We will offer two summer camps on UIUC campus in summer 2022. **Camp Epsilon** is designed for rising 8th through 10th graders. It will start on June 6th and end on June 10th. **Camp Delta** is for rising 10th through 12th graders and will run from June 20th to June 24th.

View the 2022 brochure.

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##### The applications for SIM Camp 2022 are now closed. We encourage interested students to apply next year!

##### Topics for this year's camps are:

**Counting with Symmetries**

How many different ways can you paint the faces of a cube red, green, or blue? What if you paint the edges instead of the faces, or the vertices? These simple-sounding questions can be tricky to answer, complicated by the symmetries of the cube. In this course, we'll begin by developing general combinatorial techniques to help us count more cleverly. By the end of the week, we will discuss the mathematics of symmetry and combine it with our newfound counting prowess to solve tricky problems like the ones given above.

**Representation of Integers as Sum of Squares **

One of the famous questions in Number Theory involves searching for integers which can be written as the sum of two squares. Our aim is to precisely determine which numbers have this property. We will start with basic congruence properties, followed by Fermat's Little Theorem, Wilson's Theorem etc. before proving our main result. If time permits, we will discuss the number of such representations for each integer and its connection to lattice points inside a circle.

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

Which games have a winning strategy? We will play a variety of games involving chance, strategy, social cooperation, and anticipating the actions of others, while exploring topics in probability and game theory. Through mathematical approaches, we will learn how to develop strategies to play games better.

## SIM Camp Epsilon:

Representation of Integers as Sum of Squares

- Instructor: Debmalya Basak
- Assistant Instructor: Mingqi Wang

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

- Instructor: Meghann Veronica Long
- Assistant Instructor: Laszlo Richard Toth

## SIM Camp Delta

Counting with Symmetries

- Instructor: Ada Stelzer
- Assistant Instructor: Laszlo Richard Toth

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

- Instructor: Meghann Veronica Long
- Assistant Instructor: Mingqi Wang

## Instructors

**Meghann Long** will be teaching Maximize Your Winnings: Using Math to Understand Games at SIM Camp Delta and Epsilon. Meghann is a first year graduate student in the Teaching of Mathematics. She is a secondary teacher and is passionate about finding the best methods of teaching content to her students. Meghann is also interested in running, biking, and hiking.

**Ada Stelzer **will be teaching the Counting with Symmetries course at SIM Camp Delta and will be the program coordinator for SIM Camp Epsilon. Ada is a 1st-year graduate student in mathematics interested in algebraic geometry and algebraic combinatorics. She likes thinking about polynomials and going back and forth between abstract and concrete methods for working with them. Outside of math, She is very interested in education, linguistic anthropology, and in her free time she enjoys reading, making music, and playing games. She is excited to work with you this summer!

**Debmalya Basak**** **will be teaching the Representation of Integers as Sum of Squares course at SIM Camp Epsilon and will be the program coordinator for SIM Camp Delta. Deb is a 2nd-year graduate student in mathematics interested in analytic number theory. He is very passionate about teaching mathematics to school students and college undergraduates. Other than math, He is interested in photography and football. For more details, feel free to visit his website: https://sites.google.com/view/debmalyabasak11.

## Assistant Instructors

**Laszlo Richard Toth **is an assistant instructor for the Maximize Your Winnings (Epsilon) and Counting with Symmetries courses of the 2022 SIM Camp. He is a rising senior studying Mathematics and History with a minor in secondary education. Laszlo is originally from the Southside of Chicago, and he aspires to be a teacher for Chicago Public Schools after graduation. Laszlo has participated in research in the math department concerning graph theory and combinatorics. Outside of math, he enjoys biking, reading, and cooking.

**Mingqi Wang** will be teaching the Representation of Integers as Sum of Squares course at SIM Camp Epsilon and will be the Assistant Instructor for SIM Camp Delta. Mingqi is a sophomore student in mathematics and statistics. Other than math, he is interested in soccer, badminton and photography. He enjoys listening to music and playing card games during his spare time. He hopes to have a great summer with you!

## Organizers

**Manisha Garg **is the director of the 2022 SIM Camp. She is a graduate student in mathematics interested in algebra and algebraic geometry. Outside of math, she paints and enjoys hiking and board games.

**Grace McCourt** is an organizer of the 2022 SIM Camp. She was the director of the 2021 SIM Camp. She was the program coordinator for Epsilon and instructor of Counting, Coloring, and Graphs for Delta in the 2020 SIM Camp. Grace is a graduate student in mathematics interested in combinatorics and graph theory. Outside of math, she enjoys cooking, crocheting, and board/card games.

**Keyan Ding** is an assistant organizer of the 2022 SIM Camp. He is a graduate student in mathematics interested in operations research. Outside of math, he likes reading, watching movies, and playing video games.

**Susan Tolman** is a faculty organizer at SIM Camp. She is a Professor at the University of Illinois at Urbana-Champaign Department of Mathematics and director of the Illinois Geometry Lab.

**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.

**Vera Mikyoung Hur** is a faculty organizer at SIM Camp. She is a Professor and Chair of the University of Illinois at Urbana-Champaign Department of Mathematics.

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.