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Inside the MIT Project Laboratory in Mathematics

By Eric Eng

By Eric Eng

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Inside the MIT Project Laboratory in Mathematics

The Project Laboratory in Mathematics is a groundbreaking course offered at MIT, designed to immerse undergraduate students in the fascinating world of mathematical research and discovery. This unique program provides students with the opportunity to explore open-ended problems, collaborate with their peers, and engage in an experiential learning process that goes beyond traditional classroom instruction.

By participating in the Project Laboratory in Mathematics, students gain valuable insights into the creative and collaborative nature of mathematical investigation, laying the foundation for successful careers in academia, industry, and beyond.

At the core of the Project Laboratory in Mathematics is a series of open-ended research projects that challenge students to develop and apply their mathematical skills in novel and innovative ways. Working in teams, students delve into a diverse range of topics, fostering interdisciplinary collaboration and encouraging the cross-pollination of ideas.

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The Project Laboratory in Mathematics not only serves to nurture the next generation of mathematicians but also seeks to inspire a broader appreciation for the beauty and power of mathematics in shaping our understanding of the world around us.

What is Project Laboratory in Mathematics?

What is Project Laboratory in Mathematics? The traditional approach to university education often centers around structured courses designed to introduce students to well-established knowledge in a particular subject area. While this method is highly effective in transmitting existing knowledge, it can sometimes leave students with the impression that their chosen field has already been fully explored and that there is little room for innovation or further discovery.

In contrast, the Project Laboratory in Mathematics (PLM) at MIT offers a unique and engaging educational experience that immerses students in the process of mathematical discovery and highlights the living, evolving nature of the field.

The Project Laboratory in Mathematics is designed to provide undergraduate students with a taste of the excitement, challenge, and rewards of discovering new mathematical ideas. Rather than focusing on a predetermined set of content, the course encourages students to work in teams on three open-ended projects.

Through this process, they generate and analyze data, identify patterns, develop mathematical explanations, and present their findings in written and oral formats.

The learning goals of the PLM are rooted in experiential learning, which means that there is no fixed content or syllabus for students to master. This departure from traditional course structures allows students to fully immerse themselves in the process of mathematical discovery, fostering a deeper appreciation for the creative and evolving nature of the discipline.

The PLM attracts a diverse group of math majors, from students who aspire to become professional mathematicians to those who ultimately pursue careers in unrelated fields. Regardless of their future paths, many students find the PLM to be a transformative experience that forever changes their perception of mathematics.

By participating in the PLM, students come to understand that mathematics is not a static field consisting solely of established facts and theorems. Instead, they learn to appreciate the ongoing process of discovery, refinement, and innovation that lies at the heart of the discipline. This realization often inspires students to view their mathematical education as a dynamic and ever-evolving journey, rather than a finite collection of facts to be mastered.

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Moreover, the PLM provides students with valuable skills that extend beyond the realm of mathematics. By working on open-ended projects, they develop critical thinking, problem-solving, collaboration, and communication abilities, which are transferable to a wide range of career paths and industries.

For many students, the PLM serves as a powerful reminder that the world of mathematics is far from complete and that there are countless opportunities for them to contribute to its ongoing development. This realization often instills a sense of intellectual curiosity and a passion for exploration that stays with them long after they have completed the course.

Furthermore, the PLM experience can serve as a catalyst for students to pursue advanced studies or research careers in mathematics, motivated by the desire to participate in the ongoing process of discovery and innovation. For others, the skills and insights gained through the PLM can be applied to a diverse range of professional endeavors, from engineering and technology to finance and data analysis.

To summarize, the Project Laboratory in Mathematics at MIT offers a unique and transformative educational experience that invites students to delve into the heart of mathematical discovery. By emphasizing experiential learning and open-ended exploration, the PLM enables students to appreciate the living, evolving nature of mathematics and inspires them to become active contributors to the ongoing development of the field.

How Does the Project Laboratory in Mathematics Work?

How does the Project Laboratory in Mathematics work? As the only mathematics course at MIT that fulfills the university’s laboratory requirement and the CI-M (Communication Intensive in the Major) requirement, Project Laboratory in Mathematics (PLM) is a highly sought-after course. Each semester, approximately 40 to 50 students register to take the course, reflecting the high demand and widespread interest among the student population.

