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Mathematical Contest in Modeling

The Mathematical Contest in Modeling (MCM) is an annual international competition organized by the Consortium for Mathematics and its Applications (COMAP) since , challenging teams of up to three undergraduate students from colleges and universities worldwide to develop and present mathematical models addressing open-ended, real-world problems over a continuous four-day weekend in late January or early February. Originating from an idea by Bernard A. Fusaro in 1983 to create an "applied Putnam" contest emphasizing modeling over , the MCM received initial funding from the Fund for the Improvement of Postsecondary Education (FIPSE) and held its inaugural event on February 15-18, 1985, with 158 teams from 104 institutions submitting 90 papers. The contest's format requires teams to select one of three problems—typically Problem A (continuous modeling), Problem B ( modeling), and Problem C (data-driven insights)—and produce a comprehensive report detailing their assumptions, model development, analysis, and conclusions, fostering skills in , , and practical problem-solving. Participation has grown dramatically from its early years, reaching 13,753 teams in 2020, 28,912 teams in 2024, and 27,456 teams in 2025, drawing entrants from more than 20 countries and highlighting the contest's global reach and appeal to students across STEM disciplines. Awards include designations such as Successful Participant, Honorable Mention, Meritorious Winner, Finalist, and Outstanding Winner for the top teams, with the six Outstanding teams receiving the COMAP International Scholarship Prize of $9,000 (split among members) plus $1,000 to their institution, and additional recognition like the SIAM Award in the Mathematical Contest in Modeling. The MCM is often paired with the companion Interdisciplinary Contest in Modeling (ICM), which offers three additional problems focused on operations research, environmental policy, and sustainability, further broadening its educational impact.

History

Founding and Early Development

The Mathematical Contest in Modeling (MCM) was founded in 1985 by the (COMAP) to promote modeling among undergraduate students. The initiative was led by Ben Fusaro of Salisbury State University, who secured funding through a FIPSE grant in June 1984 to support the effort. The primary motivation stemmed from the need to engage students in applying mathematical concepts to real-world problems, addressing the perceived shortcomings of existing contests like the Putnam Competition, which emphasized over practical applications. This approach was inspired by the rising interest in mathematical modeling within educational curricula during the early , aiming to foster skills in problem formulation, , and communication rather than rote computation. Fusaro envisioned the contest as an educational experience that would appeal to practically minded undergraduates, allowing teams to use tools like microcomputers for open-ended challenges. The inaugural MCM took place over a weekend starting February 15, 1985, with teams of three students selecting from two applied, open-ended problems that emphasized continuous and modeling techniques. A total of 158 teams from 104 colleges registered, though only 90 papers were ultimately submitted for judging, reflecting the 's initial scale and the logistical hurdles of coordinating nationwide participation. Submissions were evaluated based on mathematical rigor, clarity of exposition, and the effectiveness of the modeling process, with awards categorized into levels such as Outstanding and Meritorious. Early years presented several challenges, including limited initial participation—hovering around 100-200 teams annually through the late 1980s—and strains on judging resources due to the volume of paper-based submissions. Publicity was constrained by short timelines, and the lack of standardized formats led to variability in team preparedness and problem accessibility. Over time, the contest refined its weekend structure with improved judging protocols and the addition of a third problem category, helping to accommodate growth while maintaining focus on educational outcomes. By the mid-1990s, steady increases in participation had begun to establish the MCM as a key platform for undergraduate modeling.

Expansion and Milestones

Following its founding, the Mathematical Contest in Modeling (MCM) experienced steady growth throughout the 1990s, with participation increasing from 158 teams in 1985 to 320 teams representing 199 institutions in 1995. This expansion reflected growing awareness among U.S. colleges and the onset of international involvement, particularly from institutions in and , as teams began addressing complex, real-world modeling challenges. By 1999, participation reached 478 teams from 229 institutions across multiple countries, underscoring the contest's appeal in fostering interdisciplinary mathematical skills. A significant milestone occurred in 1999 with the launch of the concurrent Interdisciplinary Contest in Modeling (ICM), which broadened the MCM's scope by incorporating problems from fields like and , attracting 40 teams initially and growing to 164 teams from four countries by 2005. The 2005 contest, marking the MCM's 21st year, saw 828 teams from over 300 institutions in 11 countries, highlighting two decades of evolution and the publication of a commemorative volume featuring outstanding solutions. That year also introduced institutional support through the SIAM Award, recognizing six outstanding teams annually to emphasize excellence. In recent years, the MCM/ICM combined contests saw significant growth, with 20,956 teams from 23 countries and regions participating in 2020. The prompted a shift to fully online formats starting in 2020, enhancing accessibility for international participants and enabling secure submission of modeling papers without in-person coordination. This adaptation sustained high engagement, with over 27,000 teams in 2022, approximately 20,858 teams in 2023, a record 28,912 teams in 2024, and 27,456 teams in 2025, solidifying the contests' role in undergraduate mathematical training worldwide.

