This volume includes eight chapters that discuss recent advancements in mathematics research. Chapter One introduces hybrid direction, which is a new method for solving linear programming problems. Chapter Two reviews the theory of p-adic Galois representations and analyzes examples of the ones arriving from elliptic curves. Chapter Three investigates the structure of bicyclic rings and describes some of their properties. Chapter Four presents a numerical simulation of the atmospheric boundary layer related to experiments for stable atmospheric conditions. Chapter Five explains the Extreme Physical-Information (EPI) principle of physics. Chapter Six introduces numerical methods for solving ordinary differential equations with fractional derivatives. Chapter Seven provides a deeper understanding of the phase of the quaternion number and its relation to fluctuation. Lastly, Chapter Eight discusses pension funds, specifically ones that are not auto financed.