Gateway to Exploring Mathematical Sciences (GEMS)

GEMS is designed to reach eighth, ninth and tenth grade students who may have an interest in mathematics or science. The workshops present mathematics and science applications in an exciting way that catches young students’ interest. Professors, undergraduates and graduate students from all of the Claremont Colleges take part in the GEMS program, thus offering participating students, their parents, and teachers a chance to meet and work with excellent and award winning faculty, staff, students and alumni. The GEMS program helps excite the interests and curiosity of young students and shows them how amazing and satisfying the mathematical sciences can be.

The workshops are stand alone and are offered once a month.

Details regarding the workshop on December 7, 2024:

Session Facilitator: This GEMS session will be facilitated by Professor of Mathemacis, Dr. Lenny Fukshansky, from Claremont McKenna College

Title: From Knapsacks and Changing Coins to Geometry

Session Description: Suppose you have a bag that can hold a fixed amount of weight, and you are trying to fill it with several types of objects of different weights and prices. The goal is to maximize the value of your bag. How do you do it? This is a notoriously difficult optimization problem, which often arises in resource allocation with financial constraints. Another famous optimization problem asks what amount of change can you give with coins of prescribed denominations? Surprisingly, not only are the two closely related to each other, they both can be restated in the geometric language of polygons, points with integer coordinates, and their higher-dimensional generalizations! We will discuss these important problems and their beautiful connection to a classical problem in geometry: how can we count the number of integer points in a fixed polygon? The answer is given by the celebrated 19th century theorem of Georg Alexander Pick, who proved a remarkable formula for this number in terms of the area and perimeter of the polygon. We will talk about Pick’s theorem and perform a hands-on exploration of this fascinating area of geometry.

Picture from our GEMS session on October 5, 2024 with Professor Mark Huber, on how to use coins to make a 7-sided die.

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