Organization and Administration

Role of COMAP

The Consortium for Mathematics and Its Applications (COMAP) is a non-profit organization founded in 1980 that focuses on enhancing through the promotion of , particularly mathematical modeling. COMAP achieves this mission by developing curriculum resources, offering programs, and organizing multidisciplinary contests that engage students from through in real-world problem-solving. Although established prior to the inception of the Mathematical Contest in Modeling (MCM) in 1985, COMAP has served as the primary organizing body for the MCM since its early years, integrating it into a broader suite of initiatives aimed at fostering analytical skills and interdisciplinary thinking. In administering the MCM, COMAP handles key operational responsibilities, including the annual development of contest problems, which consist of three open-ended modeling challenges (typically one continuous, one , and one data-driven). It manages participant registration through a dedicated online portal, where faculty advisors submit team entries for a nominal fee, ensuring eligibility verification and logistical coordination for the international event. COMAP also oversees the judging process by recruiting volunteers—primarily academics, mathematicians, and industry professionals—who evaluate thousands of team submissions during the spring following the contest. These papers are judged based on the quality of the team's thought processes, problem analysis, modeling approaches, and mathematical methods, as well as the clarity and effectiveness of the written presentation. A final then reviews top-scoring entries to determine awards, with results announced by early May. To support participants and educators, COMAP provides a range of preparatory resources, including an online archive of past MCM problems and solutions dating back to the contest's origins, accessible via its MathModels.org platform. It also offers practical guides such as the Teachers College Mathematical Modeling Handbook, which outlines modeling techniques and contest strategies, and hosts webinars led by experts to cover topics like problem analysis, team collaboration, and report writing. These materials emphasize conceptual approaches to modeling, helping teams build skills in , validation, and communication without relying on exhaustive lists of historical data. COMAP concurrently administers the related Interdisciplinary Contest in Modeling (ICM), applying similar administrative processes to ensure cohesive management of both events.

Related Contests

The Interdisciplinary Contest in Modeling (ICM), founded in 1999 by the Consortium for Mathematics and Its Applications (COMAP) as a sister event to the Mathematical Contest in Modeling (MCM), emphasizes interdisciplinary approaches to real-world problems. Since 2011, the ICM has been integrated with the MCM for registration, with teams selecting ICM problems D, E, or F alongside MCM's A, B, or C. It challenges teams of up to three undergraduate students to develop models incorporating fields beyond , such as , , , and . Like the MCM, the ICM runs over a four-day weekend in late January or early February, with teams selecting from three open-ended problems and submitting a comprehensive report; however, it differs by requiring integration of non-mathematical disciplines to address complex, multifaceted issues. This format fosters collaborative problem-solving skills applicable to professional settings in science, , and social sciences. The High School Mathematical Contest in Modeling (HiMCM), launched in 1998 by COMAP, extends the MCM's team-based modeling experience primarily to high school students and those in equivalent grades, with eligibility expanded as of to include math circles, magnet programs, homeschool groups, and other non-traditional educational settings. Held annually in over a 14-day period, it allows teams of up to four students to tackle one of two real-world problems using high school-level , culminating in an electronic submission of their modeling process and solution. The contest aims to build analytical, problem-solving, and communication abilities in a supportive environment, often aligned with events like the Mathematical Association of America's MathFest for presentations and feedback. In contrast to the MCM's focus on college undergraduates and stricter timelines, HiMCM features more accessible problems and extended submission windows to accommodate younger participants' skill levels. Regional variants of the MCM have emerged to provide localized practice, adapting its core format for broader accessibility. The Midwest Mathematical Modeling Competition (MMMC), initiated in 2008 by the , serves as an example, hosting an on-site 24-hour event for undergraduate teams from Midwest institutions. Participants select from two open-ended problems, develop models, deliver oral presentations, and receive immediate feedback, mirroring MCM rules on sourcing and collaboration while emphasizing preparation for the international contest. These regional events differ from the MCM by their shorter duration, in-person focus, and smaller scale, typically involving dozens of teams rather than thousands globally.

