If you’re a high schooler interested in studying mathematics beyond the classroom, consider participating in a math program. These programs often allow you to explore topics such as problem solving, mathematical modeling, statistics, computational mathematics, and applications in fields like computer science, finance, and engineering. You will also get to attend lectures, complete structured problem sets, work on research projects, and collaborate with peers on analytical challenges. Many math programs also introduce tools such as programming, data analysis, and mathematical simulations. Through these experiences, you can strengthen logical reasoning, quantitative thinking, and communication of mathematical ideas.
Why should you spend your summer in Maine?
Maine offers a range of STEM learning environments through universities, research centers, and statewide education initiatives. Programs hosted across the state often combine academic coursework with hands-on projects and research experiences. You may study mathematics directly or explore related fields such as robotics, data science, engineering, and computational modeling. Many programs also allow you to interact with faculty mentors, researchers, and other students interested in STEM topics.
You can also check out these guides on math research programs in Florida or math competitions for high schoolers.
Key Takeaways
- Several programs connect mathematics to research experience rather than classroom instruction alone. PRIMES-USA has students work on unsolved problems in mathematics under MIT mentors over a full year, culminating in a research paper and conference presentation.
- Advanced coursework options are common for students ready to move beyond a typical high school curriculum. Stanford’s Discrete Mathematics and Number Theory courses cover topics like combinatorics, graph theory, and cryptography systems such as RSA and Diffie-Hellman.
- Many of these programs are fully virtual, including PRIMES-USA, AP4ME, Illinois Tech Elevate, SUMaC, IMACS Summer Sessions, and both Stanford Pre-Collegiate courses, which makes them accessible to students across Maine regardless of proximity to a university campus.
- Some programs blend math with adjacent fields like engineering, robotics, and data science rather than treating math as a standalone subject. UNE NextWave, University of Southern Maine STEM Camps, and MCEC Summer Camps all incorporate mathematical reasoning into broader hands-on STEM projects.
- Math programs are a strong way to build quantitative reasoning and research skills, but they are not the only path for a student interested in independent research in other subjects. Students who want to explore fields like political reporting, media studies, or data journalism might consider Horizon’s Research Seminars and Labs, a mentored virtual research program with 600+ specializations.
1. Maine Research Internships for Teachers and Students (MERITS)
Location: Maine Space Grant Consortium, Augusta, ME
Stipend: Paid
Application Deadline: February 13
Dates: 6 weeks in the summer
Eligibility: Rising 11th graders with a GPA equivalent to A
The Maine Research Internships for Teachers and Students (MERITS) Program offers a six-week summer research experience for Maine high school juniors. During the program, you’ll work at host research institutions across the state while participating in STEM-focused research activities. The internship introduces you to real-world applications of science, technology, engineering, and mathematics in research environments. You’ll engage in projects related to research and technology development within host organizations.
2. Horizon Academic Research Program (HARP)
Location: Virtual
Cost: Varies depending on program type. Financial aid available.
Dates: The spring and fall cohorts run 15 weeks, while the summer cohort runs 10 weeks (June-September).
Application Date: Multiple deadlines throughout the year for the Spring, Summer and Fall cohorts.
Eligibility: High school students with good academic standing (>3.67/4.0 GPA) can apply. Most accepted students are 10th- or 11th-graders! A few tracks require prerequisites; see here.
Horizon offers trimester-long research programs for high school students in subjects such as data science, machine learning, political theory, 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 you can use to improve future projects. Apply here!
3. UNE NextWave Pre-College Experience
Location: University of New England, Biddeford, ME
Cost: $2,000
Application Deadline: Not specified
Dates: July 5 – 11
Eligibility: 10th-12th graders
With a cohort of around 40 students, the University of New England’s NextWave Pre-College Experience is a week-long residential summer program for high school students. During the program, you will work with faculty across fields such as science, mathematics, business, health care, and education. You will conduct research and collaborate in teams to explore solutions to real-world problems connected to sustainability themes. Activities involve analyzing issues from environmental, social, technological, and economic perspectives. The experience concludes with a final presentation where you’ll pitch your research findings and proposed solutions to industry decision-makers.
