Speaker: Gourab Ray
Title: Measuring Distance Between Two (Random) Objects
Abstract: In this session, we will explore a mathematical abstraction called “the metric”. We will learn how to measure the distance between various objects, such as:
-
- Two points in 2D or 3D space – Easy!
- Two points on the globe – What is the distance between Victoria and the North Pole?
- Two data sets – For example, the amount of rainfall in Victoria vs Vancouver
- Two shapes drawn on a paper – How far apart are an apple and an orange?
- Two shapes, but you ran out of paper – An apple in Victoria can’t be very far from an apple in Hong Kong, as they are both apples!
- Two random points – Now the distance is not fixed, it’s random! How do we make sense of this?
- Two random shapes???
Bio: Gourab Ray is an Associate Professor working in the math department of the University of Victoria who loves doing math.
Speaker: Peter Dukes
Title: Pairs and Triples – What’s the Difference?
Abstract: In this session, we will explore modular arithmetic. Let n be a positive integer, say n=7. When working with numbers “mod n”, we add or subtract numbers with “wrap-around”; that is, numbers are reduced to the remainder they leave when divided by n, which is always between 0 and n-1 (inclusive). For example, when n=7, we have the sum 4+5=2 since 9 has remainder 2 when divided by 7. And 4-5 is -1, but we can add 7 to this and get the answer 6.
The set A={1,2,4} in the integers mod 7 has an interesting property: every number between 1 and 6 occurs exactly once as a difference between two elements of A. In 1939, Rose Peltesohn completely determined when families of triples with this property exist in the integers mod n. In this session, we will explore Peltesohn’s work in more detail. After experimenting with some small cases, we will see some of the beautiful geometric configurations resulting from Peltesohn’s constructions.
Bio: Peter Dukes is a math prof at UVic. He was a student at UVic a long time ago, then went away for grad school, and returned to UVic to start work in 2004. He enjoys research related to puzzles, games, patterns, and combinations. Either in research or teaching, Peter loves sharing mathematical ideas with students of all levels.
Speaker: Shannon Ogden
Title: Puzzling Polyomino Problems
Abstract: A polyomino of order n is a generalization of a domino made from n squares of equal size joined edge to edge. You may recognize polyominoes from games such as Tetris and Blokus. In this session, we will explore various games and puzzles involving tiling grids with polyominoes.
Bio: Shannon is a PhD candidate at UVic and 2023 Vanier Scholar. While her research focuses on extremal graph theory, she loves to explore the beautiful patterns found in all areas of math. Deeply passionate about making math accessible to those without advanced degrees, Shannon created IMAGINING UVic in an effort to inspire young women to pursue STEM fields. She enjoys playing the piano (never mind how poorly) and the unequaled satisfaction of a well-organized bookcase brimming with gorgeous editions of classic novels. When not buried in math papers, Shannon can often be found rock climbing, hiking, or simply looking for the perfect tree under which to read.
Speaker: Jane Butterfield
Title: Constructive Constructions and Historical Triangles
Abstract: These days, geometry is often people’s first introduction to proofs, but its roots are far more practical. In this session we’ll explore three different paradigms of geometrical constructions, starting from the Śulbasūtras of Ancient India, moving through Euclid’s axioms, and exploring a very practical problem from medieval Baghdad with an elegantly mathematical solution.
Bio: Jane Butterfield studies graph theory and math education. She has successfully talked about graph theory and combinatorics to many different types of audiences and age ranges. Her PhD research was in extremal graph theory, but she also enjoys topological graph theory, Ramsey games, and pursuit games on graphs. While a graduate student at the University of Illinois in Urbana-Champaign, she received three teaching awards, including the Campus Award for Excellence in Undergraduate Teaching. She spent two years teaching calculus to talented high school students for the Math Center for Educational Programs at the University of Minnesota, and is now an Associate Teaching Professor at the University of Victoria. At UVic, she manages the Math & Stats Assistance Centre — because of the US & Canadian spelling differences, this means she has worked for both a Center and a Centre!