However, due to the labor-intensive nature of the course, enrollment is limited to 27 students per semester. This constraint is necessary to ensure that each student receives adequate support and guidance throughout the course, enabling them to fully engage with the open-ended projects and benefit from the experiential learning approach.

Enrollment Priorities and Student Demographics

To manage the high demand for the PLM, MIT has implemented a system of enrollment priorities. Mathematics majors are guaranteed the opportunity to take the course as their lab subject, and priority is given to students who urgently need the course to fulfill their graduation requirements. This approach ensures that students who are most in need of the PLM experience can access it in a timely manner.

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Unfortunately, the limited capacity of the course means that it is not always possible to accommodate as many underclassmen and non-majors as desired. Typically, about 75% of the students in the course are seniors, while the remaining 25% are a mix of juniors and sophomores. This demographic breakdown reflects the emphasis on ensuring that students who are nearing the completion of their degree programs have the opportunity to participate in the PLM.

A Diverse Range of Math Majors

The students who participate in the PLM come from a wide range of mathematical backgrounds and interests. While only about 10% of MIT’s undergraduate mathematics majors go on to become research mathematicians, the PLM attracts students with diverse career aspirations and academic goals. This diversity contributes to the richness of the learning experience, as students bring different perspectives and approaches to open-ended projects.

Prerequisites

The Project Laboratory in Mathematics (PLM) is designed for students who have a solid foundation in advanced mathematics. As such, students are required to have completed at least two advanced mathematics courses (numbered 18.100 or above) before enrolling in the PLM. This prerequisite ensures that participants have the necessary background and skills to engage effectively with the open-ended projects and contribute to the collaborative learning process.

Course Components

To provide a comprehensive and engaging learning experience, the PLM is structured to include a variety of activities that cater to different aspects of mathematical discovery and skill development. Students are expected to dedicate approximately 12 hours per week to the course, with their time divided among several key components, which are detailed below and further elaborated upon in other sections of the course site.

Class Sessions

The PLM begins with several class sessions that introduce students to the course’s philosophy and structure, as well as provide essential workshops to help them develop the skills they will need throughout the semester. In the Spring 2013 semester, for instance, there were four initial class sessions:

Introductory Lecture: This session familiarizes students with the course’s objectives, philosophy, and structure. It sets the stage for the immersive, experiential learning experience that defines the PLM.

Teamwork Workshop: As students will be working in teams on open-ended projects, this workshop focuses on building effective collaboration skills, such as communication, conflict resolution, and group decision-making.

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Presentation Workshop: Given the importance of presenting results and findings in a clear and compelling manner, this workshop equips students with essential presentation techniques and strategies to effectively share their work with others.

Writing Workshop: The ability to communicate complex mathematical ideas through written language is a critical skill for success in the PLM. This workshop helps students hone their writing skills and provides guidance on crafting clear, concise, and engaging mathematical explanations.

The Project Laboratory in Mathematics offers students a well-rounded and immersive educational experience, emphasizing not only mathematical discovery but also the development of essential collaboration, presentation, and writing skills. By requiring prerequisites and incorporating a variety of engaging course components, the PLM ensures that students are well-prepared to participate in and benefit from this unique and transformative learning journey.

What can you Expect When Participating in the Project Laboratory in Mathematics?

What can you expect when participating in the Project Laboratory in Mathematics? Participating in the PLM is a transformative experience for many students. By working on real-world problems, they gain valuable insights into the relevance and potential impact of their mathematical skills. In addition, they develop a deep appreciation for the power of collaboration and interdisciplinary thinking.

The Project Laboratory in Mathematics (PLM) offers students a unique, hands-on learning experience that immerses them in the process of mathematical discovery. The course is structured around three open-ended research projects, with each project cycle lasting five to six weeks. These project cycles are deliberately overlapped to allow time for revision in response to staff feedback. Below is a detailed outline of the various components involved in each project cycle.

Topic Selection: Teams of three students choose a project topic from a list of over 40 options, with each topic typically available for selection by only one team per semester. This ensures a diverse range of projects being explored concurrently within the course.

Mathematical Work: Students collaborate within their teams to investigate their chosen project topics. Activities during this stage may include working through examples, running computer simulations, reviewing relevant literature, refining the project’s focus, formulating conjectures, and attempting to construct proofs.

