Summer Illinois Math (SIM) Camp is a free, week-long math day camp for middle and high school students hosted by the University of Illinois at Urbana-Champaign Department of Mathematics. Campers will see the creative, discovery driven side of mathematics. By showing them some of the ways mathematicians approach problems, SIM Camp hopes to encourage them to continue studying math beyond the high school level.

We will offer three camps in 2018. As in the past, SIM Camp Epsilon is for students entering 8th or 9th grade in Fall 2018. SIM Camp Delta is now for students entering 9th or 10th grade. We are also introducing SIM Camp Omega for students entering 10th through 12th grade.

**Please consider donating to the Department of Mathematics Outreach fund, which supports our Summer Illinois Math camp and other outreach initiatives. Your support helps our department fulfill Illinois’s land grant mission.**

## Summer 2018

The camp for rising 8^{th} or 9^{th} grade (age 12-15) students will be **June 25 ^{th} to June 29^{th}**. Topics will be Counting Pigeons and Other Problem Solving Techniques and Maximize Your Winnings: Using Math to Understand Games.

The camp for rising 9^{th} and 10^{th} (age 13-16) grade students will be **July 9 ^{th} to July 13^{th}**. Topics will be Counting to Infinity (Plus One!) and Maximize Your Winnings: Using Math to Understand Games.

The camp for rising 10^{th} through 12^{th} (age 14-18) grade students will be **July 23 ^{rd} to July 27^{th}**. Topics will be Counting to Infinity (Plus One!) and From Snowflakes to Seashells: Exploring Fractals.

**Counting Pigeons and Other Problem Solving Techniques**

How do we prove that something is impossible? Campers will learn valuable mathematical techniques such as the pigeonhole principle and coloring arguments. We will ask questions (like “can the spider make his way out of this strange cube?”), convince ourselves that the answer is no, and then use our newfound skills to prove it!

**Maximize Your Winnings: Using Math to Understand Games**

Which games have a winning strategy? We will play and explore a variety of games involving chance, strategy, social cooperation and anticipating the actions of others. We will use mathematical approaches to help us understand and play games better.

**Counting to Infinity (Plus One!) **

Is infinity a number greater than all other numbers, or is it the size of a set that is larger than all finite sets? Are these two notions the same, and how do we make them mathematically rigorous? In this course students learn how to show that different infinite sets have different sizes; indeed, some infinities are bigger than others! Along the way we develop the basic elements of set theory and grapple with notions of orderings on infinite sets and maps between sets.

**Snowflakes to Seashells: Exploring Fractals**

Can a region have finite area and infinite perimeter? Is there a dimension between one and two? Fractals appear all around us in nature and art and raise many interesting questions like these that challenge our intuition. We will explore these questions and more as we learn about fractals and chaos theory in this course.

## Apply

Students attending the rising 8th and 9th grade camp must have taken a pre-algebra class, while students at the rising 9th through 12th grade camps need to have taken at least one year of algebra.

**All three weeks are full. **We will continue accepting applications for the waitlist for SIM Camp Delta and SIM Camp Omega. The application is available here.

## Directions

SIM Camp will be held in Altgeld Hall on the University of Illinois Campus at the corner of Wright Street and Green Street in Urbana.

You can find more transportation information here.

## About Us

Claire Merriman, director

Emily Heath, program coordinator

Simone Sisneros-Thiry, assistant program coordinator

Jenna Zomback, assistant program coordinator

You can find more information about us here.

If you have questions, please contact math-simcamp@illinois.edu.

## Sponsors

Support is provided by:

**Office of Public Engagement**, University of Illinois for a Public Engagement Grant- Department of Mathematics, University of Illinois
- Illinois Geometry Lab, University of Illinois
- Association for Women in Mathematics, University of Illinois
- Dolciani Mathematics Enrichment Grant , Mathematical Association of America
- National Science Foundation , Grant Number DMS-1449269

**Please consider donating to the Department of Mathematics Outreach fund, which supports our Summer Illinois Math camp and other outreach initiatives. Your support helps our department fulfill Illinois’s land grant mission.**

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This material is based upon work supported by the National Science Foundation under Grant Number DMS-1449269.