4. University of Southern Maine: STEM Camps
Location: University of Southern Maine, ME
Cost: Varies by camp; Click here for more details
Application Deadline: Not specified
Dates: Varies depending on the camp; Click here for more details
Eligibility: Students between the ages of 9-17
The University of Southern Maine STEM Camps are short academic camps offered at several locations across Maine. In these camps, you will participate in hands-on activities across science, technology, engineering, and mathematics topics. Camp options include LEGO robotics programming, coding in Minecraft, astrophysics simulations, 3D printing design, computer assembly, and CubeSat satellite projects. While not focused solely on mathematics, these camps involve programming, data analysis, engineering design, and computational thinking connected to mathematical reasoning.
5. MCEC Summer Camps
Location: Different locations across Maine
Cost: Varies by camp
Application Deadline: Rolling till the camps reach capacity
Dates: Varies by camp
Eligibility: High school students; Specifics vary by camp
MCEC’s Summer Camps offer STEM-focused learning opportunities for middle and high school students across Maine. During these camps, you’ll participate in hands-on projects involving science, technology, engineering, and mathematics topics. Camp options include robotics programming, 3D design and printing, semiconductor technology, computer science through Girls Who Code, and transportation-focused engineering activities. While the camps are multidisciplinary across STEM fields, programming and engineering challenges incorporate mathematical reasoning and problem-solving.
6. University of Maine Systems: AP4ME
Location: Virtual
Cost: $149/credit hour (online/on-campus courses); $60/credit hour (concurrent enrollment courses)
Application Deadline: Not specified
Dates: Varies, depending on the course
Eligibility: Maine high school students
AP4ME, offered through the University of Maine System, allows you to take Advanced Placement courses entirely online. In this program, you’ll enroll in courses across several academic subjects, including mathematics. The math offerings include topics such as statistics, quantitative reasoning, college algebra, pre-calculus, calculus, business mathematics, and probability. Courses follow a structured curriculum designed to introduce students to advanced mathematical concepts. Some courses require prerequisite knowledge or prior placement in college-level mathematics.
7. PRIMES-USA
Location: Virtual
Cost: Free
Application Deadline: December 1
Dates: Year-round program consisting of four distinct phases
Eligibility: U.S. high school juniors and sophomores (including home-schooled students) outside the Greater Boston area
PRIMES-USA is a year-long research program where you will work on unsolved problems in mathematics. During the program, you’ll collaborate with mentors who are graduate students or faculty from MIT and other universities through online meetings and collaboration tools. You will also participate in a structured sequence of phases that include advanced reading, active research, independent study, and final project development. The program concludes with a research paper and a presentation at the PRIMES conference.
8. Illinois Tech Elevate College Math in Action: Real-World Problem Solving
Location: Virtual
Cost: $300
Application Deadline: May 8
Dates: June 15 – 19
Eligibility: High school students
The Math in Action program is a fully virtual experience focused on understanding how mathematics applies to real-world situations. During the program, you will participate in online problem-solving sessions, demonstrations, and activities that introduce practical uses of mathematical concepts. These sessions highlight how math is applied to solve real challenges across different contexts. Over the course of the weeklong program, you will also examine how abstract mathematical ideas can connect to practical applications.
9. Stanford University Mathematics Camp (SUMaC)
Location: Virtual + In-person options
Cost: $3,750 (virtual); Financial aid available
Application Deadline: February 2
Dates: June 15 – July 3; July 6 – 24
Eligibility: Must be 10th-11th graders (15+) at the time of application submission
The Stanford University Mathematics Camp (SUMaC) is a three-week online summer program designed for high school students interested in advanced mathematics. During the program, you will study topics such as number theory, abstract algebra, and algebraic topology through live lectures and structured coursework. You will complete daily problem sets and collaborate in group problem-solving sessions focused on theoretical mathematics. You will also attend talks by professional mathematicians that introduce mathematical research and connections between theoretical concepts and real-world applications.
