A Mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences, but also in the social science (such as economics, psychology, sociology, and political science). Mathematical models can take many forms, including but not limit...

The acquiring of formal, abstract mathematical concepts by students may be said to be one of the major goals of mathematics teaching. How are such abstract concepts acquired? How does this formal knowledge interact with the students' intuitive knowledge of mathematics? How does the transition from informal mathematical knowledge to formal mathematical knowledge take place? This paper reports on...

This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defi...

This thesis proposal outlines an automated reasoning system for helping a user to navigate through a theory and discover theorems that mathematicians generally find to be interesting. The project focuses on the processes of invention of mathematical concepts, and invention (and verification) of conjectures about concepts by using a scheme-based approach. Mathematical theories usually have infin...

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this class...

Innovations in biological evolution and in technology have many common features. Some of them involve similar processes, such as trial and error and horizontal information transfer. Others describe analogous outcomes such as multiple independent origins of similar innovations. Yet others display similar temporal patterns such as episodic bursts of change separated by periods of stasis. We revie...

The work system method was developed iteratively with the overarching goal of helping business professionals understand IT-reliant systems in organizations. It uses general systems concepts selectively, and sometimes implicitly. For example, a work system has a boundary, but its inputs are treated implicitly rather than explicitly. This chapter asks whether the further development of the work s...

This study intertwined the mathematical concepts of stability and recent research works on stability of 2D space model Since Mathematics in Engineering is inevitable. In this context, this study briefly emphasizes the mathematical concepts especially in the Control Engineering field and also includes recent research works on stability of 2D state space model.

Computer software can be used for artistic design and as a means to facilitate the understanding of mathematical concepts. We discuss some of the issues that arise when we use computers in this way, and some of our own experiences teaching both art and mathematics students using software that can assist in the design and coloring of symmetric images.

General Comments: This is a well-documented and well-written article, however much of it seems to dwell on and define standard mathematical concepts (like deterministic chaos, fixed points and attractors) and seems not appropriate to include in a research publication. Furthermore, a parameter study (as done in this paper) finds different solution style regimes and a linearized stability analysi...