The AMC Mathematical Olympiad Summer Program (MOSP)

By Eric Eng

By Eric Eng

Hands using laptop with mathematical formulas.

The AMC Mathematical Olympiad Summer Program (MOSP)

For bright high school students passionate about mathematics, the AMC Mathematical Olympiad Summer Program (MOSP) is a unique opportunity to explore the depths of this fascinating subject. This prestigious program, hosted by the Mathematical Association of America (MAA), is an intensive six-week summer camp that brings together some of the brightest young mathematical minds from across the United States. In this blog, we’ll dive deep into what MOP is, what students can expect, and why it’s a must-experience event for budding mathematicians.

Mathematical Association of America (MAA): A Brief History

The Mathematical Association of America (MAA) was officially founded in 1915, but its roots can be traced back to the establishment of the American Mathematical Monthly in 1894 by Benjamin Finkel. Finkel aimed to create a journal that would be accessible and engaging for both average students and mathematics teachers.

While the American Mathematical Monthly gained popularity in the mathematical community, it became clear within two decades that it needed formal organization and support to thrive. Initially, there was an attempt to have the American Mathematical Society (AMS) oversee the Monthly, but the AMS Council decided it was best to support the creation of a separate organization dedicated to this work.

As a result, a group of mathematics faculty initiated informal efforts, culminating in a meeting in December 1915, where E. R. Hedrick of the University of Missouri was elected as the first president of the newly established Mathematical Association of America. Subsequently, he was elected as the inaugural president of the newly formed Mathematical Association of America (MAA).

During the first century of existence, the MAA has experienced growth, yet it continues to uphold its leadership position in all facets of undergraduate mathematics education.

What is the AMC Mathematical Olympiad Summer Program?

The AMC Mathematical Olympiad Summer Program (MOSP) is an advanced mathematical training program designed to nurture the talents of exceptional high school students who excel in mathematics. It serves as a bridge between high school math competitions and collegiate-level mathematics. MOSP is one of the premier programs for young math enthusiasts and is known for its rigorous curriculum, expert faculty, and vibrant community of like-minded peers.

students looking out into the university

Why should you join the Mathematical Olympiad Summer Program (MOSP)

The Mathematical Olympiad Summer Program (MOSP) offers a mathematically enriching experience. Its primary purpose is to expand participants’ perspectives on mathematics and ignite their enthusiasm for further mathematical study.

MOSP functions as a training initiative by the Mathematical Association of America (MAA) AMC, with a specific focus on nurturing the long-term development of students displaying exceptional mathematical talents.

This educational program has two primary goals. Firstly, it seeks to substantially supplement the standard mathematical instruction received in schools by imparting advanced mathematical theorems and techniques typically encountered at the university level.

Secondly, it aims to significantly enhance students’ problem-solving skills.

Since its establishment in 1974, the Mathematical Olympiad Summer Program (MOSP) has consistently provided a mathematically stimulating experience designed to broaden participants’ perspectives on mathematics and cultivate their passion for further exploration.

MOSP is offered free of charge to invited students. MOSP represents a unique opportunity for students to challenge their intellect, assess their abilities, and get a taste of the college environment.

In the evenings, participants can engage in optional enrichment activities, including presentations on advanced mathematical concepts by visiting speakers, as well as avail of staff office hours and partake in recreational panel activities.

The program is committed to furthering the training of the next generation of leading mathematicians and scientists. In 2021, over 132,000 participants from the AMC 10/12 were considered, and just over 60 students received invitations to this highly selective program.

MOSP instructors conduct dynamic introductory courses covering a range of topics such as Number Theory, Combinatorics, Euclidean Geometry, and other specialized areas.


The MAA AMC Pre-MOSP initiative was established to provide female participants in MOSP an opportunity to acclimate themselves to the environment, meet instructors, practice problem-solving skills, and ultimately enhance their abilities before the start of the MOSP summer camp.

During this preparatory phase, students engage in problem-solving exercises, games, and share meals with MOP staff. This alternative environment fosters connections and camaraderie among students.

It also offers a secure space for girls to practice mathematics, easing competitive pressures and nurturing self-confidence in a collaborative and supportive learning setting.

Young female student talking to an interviewer in an office.

How hard is joining the AMC Mathematical Olympiad Summer Program (MOSP)?

Getting into MOSP is a prestigious achievement in itself. The selection process is highly competitive and begins with excelling in the American Mathematics Competitions (AMC). The top-performing students from the AMC exams are invited to the American Invitational Mathematics Examination (AIME), and from there, a select group is chosen to attend MOSP.

Students become eligible for the program through their performance in the United States of America Mathematical Olympiad (USAMO).

The top twelve scorers in the United States, regardless of their grade level, constitute the “black” group. Following them, approximately eighteen students from 11th grade and below with the next highest scores from the “blue” group.

In 2004, the program underwent an expansion, including roughly thirty of the highest-scoring American freshmen and sophomores each year, referred to as the “red” group initially.

This group was subsequently divided into two: the “green” group, consisting of approximately fifteen of the highest-scoring freshmen and sophomores who qualified through the USAMO, and the “red” group, comprising those who qualified via the USA Junior Mathematical Olympiad (USAJMO).

