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Mathematical Inequalities, Amy Dreiling

Master's Theses

In this thesis, we discuss mathematical inequalities, which arise in various branches of Mathematics and other related fields. The subject is a vast one, but our focus is on inequalities related to complex analysis, geometry, and matrix theory.

We investigate recently proven trigonometric and hyperbolic inequalities. This includes Katsuura's string of seven inequalities for the sine and tangent functions and Price's Inequality (with new proofs derived by Katsuura and Obaid). We also discuss complex hyperbolic inequalities and inequalities from infinite products.

We then establish geometric inequalities, including those relating parts of the triangle as well as conic sections and their …

Galois Theory And The Hilbert Irreducibility Theorem, Damien Adams

Master's Theses

We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theory and Hilbert's Irreducibility Theorem: given any irreducible polynomial f(t₁, t₂, …, t_n, x) over the rational numbers, there are an infinite number of rational n-tuples (a₁, a₂, …, a_n) such that f(a₁, a₂, …, a_n, x) is irreducible over the rational numbers.

We take a preliminary look at linear algebra, symmetric groups, extension fields, splitting fields, and the Chinese Remainder Theorem. We follow this by studying …

Geometric Algebra: An Introduction With Applications In Euclidean And Conformal Geometry, Richard Alan Miller

Master's Theses

This thesis presents an introduction to geometric algebra for the uninitiated. It contains examples of how some of the more traditional topics of mathematics can be reexpressed in terms of geometric algebra along with proofs of several important theorems from geometry. We introduce the conformal model. This is a current topic among researchers in geometric algebra as it is finding wide applications in computer graphics and robotics. The appendices provide a list of some of the notational conventions used in the literature, a reference list of formulas and identities used in geometric algebra along with some of their derivations, and …