**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!*

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

A sample morning class at 500x speed

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

**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-Er 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 grantsfor students who have been members for at least a semester. Past MathILy-Er students have benefitted from this excellent program!

**Number of students:** about 30.

**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 a more advanced Branch Class in the final two weeks.

**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, binary linear algebra, infectious disease modeling, and number theory, and are likely to include proof techniques, combinatorial game theory, and ring theory. Some of that may sound familiar, but at MathILy-Er we look at aspects of the material that will be new to you. Each topic will be treated in depth, or at an advanced level (or both!), and there is no overlap with the MathILy Root curriculum.
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 hyperplane arrangements, cryptography, quadratic forms, generating functions, finite automata, ordinal numbers and more. For 2021, the Branch Class topics are likely to include Combinatorial Game Theory and non-Euclidean geometry.

**Differences from MathILy:** MathILy-Er is designed for students who are slightly earlier in their chronology or mathematical development, but who still want the intensity of a five-week residential summer program. MathILy-Er is highly selective, and the curriculum often includes current research-level mathematics. The topics studied at the two programs are entirely different from one another, so MathILy-Er alumns are encouraged to apply to MathILy in future summers.

**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.

**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-Er 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 making anagrams.

**Not-exactly-math things:** Part of MathILy-Er is a "life
seminar." We'll have a program-wide discussion about college choices, and a
session on career possibilities in and outside of the mathematical sciences. There will regularly be surprising cool activities (no details or they wouldn't be surprising).
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..*