Contest Format

Timeline and Structure

The Mathematical Contest in Modeling (MCM) is held annually over a four-day period spanning a in late or early . For instance, the 2026 contest is scheduled from January 29 to February 2. This timing allows undergraduate teams worldwide to participate synchronously, with the contest beginning at 5:00 p.m. EST on and concluding at 8:00 p.m. EST on the following , providing exactly 96 hours of continuous work time. The core structure of the MCM emphasizes intense, self-directed problem-solving under time constraints, simulating real-world modeling pressures. Upon the contest's start, teams select one of three MCM problems (A: continuous modeling, B: discrete modeling, or C: data-driven insights) from the official website and begin developing a comprehensive solution. Teams must produce a written report of no more than 25 pages, including a one-page summary sheet, table of contents, body, references, and appendices, with no external communication or assistance permitted from advisors, peers, or online resources beyond inanimate tools like software and references. Submissions are required via an online Adobe PDF upload system by 9:00 p.m. EST on the contest's end date, ensuring all work is completed within the allotted period. The contest unfolds in distinct yet overlapping phases: problem release and selection at the outset, followed by iterative modeling and analysis to formulate and validate solutions, and culminating in report writing and submission. This flow demands effective , as teams balance mathematical development, computational verification, and clear exposition without interruptions. Running parallel to the MCM is the Interdisciplinary Contest in Modeling (ICM), which shares the identical timeline, duration, and submission protocols but offers three distinct problems (D: or , E: or agent-based modeling, F: or ) to encourage broader interdisciplinary approaches. Together, these contests highlight the emphasis on time-pressured and in .

Team Rules and Requirements

The Mathematical Contest in Modeling (MCM) requires teams to consist of up to three students, all of whom must be undergraduates or high school students enrolled at the same institution at the start of , with no exceptions allowed for this rule. Each team must also designate one advisor, who can be a faculty member, staff, or graduate student from the institution, but the advisor plays a non-participating and serves primarily as the main point of contact for registration and rule compliance. Students who have already earned a or higher are ineligible to participate. Strict rules prohibit collaboration between teams or any external assistance during the contest period, ensuring that all work reflects the team's independent efforts; this includes a ban on seeking help from advisors, other teams, or persons outside the team. Teams are permitted to use any inanimate resources, such as software, computational tools, or web pages, but must disclose their use, particularly for tools, which require a separate appended "Report on Use of AI" detailing how they were applied. All solutions must be original, with teams required to document sources using footnotes, endnotes, or in-line citations, and any detected results in immediate disqualification. Submissions must follow precise guidelines to maintain and clarity: reports are to be written in English, formatted as PDF files in 12-point font, limited to a maximum of 25 pages (including all content), and accompanied by unlimited appendices if needed for supporting materials. Each page must include the team's control number for identification, but no other identifying information about the team, institution, or advisor is allowed to ensure impartial judging. Judges emphasize reports that provide clear mathematical justification for models, assumptions, and results, including thorough to evaluate the robustness of solutions against variations in parameters. In preparation, advisors may offer guidance on modeling techniques, report writing, and past contest strategies before the event begins, but they are explicitly barred from providing any input or resources during the contest weekend to uphold the independence requirement. Teams are encouraged to review historical problems and winning solutions available on the official COMAP website to familiarize themselves with effective approaches, such as balancing mathematical rigor with practical applicability.

Problems

Problem Categories

The Mathematical Contest in Modeling (MCM) features three distinct problem categories designed to challenge teams with different mathematical emphases. Problem A focuses on continuous modeling, typically involving differential equations and other techniques to analyze dynamic systems, such as or . Problem B emphasizes discrete modeling, drawing on tools like , , or algorithms to address problems in optimization or network structures, for instance, scheduling or routing scenarios. Problem C centers on data-driven insights, requiring statistical analysis, elements, or visualization of datasets to uncover patterns and make predictions, often applied to real-world data sets in fields like or . In contrast, the Interdisciplinary Contest in Modeling (ICM), held concurrently with MCM, offers three categories that integrate mathematical modeling with broader societal and scientific contexts. Problem D targets and , employing optimization models, , or graph-based methods to solve logistical or connectivity issues, such as supply chain disruptions. Problem E addresses , where teams develop models to assess environmental impacts, , or , incorporating ecological data and long-term forecasting. Problem F explores policy modeling, simulating social, economic, or scenarios through agent-based models or to evaluate policy interventions. Teams participating in either MCM or ICM select one problem from their respective contest's categories at the start of the event, allowing flexibility based on strengths and interests. All problems are intentionally open-ended, necessitating that teams state assumptions, validate their models against real data where possible, and discuss limitations to ensure robustness and applicability. Over the years, these categories have evolved to reflect emerging global challenges and interdisciplinary advances. The ICM, introduced in 1999, initially emphasized environmental themes but expanded in 2015 to two dedicated problems on and , and further to three problems in 2016 by adding policy modeling, incorporating modern topics like climate modeling. Similarly, MCM's Problem C was introduced in 2016 to highlight data insights, aligning with the rise of and computational tools, while maintaining the core continuous and discrete frameworks established since the contest's founding in 1985.

