Mathematics Commons^™

Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic

Masters Theses

Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.

A Multiple Linear Regression Analysis On Mathematics Placement At The University Of Tennessee, Knoxville, Steven K. Moore

Masters Theses

This paper looks at solving the least squares problem and then using that theory to solve a simple multiple regression analysis for placing students into mathematics courses at the University of Tennessee, Knoxville.

The first chapter is an introduction and a basic outline of the problem. Chapter 2 outlines the theory behind solving an actual least squares problem for both the general case and for the particular case of nonsingular matrices. Chapter 3 discusses assumptions that must be made when running the analysis.

In chapters 4 and 5 computers are discussed and software output is explained. Finally, Chapter 6 gives …