Master of Science (MS)
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 tangent lines. We also develop proofs of the Arithmetic-Geometric Mean and Erdos-Mordell inequalities.
Finally, we explore inequalities for univalent functions, including the famous Bieberbach Conjecture, Area Theorem, and Koebe's One-Quarter Theorem. We finish with Hadamard's Inequality for determinants.
Dreiling, Amy, "Mathematical Inequalities" (2013). Master's Theses. 4334.