Sample Problems and Solutions

The Mathematical Contest in Modeling (MCM) features open-ended problems that require teams to develop mathematical models addressing real-world scenarios. One early example is Problem B from , titled "The Animal Population Problem," which tasked teams with selecting a or species and modeling its and interactions with its environment using available data. A more recent illustration is Problem A from 2015, "Eradicating ," which required modeling the spread of the virus in based on epidemiological data and evaluating intervention strategies like and . Typical MCM solution structures follow a systematic approach: stating explicit assumptions (e.g., homogeneous mixing in populations or constant transmission rates), formulating the with equations and algorithms, validating results against real data through or goodness-of-fit metrics, and discussing broader implications such as policy recommendations. COMAP publishes selected winning solutions annually in The UMAP Journal, providing detailed examples of these strategies for educational purposes.

Participation

Eligibility and Registration

The Mathematical Contest in Modeling (MCM) is open to full-time undergraduate and high school students worldwide, regardless of their major or prior experience in mathematical modeling. Participation requires teams to be composed of up to three students currently enrolled at the same , with no limit on the number of teams a single school can enter. Each team must be sponsored by an advisor, typically a faculty member, staff, or graduate student affiliated with the institution, who serves as the primary contact and ensures compliance with eligibility rules. Registration for the MCM occurs entirely through the official COMAP , involving a two-step process managed by the team's advisor: initial advisor account creation followed by team enrollment. A non-refundable fee of $100 per team is required, payable via credit card at the time of registration. The deadline for registration is typically in mid-to-late January each year—for instance, 3:00 p.m. EST on January 29, 2026, for that year's contest—with advisor verification of student enrollment integrated into the process to confirm eligibility. To promote broad and inclusive participation, COMAP encourages the formation of diverse teams from various backgrounds and regions, fostering global collaboration in mathematical modeling. While there are no dedicated registration fee waivers specifically for underrepresented groups, the organization supports accessibility through initiatives like the COMAP , which provides $9,000 to each of the top six MCM teams from participating countries or regions annually, helping to recognize and incentivize contributions from diverse participants. Upon approval of registration and payment, advisors receive a unique control number for their team, which is essential for accessing the contest problems at the start of the event and for submitting the final solution paper. Advisors must affirm the full-time student status of all team members during this verification step, and COMAP reserves the right to request additional documentation if needed to validate eligibility.

Global Participation Trends

The Mathematical Contest in Modeling (MCM) has experienced significant growth in participation since its inception, reflecting increasing global interest in education. In its inaugural year of 1985, 158 teams from 104 colleges registered, with 90 papers ultimately submitted. By 2005, participation had expanded to 828 teams. This upward trajectory continued, reaching 3,697 teams in 2012, 13,753 teams in 2020, 28,912 teams in 2024, and over 27,000 teams in 2025. The steady increase, particularly post-2010, has been facilitated by enhanced online registration and submission processes, broadening access beyond . Demographically, MCM participation is dominated by undergraduate students, though the contest is open to both college undergraduates and high school students, allowing teams from secondary institutions to compete alongside university groups. In terms of geographic distribution, the contest has shifted from a primarily U.S.-centric event to a truly one; for instance, in 2020, only about 3% of the 13,753 teams were from the , with the remaining 97% from foreign institutions across regions including , , and . has emerged as the leading participant country in recent years, contributing the majority of teams, followed by the U.S. and a growing number from , the , and other European nations. This diversification underscores MCM's role in fostering global collaboration in mathematical modeling. Key trends in participation include the rising involvement from developing regions, aided by the contest's fully remote format, which requires no travel and relies on submission of reports. Held annually over a 96-hour weekend in late or early , teams work from their home institutions, a structure that has enhanced accessibility since the widespread adoption of internet-based tools for contest materials and judging around the . Additionally, female participation has shown positive growth, aligning with broader efforts to promote gender equity in competitions, though specific MCM data highlights continued underrepresentation relative to overall in programs. Despite these advances, challenges persist, particularly language barriers for non-native English speakers, as all solution reports must be written and submitted in English to ensure fair evaluation by international judges. COMAP addresses this to some extent through multilingual advisor resources and problem statements available in select languages on its website, but full translations of judging criteria remain limited, potentially disadvantaging teams from non-English-dominant regions.

