**Who:** Mathematically talented high-school students. More details.

**What:** Five weeks of intense interactive inquiry-based
individualized instruction. More details.

**When:** June 24 - July 31.

**Where:**The Internet.

**Why:** Because math is *cool!* (So are bowties. And suspenders.)

**The application process:** Has three parts (short form, Exam
Assessing Readiness , not-as-short form). More details.

**Note about SARS-CoV-2/COVID-19:** MathILy *will* take place in 2021, synchronously online.

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

**Fee:** $2150, which is $430/week.

**Financial Aid:** With the generous support of the AMS Epsilon Fund and individual donors, we are able to award financial aid for MathILy 2021.
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 2021. 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.

**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.

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 2021, the Branch Class topics are likely to include topological graph theory, discrete and computational geometry, and persistent homology.

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 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:**

- dreamers who love mathematics
- future computer scientists and engineers who want to strengthen their problem-solving abilities
- students who find mathematics class boring but suspect there may secretly be more to the mathematical world than they currently perceive.

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.)

**Practical stuff:** We'll tell you technical 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..*