Virtual SIM Camp Epsilon ran from June 7th through June 11th, and Virtual SIM Camp Delta ran from June 21st through June 25th.

No cyber bullying will be tolerated at Virtual SIM Camp. No inappropriate messaging or sharing of explicit images will be tolerated. All virtual camp sessions will be password protected.

Topics for the online camp in 2021 are:

**Graphs, Paths, and Bridges**

A riverside town contains several bridges. Can a visitor take a walking tour if each bridge must be crossed exactly once? This course equips campers with the tools to analyze this question, and others, through the lens of graph theory.

**Topological Invariants: How to Distinguish Spaces**

Have you ever wondered about why the countries on a world map seem distorted when compared to the globe? Or about what is the shape of the universe? To find answers to these questions, mathematicians study spaces and their invariants. We will use these invariants to answer many related and interesting questions about spaces.

**The Continued Fraction Universe**

In this course, students will learn how to use Continued Fractions to identify patterns and solve Diophantine equations. We will explore the leaf growth patterns in plants and decide what gears to use when building a solar system model. Along the way, we will introduce standard problem-solving techniques and math ideas such as induction, *n*-ary expansions, limits, and probability.

## SIM Camp Epsilon:

Graphs, Paths, and Bridges

- Instructor: Rachel Barnett
- Assistant Instructor: Emily Lee

Topological Invariants: How to Distinguish Spaces

- Instructor: Venkata Sai Narayana Bavisetty
- Assistant Instructor: Garrett Credi

## SIM Camp Delta

The Continued Fractions Universe

- Instructor: Maria Siskaki
- Assistant Instructor: Emily Lee

Topological Invariants: How to Distinguish Spaces

- Instructor: Venkata Sai Narayana Bavisetty
- Assistant Instructor: Garrett Credi

## Instructors

**Venkata Sai Narayana Bavisetty** will be teaching Topological Invariants: How to Distinguish Spaces at SIM Camp Delta and Epsilon. Sai is a graduate student in mathematics interested in algebraic topology. In his free time, he enjoys cooking, snorkeling, hiking, and learning new languages.

**Maria Siskaki **will be teaching the The Continued Fractions Universe course at SIM Camp Delta and will be the program coordinator for SIM Camp Epsilon. Maria is a graduate student in mathematics interested in ergodic theory. Outside of math, she enjoys hiking, snorkeling, and board games.

**Rachel Barnett **will be teaching the Graphs, Paths, and Bridges course at SIM Camp Epsilon and will be the program coordinator for SIM Camp Delta. Rachel is a graduate student in mathematics with interests in analysis and topology. Outside of the classroom you can find Rachel ascending mountains, running in local races, and scouring thrift shops for unique finds.

## Assistant Instructors

**Garrett Credi** will be assistant teaching the Topological Invariants: How to Distinguish Spaces at SIM Camp Delta and Epsilon. Garrett is a rising sophomore in Mathematics and is currently interested in Algebraic Geometry, Algebraic Topology and their connections to Homotopy Theory. When he’s not studying math, he enjoys programming, writing stories, cooking, and running!

**Emily Lee **will be assistant teaching the Graphs, Paths, and Bridges course at SIM Camp Epsilon and The Continued Fractions Universe course at SIM Camp Delta. She is a rising senior, majoring in mathematics and minoring in secondary education. In her free time, she enjoys calligraphy, traveling and spending time with friends.

## Organizers

**Grace McCourt** is the director of 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.

**Grace Jaffe** is an assistant director for the 2021 SIM Camp. She was the director for the 2020 SIM Camp and ran the Number Theory courses at SIM Camp Epsilon and Delta in 2019. Grace is a graduate student in mathematics interested in number theory, especially the Stern sequence and the Riemann zeta function. Outside of math, she likes singing, knitting, and baking.

**Philipp Hieronymi** 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.

**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 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.