10. Imacs Summer Sessions
Location: Virtual
Cost: $359 per session; Early bird discount offered
Application Deadline: Not specified
Dates: Multiple 1-week sessions from June – August
Eligibility: 9th-12th graders
IMACS Summer Sessions offer short-term academic courses for high school and advanced middle school students interested in computer science and mathematical logic. During the summer, you can enroll in advanced university-level classes offered across seven one-week sessions. Before enrolling, you must complete a free aptitude test used to determine readiness for the coursework. The program focuses on topics in computer science and mathematical logic taught at an advanced level. These courses are part of IMACS’ broader curriculum of self-paced university-level instruction.
11. The Chip Moody Consider Engineering Program
Location: University of Maine, Orono, ME
Cost: Free
Application Deadline: April 15
Dates: July 12 – 15, July 19 – 22, July 26 – 29
Eligibility: Current high school juniors
The Chip Moody Consider Engineering Program is a four-day residential summer program that introduces high school juniors to engineering through hands-on experiments and problem-solving challenges. You’ll spend time on the University of Maine campus while gaining exposure to college life and engineering studies. The program includes opportunities to work with faculty, practicing engineers, and fellow participants on technical activities and field experiences. Mathematics is used in engineering tasks involving measurements, calculations, and data analysis. Students also learn about engineering careers, industry expectations, and different areas within the profession.
12. Stanford Pre-Collegiate Program: Discrete Mathematics
Location: Virtual
Cost: $3,200; Financial aid offered
Application Deadline: March 13
Dates: June 15 – 26; July 6 – 17
Eligibility: Must be 9th-11th graders at the time of application
The Discrete Mathematics course in the Stanford Pre-Collegiate Program introduces high school students to advanced mathematical topics beyond the typical school curriculum. In this course, you’ll study discrete mathematical structures that form the foundation of areas such as computer science and theoretical mathematics. Topics include number theory, combinatorics, graph theory, Boolean algebra, logic design, and the Pigeonhole principle. You will also examine applications such as public key cryptography systems, including RSA, Diffie-Hellman, and ElGamal.
13. Number Theory Stanford Pre-Collegiate Program
Location: Virtual
Cost: $3,200
Application Deadline: March 13
Dates: June 15 – June 26 | July 6 – July 17
Eligibility: Students in grades 9-11 at the time of application
Stanford’s Pre-Collegiate Number Theory course focuses on the mathematical study of integers and their properties. During the program, you examine patterns and relationships that occur within numbers through investigation and reasoning. Students develop mathematical ideas by observing patterns, forming hypotheses, and constructing proofs. Coursework involves presenting solutions and discussing mathematical concepts with peers. The program emphasizes logical reasoning and formal proof writing. Through these activities, you gain experience working with mathematical ideas often studied in advanced mathematics.
Frequently Asked Questions
Do I need to be strong in math already to apply to these programs?
It depends on the program. PRIMES-USA and Stanford’s Number Theory and Discrete Mathematics courses expect students to already be comfortable with advanced concepts, while programs like Illinois Tech Elevate’s Math in Action and the University of Southern Maine STEM Camps are designed to be accessible without heavy prerequisites.
Which of these programs are free to attend?
MERITS, PRIMES-USA, and the Chip Moody Consider Engineering Program are free. MERITS and other research based programs may also offer a stipend, since MERITS is described as paid.
Can I participate if I am not located in Maine?
Yes, for the virtual programs. PRIMES-USA, AP4ME, SUMaC, IMACS Summer Sessions, and both Stanford Pre-Collegiate courses are conducted online, though AP4ME is specifically intended for Maine high school students. In-person programs like UNE NextWave and the Chip Moody Consider Engineering Program require attendance on a Maine campus.
What kind of research output can I expect from a program like PRIMES-USA?
PRIMES-USA runs for a full year across four phases, including reading, active research, independent study, and final project development. By the end, participants complete a research paper and present their findings at the PRIMES conference, working closely with mentors from MIT and other universities throughout.
What if I want to pursue research in a subject outside of mathematics?
These programs are focused specifically on mathematics and related computational fields, but students looking for a research based credential in a different subject area might consider Horizon’s Research Seminars and Labs, a selective virtual research program that has worked with over 1,000 high school students and offers 600+ specializations, including subjects like investigative journalism, political reporting, and the ethics of news and information.
Image source: Horizon Academic Research Program