Fast Facts about MathILy!

Who: Mathematically talented high-school students. More details.
What: Five weeks of intense interactive inquiry-based individualized instruction. More details.
When: Exact dates to be determined, but 5 weeks including July 2022.
Where: To be determined (On Campus vs. The Internet).
Why: Because math is cool! (So are bowties. And suspenders.)
The application process: Has three parts (short form, Exam Assessing Readiness ear, not-as-short form). More details.

Note about SARS-CoV-2/COVID-19: MathILy will take place in 2022, hopefully in person (with full vaccination required), but if that is not possible, then MathILy will again take place synchronously online.


a typical class

As groups of students work at the board, the instructors listen in on groups of students working at tables.

Fee: If MathILy is in person, the fee will be $4950 ($990/week); if MathILy is online, the fee will be $2150 ($430/week).
Financial Aid: With the generous support of individual donors, we are able to award financial aid for MathILy 2022. All financial aid is based entirely on need, and yes, the entire fee may be waived for an admitted applicant with significant need. In the past we have been able to meet the demonstrated financial need of almost all admitted students, and we expect this will be the case again in 2022. Priority is given to U.S. students over international students, and we do not currently award financial aid to interplanetary or interstellar students. In addition, Mu Alpha Theta has grants for students who have been members for at least a semester. Past MathILy students have benefitted from this excellent program!
Number of students: approximately 45, this year.

Yes, we existed in several previous summers. More details.

Slow Facts about MathILy!

Academic details: Class meets for about 7 hours per day, in two shifts (morning and evening), 6 days per week. Each class has a Lead Instructor who is a mathematician with a Ph.D. and one or two Apprentice Instructors who are graduate or undergraduate mathematics students. The weeks break down into a 2-1-2 schedule: We start with two weeks of Root Class, which consists of a gallimaufry and melange of mathematics that gives all students a base on which to grow. This is followed by Week of Chaos, in which there are many many short classes with topics suggested by students and instructors alike. The denouement of the program offers more advanced Branch Classes in the final two weeks.


Root class in progress

As can be seen on the board, aliens attacked Devil's Tower on the first day of Root class 2018.

Mathematical content: It's undergraduate- and graduate-level mathematics not usually encountered in high school. (You may correctly conclude that calculus is not one of the topics on offer---we don't want to spoil anyone's fun!) The core of the curriculum is discrete mathematics, with additional material determined partly by the interests and direction of the class. Topics for Root Class will certainly include combinatorics, graph theory, affine geometry, and theoretical linear algebra, and are likely to include some proof techniques, number theory, probability, group theory, and cardinality. Some of that may sound familiar, but at MathILy we approach the material with perspectives that will be new to you. Each topic will be treated in depth, or at an advanced level (or both!). There is additional material available for returning students and new students with particularly strong backgrounds. If there's a topic you want to learn about and your class doesn't discuss it, ask that it be offered during Week of Chaos! Topics could include alternate geometries, ciphers and cryptography, combinatorial optimization, generating functions, information theory, knot theory, Markov chain modeling ... and that's just from the first half of the alphabet. For 2022, the Branch Class topics are likely to include polytopes, chip-firing games, and the mathematics of paperfolding. the mathematics of computation.


Branch class in progress

The persistent homology Branch class works on a variety of colorful examples.

Class format: Each class is taught in an entirely interactive way, with students discovering mathematics and leading the way in sharing conjectures and providing proofs. Classes include independent and collaborative problem solving as well as lots of laughter; in this way, students learn creative and rigorous mathematical thinking and writing.


students generate examples

Students are using Sage to generate 3- and 4- dimensional polytopes.

Daily schedule: Breakfast, then class, then lunch, then mostly-free afternoon, then Daily Gather, then dinner, then class, then... maybe you'll be tired and want to go to bed. The afternoon is only mostly free because (a) in some afternoons, you'll work on writing summaries of what's happened in class, and (b) you and your newly-made friends will play frisbee and music and games and do new and interesting things never yet conceived. By the way, the instructors live in the dorm with students so they're around for every activity in the list that starts this paragraph.

We seek:

MathILy is for high-school students. If you're not in high school, we will still consider your application, but high-school students generally take precedence in admissions. See the application process page for more details.

Skills Enhanced: You'll learn how to be a mathematician---that includes acquiring good thinking habits, good problem-solving habits, and good writing habits. That will help you excel in collegiate mathematics classes and other collegiate classes, and for that matter in internships and research programs in many fields. You'll practice asking questions and using mathematical language and playing catch on one foot. (That last skill is probably the hardest of all of them! Seriously, have you ever tried it?)

Not-exactly-math things: Part of MathILy is a "life seminar." There we'll have a program-wide discussion about college choices, a session on career possibilities in and outside of the mathematical sciences, and talk about mathematical insecurity, preferred gender pronouns, and how to properly use chalk. We will regularly show short mathematical animations and films. There will be at least one program trip to Philadelphia. At the end of the summer, instructors will write individual evaluations that include descriptions of student work and progress as well as suggestions for improvement. (In most cases, these can easily become letters of recommendation.)


visiting the Haverford Duck Pond


MathILy closing meeting

Practical stuff: We'll tell you practical details, what the precise daily schedule is, and more, after you've applied and if you are admitted.

If after reading this whole page you still have questions, please do contact us at .

MathILy, MathILy-Er, and MathILy-EST are projects of the nonprofit organization Mathematical Staircase, Inc..