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Primes Logo MIT PRIMES: Program Details

MIT PRIMES is a free, year-long program, in which high school students work on individual and group research projects in mathematics and participate in reading groups under the guidance of academic mentors, usually graduate students or postdoctoral scholars.

Timetable

The program operates throughout the calendar year in four distinct phases:

  • Phase I, January 1 – Pi Day:

    Advanced reading period. By early January students are notified of the admission decision and assigned a mentor, who will recommend advanced readings that may be useful for a future research project. To successfully complete Phase I, a student must submit a brief 5-page reading report approved by the mentor by early March. PRIMES will then evaluate the student's readiness for research and invite the ones with strongest motivation, commitment and progress to proceed to Phase II.

    Time commitment : at least 10 hours per week, including home study and a 1.5-hour weekly meeting with the mentor. The day/time of the meeting will be chosen to suit both the student and the mentor.

  • Phase II, Pi+0.01 Day – May 31:

    Active research period. Students work on their projects under the guidance of their mentors and may occasionally discuss their projects with the MIT faculty member who suggested the project and with the head mentor. At the end of May, students submit an interim report on the progress of their research projects.

    Time commitment : at least 10 hours per week.

  • Phase III, June 1 – August 31:

    Independent study period. Students continue working on their projects independently, staying in e-mail contact with their mentors. PRIMES does not conflict with any summer programs , since it has a flexible schedule in the summer.

    Time commitment : flexible.

  • Phase IV, September 1 – December 31:

    Write-up period. Students meet with their mentors as needed and stay in regular e-mail contact. With the help of the mentor, students finalize their projects and present them at the Fall-Term PRIMES conference in mid-October, which family members and friends will be welcome to attend. By the end of the year, students also write a final paper summarizing their results, which will be posted on the PRIMES website. This paper may be submitted to national science competitions for high school students and/or sent to professional research journals for publication.

    Time commitment : as needed to complete program requirements.

Milestones

  • March 14: brief reading report
  • June 15: interim research report
  • Mid-October: conference presentation
  • December 1: penultimate draft of the final paper
  • December 31/January 15: final research paper

Reading groups

The Math section includes a research track and a reading group track .

Participation in the research track will require very advanced mathematical background. Participation in a reading group would serve as an excellent preparation for future research at PRIMES and beyond.

Reading mathematical literature is a vital part of professional life of any mathematician. It is of key importance at all ages, but especially so for students. For many students, guided reading proves more intellectually stimulating and beneficial than an immediate plunge into research. Devoting your first year at PRIMES to guided reading would build a solid foundation for attacking a challenging research problem the following year.

A PRIMES reading group is a pair of high school students who actively study an advanced mathematical book under the guidance of a mentor, with whom they meet weekly at MIT (for about 2 hours) in the spring and fall semesters. In between meetings, they read assigned chapters, solve homework problems, and discuss the material with each other and with the mentor by e-mail or skype. In December (for seniors: in May), they make oral presentations and submit an expository paper on the material they have studied.

Reading groups study advanced books, usually assigned to advanced undergraduates and graduate students, such as:

  • Adams, The Knot Book
  • Alekseev, Abel's Theorem in Problems & Solutions
  • Alon and Spencer, The Probabilistic Method
  • Apostol, Introduction to Analytic Number Theory
  • Cox, Primes of the form x^2+ny^2
  • Davenport, The Higher Arithmetic
  • Etingof, Introduction to Representation Theory
  • Gallian, Contemporary Abstract Algebra
  • Graham, Knuth and Patashnik, Concrete Mathematics
  • Herstein, Topics in Algebra
  • Hoffstein, Pipher and Silverman, An introduction to mathematical cryptography
  • Iwaniec and Kowalski, Analytic Number Theory
  • Lang, Algebra
  • Niven, Zuckerman, and Montgomery, An Introduction to the Theory of Numbers
  • O'Donnell, Analysis of Boolean Functions
  • Rotman, An Introduction to the Theory of Groups
  • Silverman, A Friendly Introduction to Number Theory
  • Silverman and Tate, Rational Points on Elliptic Curves
  • Stanley, Enumerative Combinatorics
  • Stillwell, Geometry of Surfaces
  • Strogatz, Nonlinear Dynamics And Chaos

The reading group track is highly recommended for students who are just entering PRIMES (especially younger students - freshmen and sophomores). This track is also suitable It for seniors, who would be in PRIMES for only half a year before going to college.

When we consider applications, we may decide that a student needs more background before s/he can work on a research project. In this case, we might admit this applicant to the reading group track, if s/he has applied for it. This is why we encourage you to apply to the reading group track, whether or not you also apply to the research track.

Admissions

PRIMES is a free program. The students are selected on the basis of their demonstrated extraordinary mathematical ability, potential for conducting original research or advanced reading, and self-motivation for independent study. A small number of candidates is admitted, and a very advanced background is expected. For details, see How to Apply to MIT PRIMES .

Academic Integrity Rules

PRIMES expects its participants to adhere to MIT rules and standards for honesty and integrity in academic studies. As a result, any cases of plagiarism, unauthorized collaboration, cheating, or facilitating academic dishonesty during the application process or during the work at PRIMES may result in immediate disqualification from the program, in the sole discretion of PRIMES. In addition, PRIMES reserves the right to notify a participant's parents, schools, and/or recommenders in the event it determines that a participant did not adhere to these expectations. For explanation of these expectations, see What is Academic Integrity?

Contact

With questions, contact PRIMES Program Director Slava Gerovitch at