Physical Sciences and Mathematics Commons^™

Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle

Honors Theses

This senior project outlines potential lecture activities for a guest speaker or teacher in a high school classroom to present interesting applications of linear algebra. These applications are meant to be pertinent to things students at this age level are already learning or are interested in. The activities are designed such that the ideas of upper-level math are introduced in a very guided and non-intense way. The intent of the activities is mostly applications and interesting results rather than mathematical lecturing or instruction.

The high school level courses explored in this project are chemistry, economics, and health/physical education. For these …

The Central Hankel Transform, Matthew J. Levine

Honors Theses

This honors thesis presents the Hankel transform on an integer sequence, a function with colorful mathematical history and rich theoretical background. We then introduce a matricial Toeplitz transform that parallels some of most famous qualities of the Hankel transform, especially when in consideration of popular sequences like the Fibonacci numbers. The result is a characterization of the injectivity of this new function, a description of some of its interesting behaviors, and a discussion of a few new Fibonacci identities.