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• Formal models and modeling techniques: mathematical descriptions involving simplifying assumptions<br />

and avoiding detail. Examples of techniques include:<br />

o Monte Carlo methods<br />

o Stochastic processes<br />

o Queuing theory<br />

o Petri nets and colored Petri nets<br />

o Graph structures such as directed graphs, trees, networks<br />

o Games, game theory, the modeling of things using game theory<br />

o Linear programming and its extensions<br />

o Dynamic programming<br />

o Differential equations: ODE, PDE<br />

o Non-linear techniques<br />

o State spaces and transitions<br />

• Assessing and evaluating models and simulations in a variety of contexts; verification and validation of<br />

models and simulations<br />

• Important application areas including health care and diagnostics, economics and finance, city and urban<br />

planning, science, and engineering<br />

• Software in support of simulation and modeling; packages, languages<br />

Learning Outcomes:<br />

1. Explain and give examples of the benefits of simulation and modeling in a range of important application<br />

areas. [Familiarity]<br />

2. Demonstrate the ability to apply the techniques of modeling and simulation to a range of problem areas.<br />

[Usage]<br />

3. Explain the constructs and concepts of a particular modeling approach. [Familiarity]<br />

4. Explain the difference between validation and verification of a model; demonstrate the difference with<br />

specific examples 1 . [Assessment]<br />

5. Verify and validate the results of a simulation. [Assessment]<br />

6. Evaluate a simulation, highlighting the benefits and the drawbacks. [Assessment]<br />

7. Choose an appropriate modeling approach for a given problem or situation. [Assessment]<br />

8. Compare results from different simulations of the same situation and explain any differences. [Assessment]<br />

9. Infer the behavior of a system from the results of a simulation of the system. [Assessment]<br />

10. Extend or adapt an existing model to a new situation. [Assessment]<br />

1 Verification means that the computations of the model are correct. If we claim to compute total time, for example,<br />

the computation actually does that. Validation asks whether the model matches the real situation.<br />

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