The camp for rising 8^{th} or 9^{th} grade (age 12-15) students was 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 was 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 was 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 learned valuable mathematical techniques such as the pigeonhole principle and coloring arguments. We asked questions (like “can the spider make his way out of this strange cube?”), convinced ourselves that the answer is no, and then used our newfound skills to prove it!

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

Which games have a winning strategy? We played and explored a variety of games involving chance, strategy, social cooperation and anticipating the actions of others. We used 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 learned how to show that different infinite sets have different sizes; indeed, some infinities are bigger than others! Along the way we developed 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 explored these questions and more as we learned about fractals and chaos theory in this course.

## About Us

## SIM Camp Epsilon:

Counting Pigeons and Other Problem Solving Techniques

- Instructor: Jenna Zomback
- Assistant Instructors: Yasir Badillo Acosta, Iris Tong

Maximize Your Winnings: Using Math to Understand Games

- Instructor: Emily Shinkle
- Assistant Instructors: Jack Bernard, Alice Lam

## SIM Camp Delta

Counting to Infinity (Plus One!)

- Instructor: Alexi Block Gorman
- Assistant Instructors: Yasir Badillo Acosta, Iris Tong

Maximize Your Winnings: Using Math to Understand Games

- Instructor: Emily Shinkle
- Assistant Instructors: Jack Bernard, Alice Lam

## SIM Camp Omega

Counting to Infinity (Plus One!)

- Instructor: Alexi Block Gorman
- Assistant Instructors: Yasir Badillo Acosta, Iris Tong

From Snowflakes to Seashells: Exploring Fractals

- Instructor: Emily Shinkle
- Assistant Instructors: Jack Bernard, Alice Lam

## Instructors

**Alexi Block Gorman** will be teaching Counting to Infinity (Plus One!) at SIM Camps Delta and Omega. She is a graduate student in mathematics working in logic on problems in model theory. Her favorite theorem is Gödel's First Incompleteness theorem, because it guarantees that mathematicians will not be out of a job any time soon.

**Emily Heath** will be teaching From Snowflakes to Seashells: Exploring Fractals at SIM Camp Omega. She is also the program coordinator for SIM Camp. She is a third year graduate student in mathematics interested in graph theory and combinatorics. In her free time, Emily loves reading and watching Netflix.

**Emily Shinkle **will be teaching the Maximize Your Winnings: Using Math to Understand Games course at SIM Camps Epsilon and Delta. She is is a graduate student in mathematics. She has a bachelor's degree in math education and loves exploring interesting mathematics with students. When she's not doing math or teaching, she enjoys playing the flute, spending time with friends, and visiting new places.

**Jenna Zomback **will be teaching the Counting Pigeons and Other Problem Solving Techniques course at SIM Camp Epsilon and will be the assistant program coordinator this summer. She will be a second year graduate student in mathematics.

## Assistant Instructors

**Yasir Badillo Acosta **will be a sophomore studying Mathematics in the Fall of 2018. Yasir is looking forward to being an assistant instructor for Sim Camp Epsilon: Counting Pigeons and Other Problem Solving Techniques, and Sim Camp Omega: Counting to Infinity (Plus One!). Additionally, he enjoys playing Clarinet and is also a part of the University of Illinois: Marching Illini!

**Jack Bernard** is a junior majoring in Engineering Physics. He is an assistant instructor on Maximize Your Winnings SIM Camp Epsilon and Delta, as well as Exploring Fractals SIM Camp Omega. He worked on the Veech Jigsaw Project for the Illinois Geometry Lab in 2017.

**Alice Lam **will be a sophomore in the Fall of 2018. For this summer's SIM Camp, she is an assistant instructor for Maximize Your Winnings and Exploring Fractals.

**Iris Tong **will be a junior in the Fall of 2018. She is studying statistics and mathematics with a Concentration in Teaching. Outside of doing math, she likes to paint and play trombone.

### Organizers

**Emily Heath** is the program coordinator for SIM Camp.

**Claire Merriman** is the director of SIM Camp. She will be a sixth year graduate student in mathematics, interested in differential geometry and number theory. She ran the Making and Breaking Codes course at SIM Camp Epsilon in 2016, and created and ran the Number Theory and Cryptology class at the 2015 camp.

**Simone Sisneros-Thiry** is an assistant program coordinator for the 2018 SIM Camp, and was program coordinator in 2016 and 2017. She will be a fifth year graduate student in mathematics interested in combinatorial number theory and mathematics education. Simone studied secondary education at the University of Maine at Farmington, and continues to split her time between learning math, teaching math, and learning about teaching math.

**Jenna Zomback **is an assistant program coordinator.

**Jennifer McNeilly** is a faculty organizer at SIM Camp. She has been Director of the Math Merit Program for Emerging Scholars since 2001. She has won multiple teaching awards, primarily teaching courses at the precalculus level. She is also an advisor to the math majors in the secondary education program.

**Jeremy Tyson** is a faculty organizer at SIM Camp. He is a Professor in the University of Illinois at Urbana-Champaign Department of Mathematics and director of the Illinois Geometry Lab.

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.