SWiM 2022


Representation of a Number as a Sum of Powers

Ruby Kim Photo

Instructor:  Ruby Kim

In 2025, we will reach the first “square” year of this millennium and the only “square” year of this century. Indeed 2025=45^2, preceded by 1936 and followed by 2116. More common are years which are sums of two squares. For example, the last was 2020=42^2+16^2, and the next (not counting 2025) is 2026=45^2+1^2. What do these numbers have in common, if anything? Can 2023 be written as a sum of two squares? If not, what about a sum of three squares, or four? How can we be sure—must we check every possibility? Together we will explore these mysteries of sums of squares and their role in encoding the secrets of the integers.

Squeezing Shapes

Aygul Galimova photo

Instructor:  Aygul Galimova

We’ll explore the field of topology, the study of shapes up to stretching and squeezing, comes into play here. Topology studies the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, and bending, but no cutting. Topology comes up in the study of knots and objects, billiards and pool, and even breast cancer detection. This course will cover how to play tic-tac-toe on a donut, glue spaces to get new ones, orientation, knots, the rent-sharing problem, and a few applications. No prerequisites except curiosity.

Group Projects

Three Player Hat Game
Noisy Images
Alien DNA Coding
Persistent Homology
Graph Theory


Madeleine Mac Gagne_photo

Madeleine (Mac) Gagné
Duke Alumni

Madeleine “Mac” Gagné is a current Systems and Operations Research Intern for Northrop Grumman through the Brooke Owens Fellowship program and is a rising Operations Research PhD student at North Carolina State University. Her work spans areas of applied mathematics including operations research, game theory, decision analysis, causal inference, information systems, and optimization particularly as they apply to the worlds of emergency response and aerospace. Gagné is a recent graduate of Duke Mathematics through the university’s Program II department and started the department’s social mathematics club The Lyceum. She is also an aspiring pulp fiction author, and currently lives with her partner and their cat Elvira Mistress of the Dark in Washington D.C.

Camey VanSant

Camey VanSant
Assistant Director of Admissions at Duke University

Camey VanSant is Assistant Director of Undergraduate Admissions at Duke University and a Duke alumna (class of 2009). At this presentation, she’ll provide information on the undergraduate experience at Duke, including academic opportunities and student life. She’ll also offer an overview of the admissions and financial aid processes. Camey’s academic interests are in the humanities but she is always very excited to meet great math people!

Ingrid Daubechies
Co-director of SWiM

Ingrid Daubechies is a James B. Duke Distinguished Professor of Mathematics and Electrical and Computer Engineering at Duke University.  She is best known for her work with wavelets in image compression.  Ingrid is passionate about her work with Mathemalchemy, a collaborative art installation celebrating the creativity and beauty of mathematics.  She was the first woman to be president of the International Mathematical Union.  She is part of the 2019 class of fellows of the Association for Women in Mathematics and was named the North American Laureate of 2019 L’Oréal-UNESCO International Award For Women in Science.