These colorful group names were inspired by the martial art of Karate. With this new system, the “black” group primarily includes members of the International Mathematical Olympiad (IMO) team, which may not necessarily include all USAMO winners.

Typical Summer Math Program

Until 2011, only MOSP participants from the “black” group were considered for selection to the USA IMO team, determined by combining USAMO results with the Team Selection Test (TST) outcomes.

Starting in 2011, a new competition called the Team Selection Test Selection Test (TSTST) was introduced, open to any MOSP attendees. Alongside USAMO results, this competition helps determine students who advance to the TSTs and, ultimately, the IMO team.

Canadian students are allowed to take the USAMO, but they are not eligible to participate in MOSP unless they are U.S. residents.

Occasionally, when Canadian students achieve top scores in the USAMO, they may be added to the “black” group as top-scoring honorable mentions. These additional students are also eligible for the IMO team.

Since 2016, approximately 15 to 20 international students have been invited each year (with exceptions in 2020 to 2022 due to the COVID-19 pandemic) in an effort to create a diverse and globally interconnected experience at MOSP.

a male student solving a math problem

What do people mean when they mention the colors associated with MOSP?

During the Mathematical Olympiad Summer Program (MOSP), there are typically four distinct tracks for classes and tests, and these tracks are commonly referred to as Black, Blue, Green, and Red. This practice started around 2002 and serves as a convenient way to categorize participants.

The assignments to these groups are determined based on various factors, including the participant’s performance on the USAMO, their rank in the Team Selection Test, their grade level, previous attendance at MOP, and their scores in competitions like the RMM/EGMO.

It’s important to note that this assignment process is entirely separate from the initial invitation process, which follows a different set of criteria and is conducted weeks before class assignments.

For example, in online discussions, the term “blue” cutoff might be used to signify the minimum score required for an 11th-grade student to receive an invitation to MOSP through the USAMO, even though the student could ultimately be placed in any of the class groups.

It’s crucial to understand that these color groups are not of significant importance once the USA students arrive at MOSP.

When it comes to team selection, all participants are treated equally, regardless of their color group, past USAMO performance, gender, or any other factors. The team selection process is not based on a caste system but on merit and ability.

a math problem with a pencil

How Do I Get Invited for MOSP?

Each year, middle and high school students take part in the American Mathematics Competitions (AMC).

Following their participation in the AMC, the final phase of the AMC program is the Mathematical Olympiad Summer Program (MOSP), a concentrated three-week summer camp designed for the top 60 qualifying students who aspire to compete in the International Mathematics Olympiad (IMO).

To earn eligibility for MOSP, middle and high school students engage in a series of rigorous competitions, starting with the AMC, followed by the American Invitational Mathematics Examination, and subsequently either the United States of America Mathematical Olympiad (USAMO) or the United States of America Junior Mathematical Olympiad (USAJMO).

Based on their outstanding performance in these competitions, students are selected to attend the MOP camp, where they receive focused training and practice, preparing them for the opportunity to represent the United States in the International Mathematics Olympiad.

When does the AMC Mathematical Olympiad Summer Program (MOSP) take place?

Outstanding performers in the USA Junior Mathematical Olympiad (USA(J)MO) receive invitations to attend the Mathematical Olympiad Program (MOP) during the subsequent summer.

Those who participate in the Mathematical Olympiad Program become potential candidates for selection to the six-member team representing the United States of America at prestigious international competitions like the IMO, EGMO, and RMM the following summer.

Where is the AMC Mathematical Olympiad Summer Program (MOSP) going to be held?

The Mathematical Olympiad Summer Program, or MOSP, is hosted at Carnegie Mellon University.

What to Expect at MOSP

Rigorous Mathematical Training

MOSP is an intensive program where students delve into advanced mathematical topics and problem-solving techniques. They are exposed to a wide range of mathematical subjects, including algebra, number theory, combinatorics, and geometry.

World-Class Faculty

Renowned mathematicians and educators serve as instructors, providing students with invaluable insights and guidance. Faculty members often include past Olympiad winners, making it a unique opportunity to learn from the best.

Challenging Problem Sets

MOSP is known for its challenging problem sets that require creative thinking and deep mathematical understanding. Students work on a series of increasingly difficult problems, often tackling open-ended questions that encourage exploration.

Asian students taking an exam

Collaborative Environment

MOSP fosters a sense of community among like-minded students who share a passion for mathematics. Collaboration is encouraged, and friendships formed during the program often last a lifetime.

Guest Lectures and Seminars

Students have the opportunity to attend guest lectures by distinguished mathematicians, providing insights into cutting-edge research and its real-world applications.

What Are the Benefits of Joining MOSP?

Skill Development

MOSP hones problem-solving skills, critical thinking, and mathematical intuition.

It prepares students for national and international math competitions like the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO).

Boosts College Admissions

Participation in MOSP is a significant achievement that can enhance college applications. Top universities value the skills and dedication demonstrated by MOSP participants.

