Fall 2023 Project
This semester, the theme of the Directed Reading Program (DRP) will be "A mathematician's introduction to physics." It is interesting to see the application of mathematical concepts to derive physical insights, which inspire mathematical theories. For instance, classical mechanics serves as a motivation for symplectic geometry, while quantum mechanics motivates the development of functional analysis, among other examples.
Our initial focus will be on studying Lagrange's equations for motion, which emerge from the principle of least action, and delving into the widely celebrated Noether's theorem. As we progress, we'll consider additional topics, with a strong inclination towards comprehending Yang-Mills theory, a subject demanding a deeper mathematical maturity. Nevertheless, we would consider already a success if the student learns how to solve problems relating Noether's theorem, and Lagrange's equations.
Our plan is to meet weekly meeting touching a specific concept following the notes by Dolgachev. The reading can be quite heavy so videos from YouTube will be suggested, this in order to view the concept from a less mathematics heavy approach. During the meetings, we will solve physics problems with a strong emphasis on outlining the problem-solving methods, essentially providing a kind of recipe. This approach enables students to attempt problem-solving independently, even if they haven't fully mastered the necessary mathematical rigor.
Mentee Application for students which have taken Ordinary Differential Equation.
We were particularly inspired by this quote from Felix Klein,
It is the great need of the present in mathematical science that the pure science and those departments of physical science in which it finds its most important applications should again be brought into the intimate association which proved so fruitful in the work of Lagrange and Gauss.
Graduate Student Leads
Dr. Svetlana Roudenko, firstname.lastname@example.org
The aim of the Directed Reading Program is to expose undergraduates to advanced mathematical topics and research methods. It also provides a team-based setting where students can hone their research skills through study and presentations. Each undergraduate, or pair of undergraduates, is paired with a knowledgeable graduate student in the relevant field. Throughout the semester, these teams meet weekly to work on a specific project, such as a presentation, manuscript, or research paper, which they aim to complete by the semester's end. This program benefits undergraduates by preparing them for graduate-level studies and research, while also offering graduate students valuable experience in teaching and mentorship.
The Directed Reading Program offers an invaluable experience for students aiming to advance their studies in mathematics or related disciplines beyond their undergraduate degree. Participants will acquire hands-on experience in mathematical research and public speaking through presentations. Additionally, undergraduates will receive tailored advice on applying to graduate programs or exploring career opportunities in related fields after graduation. Beyond the academic advantages, the program strengthens the sense of community within FIU's mathematics department by fostering meaningful connections between graduate and undergraduate students.