PROMYS (Program in Mathematics for Young Scientists) is an intensive six-week summer math programme that has been running for over 30 years. It is designed for high school students who are passionate about mathematics and an interest in exploring the world of mathematical thinking alongside other motivated young people.
Overview of the Programme
Each year, typically between late June to early August, around 60 students from around the world join a further 20 returning students to attend the six week PROMYS summer camp at Boston University. The focus of the work is on topics in number theory, and other areas of mathematical thinking are explored as well.
Monday to Friday mornings at PROMYS start with a daily lecture on number theory. At the end of the session, participants receive their daily problem set which is intended to encourage participants to design their own numerical experiments and to employ their own powers of analysis to discover mathematical patterns, formulate and test conjectures, and justify their ideas by devising their own mathematical proofs.
The rest of the time at PROMYS is relatively unstructured. Instead of attending classes, students will work on their assigned number theory problem sets, either independently, or in small groups. PROMYS counsellors review the responses to these problem sets and then are available to provide further guidance and support to enable students to gain new insight as to how the problems can be worked.
Students who are particularly motivated or have attended PROMYS in previous years can participate in more advanced seminars on specific math topics. The topics for these seminars will change from year to year but in 2022 the topics included Graphs, Matroids, and Polynomial Countability; Number-theoretic Cryptography; and Linear Algebra, Bernstein Polynomials, and Visualization. The seminars are led by some of the guest lecturers that visit the programme.
All PROMYS students will engage in research. For first year attendees, this takes the form of an Exploration Lab while returning students get to select a problem posed by a research mathematician that they then work through in teams of four. At the end of the programme, students write up their work and present it to the other students, faculty and guest lecturers.
PROMYS is a residential programme. Participants live in Boston University residential housing, which they share with the counsellors that support them during their course. While many find that their so called ‘non-class time’ is spent working on their problem sets there is also the opportunity to make use of the university sports facilities and go on visits to local attractions in and around Boston.
There are two non US based programmes, PROMYS India and PROMYS Europe. PROMYS India takes place at the Indian Institute for Science in Bangalore between May and June while PROMYS Europe is based in Oxford. Both programmes run along very similar lines to the US programme with a mix of number theory and problem sets.
Entry Requirements and Cost
The entry requirements are fairly minimal, applicants must be at least 14 and have completed 9th grade or its equivalent and so have done at least one year of high school maths, but not have started at college or university.
The cost of the programme is $6,000 for tuition, room and board. However, financial aid is available for domestic US students and successful candidates whose families have an income of less than $80,000 per year attend free of charge. International students can submit a financial aid form for consideration alongside their application for the programme The programme also offers several scholarships to outstanding students, some of which are open to both US and international students. There are some scholarships available to specific groups of students, most noticeably applicants from China. Indian students who require financial aid should apply to PROMYS India which offers full scholarships to all successful students.
How to Apply
Applications to PROMYS are typically later than for many of the other summer programmes, application material is normally released around the beginning of February and closes six weeks later. The application process seeks to evaluate the mathematical understanding of the applicant, in particular, they seek to understand the applicants’ desire and ability to think deeply about fundamental mathematical principles and whether they are likely to be a good fit for this type of intensive, immersive summer program. While there is no set requirement to have studied specific topics, the application will test your skills to breaking point.
The PROMYS application requires an appreciable amount of work. In addition to providing basic information about themselves, applicants will also need to answer several questions about their interest in Maths and what they hope to gain from attending the program. Applicants also need to submit an official transcript from their school and a recommendation from a recent math teacher. Similar to other math programs, PROMYS also requires applicants to submit an assigned number theory problem set as part of their application. This problem set is designed to be quite challenging, and applicants don’t always fully solve all the problems they’re assigned. However, not finishing the problem set doesn’t mean an applicant won’t be accepted. Whatever work is done toward finding a solution will show off their math skills and creative problem-solving abilities to the admissions team. The problem set is very similar to the type of work students work on during the program. So, if you don’t enjoy the problem set then PROMYS is probably not going to be for you.
Competitiveness and Types of Students Accepted
The program is highly selective, with only about 80 students accepted each year from a pool of over 600 applicants. The students who are accepted are typically highly motivated and passionate about mathematics. They come from a variety of backgrounds and from all over the world. What they all have in common is that they are absolutely absorbed in maths. Students will have already studied maths to a high level in school and then be able to demonstrate their passion for the subject through additional work that goes beyond what they will have covered in the school curriculum. Students that have been selected in the past will perhaps be actively involved in a maths circle and maybe are working on mathematical proofs with a graduate maths student. First and foremost, students need to eat, live and breathe their passion for maths. participants spend all day, every day doing maths. If that does not appeal to you, then PROMYS is not going to be a good way to spend the summer.
Final Words
In conclusion, the PROMYS summer math program is an excellent opportunity for high school students who are passionate about mathematics and are interested in pursuing a career in math, science, or engineering. The program is highly competitive and the application process is rigorous, but for those who are accepted, it is an experience that can be life-changing. If you are interested in applying, be sure to check the application deadline and start preparing early. Good luck!
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