Mathematical Modelling and Problem Solving

<p>The course is primarily intended as an introduction to mathematical modelling and problem solving for students with limited experience in the use of mathematics in engineering, but which may come to work in different areas where mathematics is useful. The main purpose of the course is to provide the student with the ability to apply the theoretical mathematics to solve problems in science and technology. With application oriented exercises, and by teaching modelling and problem solving techniques, the course then bridges the gap between the theoretical courses in mathematics and relevant applications. The course also includes a broader summary of mathematical thinking. The core of the course is a number of application oriented exercises, which are used as a starting point for the student's own learning. The problems have been carefully selected to develop the student's own skills in modelling and solving problems in a investigative way. The exercises illustrate many areas of application and are organized after the main model types. In the list below one can find examples indicating the more detailed scope:</p> <ul> <li>Functions and equations, for example how different mathematical statements can be motivated and how to select and fit functions to empirical data.</li> <li>Optimization models, e.g. mathematical programming in economics and decision support.</li> <li>Dynamic models, e.g. simulation in biology, physics and engineering.</li> <li>Probability models, e.g. stochastic simulation, Markov models for text and Bayesian inference.</li> <li>Discrete models, e.g. graphs and networks for modelling projects and activities, modelling with discrete standard problems and boolean logic, planning. One to two more modules with topics that can change from instance to instance. </li> </ul> <p>With the exercises as a starting point, we actively teach modelling and problem solving with a supervision style that develops the independence of the student. During lectures, we also discuss different problem solving strategies, reflect on solutions and compare different ways to solve the same problem. The course also demonstrates the importance of building mathematical computer models for different kinds of applications. </p>