The description of emerging mass phenomena and self-regulation in systems of large numbers of individuals has gained increasing interest from various research communities in biology, the environment, robotics and control theory, as well as sociology and economics. Applied Mathematics is concerned with the construction, analysis and interpretation of mathematical models that can highlight important problems in the natural sciences as well as our daily lives.

This set of problems belongs to the description of the collective behavior of complex systems consisting of a large number of individuals. Examples of such systems are interactive market players, potential voters during political elections, or groups of animals with a tendency to flock or herd.

Among other possible methods, this book presents a step-by-step introduction to mathematical modeling based on seasonal descriptions and the construction of effective simulation algorithms in Monte Carlo methods. The book's arguments cover various applications, from the analysis of wealth distributions, the formation of opinions and options, and the dynamics of prices in the financial market, to the description of cellular mutations and the accumulation of birds and fish. Through methods inspired by kinetic theory of induced gases, a robust approach to mathematical modeling and numerical simulation of multi-factor systems is presented in detail.

Content is a useful reference text for applied mathematicians, physicists, biologists and economists who want to identify modeling and bring these difficult phenomena closer together.

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