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• W15910871 abstract "Abstract. In this paper we present a teaching methodology for introducing stu-dents to the mean-field approximation. We also include some teaching material –in the form of computer models– that academics may want to use in their own lec-tures. The methodology emphasises the value of teaching students the intuition underlying the meanfield approximation in a graphical and in- teractive way, with the help of purpose-built computer programs. As an illustrative example, we pre-sent a simple imitation model from the field of Game Theory, which we analyse combining the theory of Markov chains with the mean-field approximation. , Jose I. Santos 1 , Jose M. Galan & Ricardo del Olmo 1 1. Introduction Many University subjects that we teach in engineering degrees (e.g. Control The-ory, Operations Research, Game Theory, Physics, Fluid Dynamics, Modelling and Control of Queuing and Production Systems, Stochastic Processes, and Network Theory) make extensive use of the so-called mean-field analysis 2,[1,4, 5, 7, 8, 10]. In these subjects, the mean-field analysis often appears as an approximation of a discrete time stochastic process where a) the inherent stochasticity of the original process is replaced with determinism, and b) the time discreteness of the original process is replaced with time continuity. Thus, the mean-field approxima-tion is presented as a continuous time differential equation that can approximate the dynamics of the discrete time stochastic process under investigation. In this paper we present a teaching methodology that we have found useful for introduc-ing students to the mean-field analysis, and we provide some accompanying teach-ing material in the form of computer models– – that other academics may want to use in their own lectures. Our approach is twofold: • First, we provide the intuition underlying the mean-field approximation, and we discuss the type of models for which the approximation can be a useful tool. For this, we use a purpose-built computer model that allows students to grasp the reasoning behind the meanfield analysis. The model, which is freely avai- l-able under the GNU General Public License, can be run as an at applethttp://luis.izqui.org/models/gardendesert/ using any Internet browser. • Then, as an illustration of the possible applications of the theory, and with the aim of fostering students’ comprehension, we discuss specific examples of dis-" @default.
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• W15910871 date "2011-09-09" @default.
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• W15910871 title "Teaching the mean-field approximation" @default.
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