2024 Diversity in Research Experiences Across Mathematics (DREAMs) Institute

The Diversity in Research Experiences Across Mathematics (DREAMs) Institute is a three-week online summer enrichment program designed to provide high school students in their last year or two of studies an opportunity to explore the pursuit of mathematics at the University level. Participants will be introduced to foundational areas of mathematics by guest lecturers during the first portion of the program and then work on inquiry based projects with the support of the lecturers and graduate student teaching assistants.

One of the DREAMs Institute’s primary goals is to help students envision a career in mathematics or STEM more broadly. We recognize that STEM fields continue to not represent the racial and gender diversity of Canadian society and we are committed to supporting students with minoritized identities in this program as they prepare to begin their University education. We strongly encourage students from underrepresented groups to apply to this program.

Eligibility:

Participants should be in their last two years of high school studies with a strong grasp of high school mathematics.

Cost:

There is no cost to participate in the DREAMs Institute, but we do expect participants to commit to attending for the full duration of the program.

Courses

Mathematics of Puzzles (Jordan Kostiuk)

Much of modern mathematics can be traced back to specific problems of interest in human history. This mini course will focus on a set of specific logic problems that, as we develop the techniques and ideas to address them, will reveal the origin of some critical branches of modern mathematics. The logic problems we pursue require little to no previous mathematics background, but lead to abstract, interesting, and playful concepts. 

Introduction to Abstract Algebra (Alicia Lamarche)

As students, we spend a lot of time learning about numbers and operations that can be done with them. Lurking within these computations lies a beautiful theoretical framework called abstract algebra, which allows mathematicians to bend, break, and reimagine all of the rules of arithmetic that we learned in school. In this mini-course we'll learn about basic algebraic structures while developing the language to create and study our own.

Special Relativity (Delilah Gates)

This mini-course will introduce special relativity, a theory of the relationship of space and time. The defining feature of special relativity is that the speed of light is constant for all observers. We will go through thought experiments which motivate us to derive relativistic effects like length contraction and time dilation, as well as learn what it means to "rotate" time and space into one another.

Scientific Computing (Stefan Mendez-Diez)

In the sciences we rely on computers to perform many complicated mathematical computations. However, computers can’t know all of the real numbers, it would require an infinite amount amount of memory. Instead, computers use something called the floating point number system that approximates the real numbers. We will explore how using this number system changes the way we must do computer computations to obtain accurate answers. We will discuss what is meant by an accurate answer and how we can “trust” the answers we get from a computer. We will learn some basics of programming using the open source language PYTHON. We will also briefly discuss how we can make computer computations more efficient, or faster.