This volume includes seven chapters that detail advances in mathematics research. Chapter 1 presents the use of matrices in mathematics and sciences. Chapter 2 focuses on the method aptly named the power series solutions of differential equations. Chapter 3 addresses the method used for deducing the properties of solutions of differential equations without finding their solutions. Chapter 4 proposes an approach to estimating parametric identifiability (PI) application of Lyapunov functions. Chapter 5 approaches the orthogonal polynomials collectively in a general setting, without choosing a specific orthogonal polynomial. Chapter 6 introduces artificial intelligence approaches for intelligent decision-making with mathematical modeling and applications of complex systems. Lastly, Chapter 7 considers 3D Euler equations for unsteady motion of a compressible medium with unknown components of the velocity vector, density and pressure.
