This volume includes some of the latest advancements in mathematics research. Chapter One aims to increase the certainty and reliability of G index through different examples and show that G index can be reached by two different paths. Chapter Two focuses on deriving exact trigonometric ratios using equations. Chapter Three presents a review of rough set theory-based feature selection approaches for small to large scale machine learning tasks. Chapter Four delivers an analytic approach to the Riemann hypothesis. Chapter Five aims to present a comparative analysis of mathematical models of transmission lines applied to two short lines of medium voltage. Finally, Chapter Six focuses on the numerical investigation of the one and two dimensional semi-linear scale-invariant wave equation with damping, mass and power non-linearity.