Mentor Meetings: For each project, student teams are assigned to one of the three mathematics instructors as their mentor. These teams meet with their mentors on a weekly basis throughout the duration of the project. Additionally, a communication instructor works with all teams to provide guidance on effectively presenting their findings.

First Draft: Approximately 1.5 weeks before the final draft deadline, teams submit a first draft of their project papers. These drafts are reviewed and commented upon by the team’s mentor and, in some cases, the communication instructor.

Debriefing Meetings: Following the submission of the first draft, teams meet with a group comprising the lead instructor, their mentor, their mentor for the next project, and often the communication instructor. During this meeting, teams present a brief overview of their research, and the group discusses both the mathematical content and the quality of the writing.

Final Draft: To complete a project cycle, students revise their papers based on the feedback received from instructors and submit a final draft.

Presentations: Each team delivers a presentation on one of their projects during the semester. Before the formal presentation, teams participate in a practice presentation attended by course instructors, who provide extensive feedback. Teams then refine their presentations before presenting to the entire class.

The Project Laboratory in Mathematics offers a dynamic, collaborative learning environment that challenges students to engage in mathematical exploration and develop essential skills in research, communication, and teamwork. Through a series of overlapping project cycles, students are exposed to the excitement and challenges of mathematical discovery, gaining valuable insights and experiences that extend far beyond the traditional classroom setting.

What is the Impact of the PLM on the Future of Mathematics?

What is the impact of the PLM on the future of mathematics? The Project Laboratory in Mathematics (PLM) has a significant impact on the future of mathematics by cultivating a new generation of mathematicians and problem solvers.

The course’s unique approach to experiential learning and collaborative problem-solving not only equips students with the skills necessary for successful careers in mathematics but also fosters a broader appreciation for the discipline among students with diverse interests and aspirations. The key impacts of the PLM on the future of mathematics can be summarized as follows:

Nurturing Mathematical Talent: By providing a hands-on learning experience focused on open-ended research projects, the PLM encourages students to explore new mathematical concepts and ideas. This approach helps to identify and nurture talented individuals who may go on to make significant contributions to the field of mathematics.

Fostering a Growth Mindset: The PLM’s emphasis on collaboration, perseverance, and critical thinking helps to instill a growth mindset among students. This mindset is crucial for success in the ever-evolving field of mathematics, as it encourages students to embrace challenges and view setbacks as opportunities for learning and improvement.

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Encouraging Interdisciplinary Collaboration: The course attracts students from diverse academic backgrounds, promoting interdisciplinary collaboration and enabling students to draw connections between seemingly disparate fields. This cross-pollination of ideas can lead to innovative solutions and novel applications of mathematical principles in various domains.

Developing Essential Skills: The PLM emphasizes the development of essential skills, such as teamwork, communication, and presentation. These skills are crucial not only for success in mathematical research but also for careers in industry, academia, and beyond, as they enable individuals to effectively share their insights and collaborate with others to solve complex problems.

Inspiring Future Mathematicians: For some students, the PLM serves as an introduction to the world of mathematical research, sparking a lifelong passion for the discipline. By inspiring students to pursue further study and careers in mathematics, the PLM helps to ensure a continuous pipeline of talented individuals who can contribute to the advancement of the field.

Ultimately, the Project Laboratory in Mathematics plays a critical role in shaping the future of mathematics by nurturing talent, fostering a growth mindset, promoting interdisciplinary collaboration, developing essential skills, and inspiring the next generation of mathematicians.

By offering a unique and transformative educational experience, the PLM equips students with the tools and insights necessary to make meaningful contributions to the field and drive innovation across a wide range of disciplines.

Conclusion

The MIT Project Laboratory in Mathematics stands as a testament to the power of mathematics in solving real-world problems and the importance of fostering a culture of collaboration and innovation. Through its unique blend of hands-on learning, mentorship, and interdisciplinary engagement, the PLM is shaping the future of mathematics and preparing students to tackle the complex challenges of the 21st century.

By immersing students in the practical applications of mathematics, the PLM is helping to bridge the gap between theory and practice, driving innovation across various industries, and contributing to the advancement of mathematical knowledge. As we look to the future, the MIT Project Laboratory in Mathematics will continue to play a pivotal role in shaping the next generation of mathematicians and fostering a culture of collaboration, creativity, and impact in the field of mathematics.

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