr College, Bryn Mawr, PA
Cost/Stipend: $6,175 total ($1,235 per week); need-based financial aid available
Acceptance Rate or Cohort Size: Approximately 45 students; selective admissions
Dates: June 28 – August 1
Application Deadline: Full consideration for applications received by April 28; rolling admissions in spring thereafter as space allows
Eligibility: Primarily high school students (generally ages 14–17); strong mathematical background and demonstrated interest in proof-based mathematics
MathILy is a five-week residential mathematics program focused on deep, proof-based exploration rather than standard high school coursework. You spend about seven hours per day in interactive classes six days a week, working through topics like combinatorics, graph theory, affine geometry, theoretical linear algebra, probability, number theory, and group theory. The program begins with two weeks of “Root Class,” followed by a flexible “Week of Chaos” with short, topic-driven courses, and ends with advanced “Branch Classes” that may include subjects like polytopes or chip-firing games on graphs. Classes are discussion-based and inquiry-driven, meaning you actively propose conjectures, construct proofs, and collaborate with peers. In addition to academics, you participate in structured discussions about college, careers, and mathematical growth, while living on Bryn Mawr’s campus with instructors and fellow students.
Location: Remote/Online (open to U.S. students outside the Greater Boston area)
Cost/Stipend: Free
Acceptance Rate or Cohort Size: Extremely selective; 47 students in a recent year
Dates: Year-long program (January 1 – December 31)
Application Deadline: Typically in the fall prior to the program year
Eligibility: High school sophomores and juniors (or homeschooled students of equivalent age) residing in the United States outside the Greater Boston area; a very advanced mathematical background is expected
MIT PRIMES-USA is a free, year-long research program in mathematics for high school students with exceptional preparation and a strong interest in original research. You will begin with an advanced reading phase, submitting a five-page report by early March to demonstrate readiness for research. If invited to continue, you work closely with a graduate student or faculty mentor on an unsolved problem in pure or applied mathematics, including areas such as theoretical computer science or computational biology. Throughout the year, you submit interim reports, present your work at a fall conference, and complete a final research paper that may be submitted to competitions or journals. The program requires a sustained weekly time commitment (often 10 or more hours) and emphasizes independence, mathematical maturity, and academic integrity.
Location: Online (virtual program)
Cost/Stipend: Not publicly specified; see application materials for details
Acceptance Rate or Cohort Size: Selective; recent cohort included 17 students
Dates: Six weeks, late June – early August
Application Deadline: March 6
Eligibility: Advanced high school students with a strong interest in mathematics
The IMD High School Summer Research Program is a six-week online research experience focused on the mathematical analysis of democratic systems. You work in small groups on projects tailored to your background, often involving real-world data from elections or the U.S. census. Past topics have included measuring gerrymandering using metrics such as the efficiency gap and partisan bias, modeling proportional representation systems, and analyzing the impact of House apportionment on presidential elections. You typically meet twice a week with a mentor and collaborate regularly with peers, while also attending weekly guest lectures by mathematicians and democracy reformers. The program concludes with student presentations of research findings and includes a session on the college application process.
Location: Online (University of Maryland Research Training Group)
Cost/Stipend: Free
Acceptance Rate or Cohort Size: Approximately 10 students per summer cohort
Dates: Summer; approximately two-week online program (specific dates vary by year)
Application Deadline: February 13
Eligibility: High school students
The MathQuantum High School Fellowship is part of the University of Maryland’s Research Training Group focused on mathematics and quantum information science (QIS). You will participate in a two-week online program that includes lectures, seminars, quantum computing activities, professional development workshops, and a mentored mini-project. The curriculum introduces mathematical tools relevant to QIS, such as algebra, scientific computing, and stochastic analysis, while connecting them to applications like quantum algorithms and cryptography. You are expected to attend all sessions and present your mini-project at the end of the program. The fellowship is designed for students who want to build foundational skills for interdisciplinary research at the intersection of mathematics and quantum science.
Location: Stanford University, Stanford, CA (online and residential options)
Cost/Stipend: Online: $3,750; Residential: $8,950; financial aid available based on demonstrated need. $65 application fee (fee waivers available)
Acceptance Rate/Cohort Size: Highly selective; 40 residential students and 64 online students
Dates: Online Session One: June 15 – July 3; Online Session Two: July 6 – July 24; Residential Session: June 21 – July 17
Application Deadline: February 2
Eligibility: Students in grades 10 or 11 at the time of application; must have significant proof-writing experience and strong mastery of high school algebra and geometry
Stanford University Mathematics Camp (SUMaC) is an intensive enrichment program for students ready to study advanced mathematics beyond the high school curriculum. You enroll in either Program I (Abstract Algebra and Number Theory) or Program II (Algebraic Topology), both of which emphasize proof-based reasoning and conceptual depth. Coursework includes daily lectures, guided problem-solving sessions, and a final research-style project, with a workload comparable to a college mathematics course. In the residential option, you live on Stanford’s campus and participate in structured evening activities and field trips, while the online option offers live instruction and virtual engagement with peers and teaching assistants. Admission is competitive and based on transcripts, a teacher recommendation, essays, and performance on a proof-based admission exam.
Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a Ph.D. student at Harvard Business School. Lumiere is a selective research program in which students work one-on-one with a mentor to develop an independent research paper.
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