2026 Diversity in Research Experiences Across Mathematics (DREAMs) Institute

Participants will be introduced to four foundational areas of mathematics by guest lecturers during the first week and then work on inquiry based projects with the support of the lecturers and graduate 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.

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.

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

Lecture Summaries 

Combinatorics: Counting all of the things 

This mini course will focus on combinatorics---the mathematical study of counting. Our main goal will be to develop a number of techniques that will help you win all of the guessing games you can imagine of the form "how many objects do you think satisfy (blah)?" Along the way, you'll learn some foundational principles of proof and mathematical communication and we will explore a variety of important mathematical objects that you'll be sure to see more of in college.

Symmetric Polynomials 

Elana will lecture on the combinatorics of symmetric polynomials. Symmetric polynomials are special polynomials that satisfy many symmetries — for example, x+y and xy are both symmetric, but x^2+y is not. Studying how to build symmetric polynomials out of basic ones leads to many interesting combinatorics, including the famous Littlewood—Richardson rule, and has had applications in many areas of mathematics.

Special Relativity

This mini-course will introduce special relativity, a theory of the relationship between space and time. The defining feature of special relativity is the following: the speed of light is constant for all observers. This simple statement has strange implications for how different observers perceive distances and the rate at which clocks tick! 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.

Mathematical Musicology

In this course we will focus on the mathematical aspects of music. The relationship between math and music has been studied for millennia, even prior to the Ancient Greeks, and research in this area persists to the present day. We will investigate the mathematics of harmony, rhythm, and tuning using familiar concepts. Using this as a springboard, we will encounter more advanced ideas (which are usually seen for the first time in college) and view them through a musical lens.