This compilation first outlines a stochastic multicriteria modelling-to-generate-alternatives approach for waste management planning that can generate maximally different sets using a modified version of the computationally efficient Firefly Algorithm. The authors present reduced-order models to pattern formations occurring in the activator-inhibitor FitzHugh-Nagumo equation, parametrized Allen-Cahn equation, non-linear Schrodinger equation, Ginzburg-Landau equation and Swift-Hohenberg equation. The subsequent chapter deals with the singularly perturbed semilinear convection-diffusion problem, serving as an introduction to the model problems which arise frequently in counterflow flames modeling, modeling in mathematical biology, semi-conductor device simulations based on the so-called drift diffusion modeling, fluid dynamics and heat conduction. The authors present a linear integer programming approach to construct efficient incomplete block designs forgiven v, b and k. The proposed approach is illustrated by constructing an A-efficient incomplete block design, and the strengths and weaknesses of this algorithm are also discussed. One included work is devoted to the issue of the Green functions that are related to some three-point boundary and eigenvalue problems. A detailed definition is given for the Green functions provided that the considered three-point boundary value problems are governed by a class of ordinary differential equations which are associated with homogeneous boundary and continuity conditions. A review on the methods of mathematical modeling used to calculate irreversible loss of capacity in polymer lithium-ion batteries is provided. In closing, the authors consider the corpus of mathematical theorems that admit formulations in natural language and offer some explanations of the existence of several types of theorems.