Tuesday

Mini-course 1. Exploring Routes in Graphs and Sets

Lisa Naples

Abstract:  Suppose that we want to run some errands at various locations throughout town.  What is the most efficient way for us to travel from location to location and then return home? 

In this course, we will begin by exploring how ideas from graph theory can help us to answer this question.

We will then extend the task by assuming that we need to visit infinitely many locations. We will see that tools from statistics and calculus can sometimes be used to determine efficient routes through sets.  We will also explore situations in which these tools can fail to help us find a reasonable route.

Relevant background from graph theory, statistics, and calculus will be introduced in the course.

Mini-course 2. How Fermat's Last Theorem influenced modern number theory

Alex Barrios

Finding Patterns with Remainders

Abstract: Ordinary arithmetic often hides patterns that become visible only after we record remainders instead of exact values. In 1801, Gauss revealed that arithmetic possesses a hidden world of patterns, one that reshaped number theory as we know it. In this lecture, we introduce modular arithmetic and discover that many questions about integers become dramatically simplified when viewed in this new realm. 

Talk: How to choose your own mathematical adventures

Pamela E. Harris.

Abstract: What is mathematical research? How does a mathematician find problems to work on? How does one build mathematical collaborations? In this talk, I will share my journey to research mathematics, what it entails, how I have developed new research ideas, and how I have found my place within the mathematical community. Mathematical topics of discussion will include lattice point visibility, parking functions, and a connection between vector partition functions and juggling. No prior mathematical background on these topics is expected nor assumed as we will introduce all of the needed concepts from first principles. All that is needed is the willingness to wonder and ask the question: “what happens if…?”

Informal conversation

Pamela E. Harris

Work time