Awards and Recognition

Award Tiers and Criteria

The awards in the Mathematical Contest in Modeling (MCM) are tiered to acknowledge varying degrees of accomplishment, with 21,092 teams participating in . Unsuccessful Participant status applies to teams with incomplete submissions or rule violations, resulting in no award. Successful Participant recognition is granted to approximately 65% of teams for demonstrating concerted effort, though responses may exhibit weaknesses or incompleteness. Honorable Mention awards go to about 11-23% of teams for above-average work featuring sound thought processes and modeling approaches. Meritorious designation honors approximately 3.5-6% of teams for excellent performance in , model development, and clear communication. Finalist status is awarded to around 0.5-2% of teams for exemplary, logical, and comprehensive solutions that advance beyond standard expectations. The pinnacle, Outstanding Winner, recognizes the top 0.05-0.2% of submissions for exceptional, publishable-quality work that exemplifies superior modeling and problem-solving. Percentages vary by year and problem. Judging employs a holistic rubric applied by expert panels, emphasizing mathematical quality and rigor (including accurate application of methods and validation), presentation clarity and organization (ensuring logical flow and accessibility), originality and insightful interpretations, and English proficiency for effective communication. These elements are weighted variably but collectively assess the team's ability to analyze the problem, develop innovative models, solve it rigorously, and present findings coherently, with all problem aspects addressed. Panels of volunteers from mathematical organizations conduct initial and final reviews over April to June. Special awards complement the main tiers, including SIAM prizes for top Outstanding teams—one per problem (A, B, C)—offering each student a complimentary one-year SIAM membership and a for the faculty advisor and institution. The COMAP Scholarship distributes $9,000 among the six highest-ranking MCM/ICM teams (regardless of problem), with an additional $1,000 per school, capped at $3,000 per student. Other distinctions, such as the Ben Fusaro Award for the most creative Finalist paper and the Frank R. Giordano Award for modeling process excellence, highlight specific strengths. Societies like INFORMS, MAA, , and also designate winners per problem. Results are announced in early May via the COMAP and releases, detailing awarded teams, advisors, and institutions. All Successful Participants receive certificates, while select Outstanding solutions are published in COMAP's UMAP Journal.

Notable Winners and Impacts

Teams from achieved remarkable success in the Mathematical Contest in Modeling during the 1990s, frequently securing top honors and demonstrating the institution's strength in . In , for instance, Harvey Mudd teams earned three Outstanding Winner designations, a feat unmatched by any other school at the time, with two of these recognized as SIAM Winners for their innovative models on asteroid impact and problems. Earlier in the decade, additional Outstanding papers from Harvey Mudd teams further solidified their dominance in the competition. More recently, international participation has highlighted emerging powerhouses, such as in . In the 2020 MCM, a Tsinghua team received a Meritorious Winner award for Problem A, which involved modeling the economic ramifications of climate change-induced in small-scale fishing communities, showcasing advanced modeling techniques. Tsinghua also secured Finalist honors in the associated Interdisciplinary Contest in Modeling (ICM) that year. In 2025, Nanjing University of Science and Technology (NJUST) achieved its first-ever Outstanding Winners in the MCM/ICM, with two such awards, alongside multiple Finalists and Meritorious Winners. Similarly, (XJTU) secured two Outstanding Winner awards and received the COMAP Scholarship Award, underscoring the growing prowess of Chinese institutions. Participation in the MCM significantly enhances participants' resumes, aiding admissions to graduate programs and employment opportunities in technical fields. Alumni often apply the interdisciplinary skills developed—such as mathematical modeling, , and —to careers in , , and . The contest fosters these abilities through real-world problem-solving, preparing students for professional challenges beyond academia. The MCM has influenced educational practices by inspiring the integration of mathematical modeling into curricula at various institutions. Winning papers, particularly those designated as Outstanding Winners, are frequently published in professional journals like The UMAP Journal, allowing participants to contribute to scholarly discourse and gain recognition in the field. Overall, the contest promotes interdisciplinary collaboration and , with its emphasis on team-based modeling equipping over decades of participants with versatile skills applicable to diverse sectors. Since its inception in , the MCM has engaged hundreds of thousands of students worldwide, building a global network of who credit the experience with shaping their professional trajectories.

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