New Friends and Connections

Building connections with fellow students and instructors opens doors to academic and professional opportunities in the world of mathematics.

The Mathematical Association of America (MAA) Fundamental Principles


  • Encourages involvement in mathematics through outreach and collaboration.
  • Strengthens the mathematical community by organizing cooperative activities for mathematics enthusiasts, professionals, and students of all levels.

Math concepts scribbled in a white pahe.


  • Advocates for inclusivity and celebrates diversity by promoting mathematics for everyone.
  • Expand access to mathematics through initiatives aimed at engaging a wide range of audiences.


  • Advances innovative mathematical discoveries and shares them with the world.
  • Conveys the role of mathematics in an evolving society.

Teaching & Learning

  • AMC Promotes the open exchange of ideas regarding mathematics education.
  • They aim to develop and champion research-based teaching resources and methodologies.
  • They uphold their mission and core values through various means, including outreach, programs, gatherings, competitions, and publications.
  • Additionally, they have national committees and 29 regional sections dedicated to advancing these principles.


AMC envisions a society that recognizes the significance and elegance of mathematics and fully embraces its potential to enhance human well-being.

progress and accomplishment for every task

How do I apply to be a part of the AMC Mathematical Olympiad Summer Program (MOSP)?

Preparing to be a part of the AMC Mathematical Olympiad Summer Program (MOSP) requires dedication, practice, and a strategic approach. If you plan on becoming a part of this program, here’s a step-by-step guide to help you prepare effectively. We hope these tips from us help!

Start Early

Begin your preparation well in advance, ideally several years before you plan to participate in MOSP. Developing strong mathematical skills takes time.

Understand the Requirements

Familiarize yourself with the eligibility criteria and requirements for MOSP, such as qualifying through the United States of America Mathematical Olympiad (USAMO) or other relevant competitions.

Build a Strong Foundation

Ensure you have a solid understanding of fundamental mathematical concepts, including algebra, number theory, geometry, and combinatorics. A deep understanding of the basics is crucial for tackling more advanced problems.

Practice Regularly

Solve a wide range of math problems from various sources, including past MOSP exams, the American Mathematics Competitions (AMC) series, and other math contests. Consistent practice is key to improving your problem-solving skills.

Learn Problem-Solving Strategies

Study various problem-solving techniques and strategies, such as mathematical induction, pigeonhole principle, modular arithmetic, and combinatorial reasoning. Understand how to apply these strategies to different types of problems.

Student solving a problem in the board

Review Past Competitions

Review previous MOSP and USAMO problems and solutions. This will give you insights into the types of questions commonly asked and the approaches used to solve them.

Seek Guidance

If possible, ask for help from experienced math teachers, coaches, or mentors! They would be more than happy to provide you with valuable insights, suggest resources, and help you identify areas for improvement.

Take Mock Tests

Simulate the competition environment by taking practice exams under timed conditions. This will help you improve your time management and test-taking strategies.

Participate in Math Clubs or Online Communities

Join a math club at your school or participate in online math communities. Interacting with peers who share your passion can be motivating and provide opportunities for learning and collaboration.

Stay Informed

Stay updated on the latest developments in mathematics and the format of the competition you’re preparing for. Understand the rules and scoring system as well.

Two students walking in the hallway talking about how to transfer colleges

Balance Your Studies

While preparing for MOSP is important, maintain a balanced approach to your overall education. Continue to excel in your regular coursework and maintain a well-rounded academic profile.

Practice Writing Proofs

A significant portion of math competitions involves writing rigorous proofs. Practice constructing clear and concise mathematical proofs to communicate your solutions effectively.

Stay Positive and Persistent

Math competitions can be challenging, and setbacks are normal. Stay positive, learn from your mistakes, and persist in your efforts to improve.

Apply for Qualification

Once you meet the eligibility criteria and have prepared sufficiently, participate in the qualifying exams, such as the USAMO, to earn your spot in MOP.

Prepare for the Program

If you qualify for MOP, prepare for the program by reviewing the program’s curriculum, schedule, and expectations. Be ready to engage in intensive problem-solving sessions and collaborative activities. Remember that preparation for MOP is a journey that requires commitment and continuous effort.

Stay focused on your goals, and use each practice session as an opportunity to enhance your mathematical skills. Good luck with your preparation!

female college student on campus and looking at the camera

Final Thoughts

Venturing into the marvelous realm of mathematics through the AMC Mathematical Olympiad Summer Program (MOP) is not just a path to sharpening your mathematical acumen; it’s a journey that will transform the way you approach problems, think critically, and persevere through challenges.

Embrace the beauty of mathematics, explore its limitless horizons, and let your journey through MOP inspire you to reach for the stars, for within the world of mathematics, there are no bounds to what you can achieve. The adventure awaits, and the possibilities are endless!

If you’re seeking a more in-depth discussion or have questions about college admissions, you’re in the right place! AdmissionSight’s experienced team is here to assist you. With over ten years of expertise, we’ve successfully guided students through the competitive admissions journey, securing spots at world-renowned universities. Don’t hesitate to schedule your initial consultation with us today.

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