# MathILy (serious mathematics infused with levity)

**{MathILy, MathILy-Er}** are a pair of intensive 5-week-long residential summer math programs for high school students.

The math instruction is interactive and inquiry-based. Math class meets for about 7 hours a day total, in a morning and evening shift, six days a week. The lead instructors are mathematicians with Ph.D.s and the apprentice instructors are graduate or undergraduate math students. The math content covered is undergraduate- and graduate-level.

Our 2024 programs will be taking place online from June 30-August 3, with MathILy at Bryn Mawr College and MathILy-Er at Arcadia University. The program fee will be $5300.

## MathILy History

MathILy was founded in 2013 by dr. Sarah-Marie Belcastro. The program took place at Bryn Mawr College between 2013 and 2019, online in 2020 and 2021, and back to Bryn Mawr in 2022, growing from 17 attendees the first year to 46 in 2023. MathILy-Er, a sister program meant for students who are a little earlier in either age or mathematical development, had its first year in 2015, and grew from 15 attendees in 2015 to 31 attendees in 2023.

## Application Process

MathILy and MathILy-Er share an application process. The two programs admit students with different degrees of mathematical prowess, with MathILy-Er intended to prepare promising students for MathILy and other very selective residential summer mathematics programs. If an applicant is admitted, placement in a given program is determined by academic suitability only.

Here's what the {MathILy, MathILy-Er} application process looks like:

- Start by filling out the Short Form, so we know you're interested in us!
- Next comes the Exam Assessing Readiness, hereafter referred to as the EAR. The EAR is generally released early in the year the program takes place. We'll send you a copy once you've sent us a short form – at least, assuming that it's ready at the time you send your short form.
- You should also fill out a Not-as-short form, components of which are: biographical information, academic information, and more information about you, including a short essay about why you want to attend MathILy.
- In order to complete your {MathILy, MathILy-Er} application, we'll also need a recommendation letter from a teacher who can speak to your mathematical preparedness; make sure to have an email address at hand for them when you fill out your Not-as-short form!

Admission to {MathILy, MathILy-Er} is determined by a combination of student performance on the Exam Assessing Readiness (hereafter referred to as the EAR), a teacher recommendation, and the information gathered on the Not-as-Short form.

## Course Structure

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. (Topics for Root Class at MathILy 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. MathILy-Er topics for Root Class will also include combinatorics and graph theory, as well as ring and matrix algebra and combinatorial game theory, and are likely to include proof techniques and number theory.) 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. (For 2020, the Branch Class topics at MathILy are likely to include polytopes, chip-firing games, and the mathematics of paperfolding, and the Branch Class topics at MathILy-Er are likely to include voting theory and non-Euclidean geometry.)

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.

## External Links

- Check out the MathILy website!
- Also check out the MathILy-Er website!
- Mathematical Staircase, Inc. is the nonprofit organization that runs MathILy.