Pacific Institute for the Mathematical Sciences - PIMS

The Diversity in Research Experiences Across Mathematics (DREAMs) Institute is a two-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 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.

Modality:

This event will be held fully online. 

Eligibility:

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

Application:

To apply for the program, please complete the following Google Form.

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:

Vectors, Matrices, and Geometry. 

In this mini-course, we'll learn some fundamentals about vectors and matrices and explore how they relate solutions of linear equations to geometry. We'll follow an inquiry-based approach, so be prepared to ask (and answer) your own questions!

Number Theory 

This mini-course will equip us with a common language to describe relationships between integers. We'll explore divisibility, prime numbers, factorization, and modular arithmetic. Once we have developed these tools, we will use them to study the structure of the integers.

Topology

The geometry of three dimensional polyhedra is far more intricate than the two dimensional story of polygons, and leads to a range of fascinating modern ideas. One such idea, topology, is the kind of geometry where we disregard the typically fundamental geometric ideas of distance, angle, and straightness, and focus on how shapes are connected. Mathematicians are still learning about and researching topology, and their insights have influenced particle physics, computer networks, genetics, game theory, data analysis, and much more. In this course we will start with polyhedra and the patterns that govern their possibilities, and this will lead to the topology of surfaces. Bring scissors, paper, and tape.

Instructors: 

Jordan Kostiuk, Brown University

Bio: Jordan Kostiuk was born and raised in Edmonton, and went to Bev Facey high school. After earning his BSc, MSc, and PhD in Mathematics from the University of Alberta, he began working at Brown University in 2018 as a postdoctoral fellow and was hired as a Lecturer in 2021. In this capacity, Jordan teaches introductory mathematics courses and has recently become engaged in education research.

Kevin Iga, Pepperdine University

Bio: Prof. Kevin Iga is a Japanese-American, born and raised in Honolulu, Hawai'i. He went to MIT and double majored in mathematics and physics, and in 1998 received his Ph.D. in mathematics from Stanford University, where he worked on the differential topology of four dimensional manifolds. He is currently Professor of Mathematics, and Frank R. Seaver Chair in Natural Science, at Pepperdine University near Los Angeles, California, where he does research in mathematical physics. Kevin attends Malibu Pacific Church, and volunteers in various capacities, including serving as a deacon and leading a Bible study.

Alicia Lamarche, University of Utah

Bio: Alicia Lamarche is currently an NSF postdoctoral researcher at the University of Utah. She received her PhD from the University of South Carolina in 2020, and attended Shippensburg University of Pennsylvania for undergraduate studies. Outside of mathematics she enjoys painting, playing with animals, and other (attempts at) artistic endeavors. 

Stefan Méndez-Diez, Bard College

Bio: Stefan Méndez-Diez is an Assistant Professor of Mathematics at Bard College. He received his Ph.D. in Applied Mathematics with a specialization in Physics from the University of Maryland, College Park, in 2010. He then held Postdoctoral positions in the Geometry and Physics research groups at the University of Alberta and then Utah State University before starting his current position in 2016. Professor Méndez-Diez’s research explores the interplay of Mathematics and Theoretical Physics with a focus on the geometry of spacetime. Stefan strives to create a learning environment where all students feel welcomed, challenged, and encouraged. He enjoys learning about his students and finding ways to apply mathematics to their interests.