SENIOR  COMPS PRESENTATIONS

in Mathematics

  

 

Introduction to Fractional Differentiation

Joshua Needleman

This talk is an introduction to the fractional differentiation operation. A small history of the creation of fractional calculus is included for background, followed by a series of definitions, formulas, and operators needed to execute fractional differentiation. Some of the properties of fractional differentiation will be discussed. A few numerical examples are included to display the use of fractional differentiation, along with a comparison to integer differentiation.

 

Representation Theory: A Framework for Tackling Problems in Quantum Mechanics

Kristina Chang

The state of a quantum-mechanical particle in a system – be it an electron in a molecule or an extended solid – is determined by wavefunction solutions to the system’s Schrödinger Hamiltonian equation. Unfortunately, the Schrödinger equation is notoriously difficult to solve and direct calculations for its solutions are accomplished at significant computational expense. Representation Theory provides a framework for tackling such problems by taking advantage of intrinsic symmetry in a system’s Hamiltonian operator to solve for solutions to the Schrödinger equation. This presentation will first elucidate the mathematical machinery of Representation Theory, then apply this machinery to prove Bloch’s Theorem, a core theorem in condensed-matter physics that allows us to predict properties of crystals based on the symmetry of their atomic arrangements.

 

Thursday, March 31st, 2016

5:00-6:30pm

Fowler 302

 

**Refreshments Will Be Served**

Everyone is invited!