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5 Modeling with Random Numbers


1 Introduction to Simulation and Modeling
2 Discrete Medeling (L-Systems)
3 Population Dynamics
4 Number Representation and Error Propagation
5 Modeling with Random Numbers
5.1 What is a Random Number?
5.2 Generating Random Numbers with Mathematica
5.3 Seeds and Probability Distributions
5.4 Integration by Random Numbers and Numerical Methods
5.5 A Drunken Man's Walk
6 Heat Transfer in a Rod (Connection Mathematica and C: MathLink)
7 Special Topics in Stochastic Finance
8 Appendix: Introduction to Mathematica
9 Population Dynamics in Vensim®PLE
     
 

5.1 What is a Random Number?

5.2 Generating Random Numbers with Mathematica

5.3 Seeds and Probability Distributions

5.4 Integration by Random Numbers and Numerical Methods

5.5 A Drunken Man's Walk

Acknowledgements

Parts of the material in this section was taken from a number of sources, which are listed below

Mathematica 4.0, S. Wolfram.
An introduction to computer simulation methods. H. Gould and J. Tobochnik. Addison Wesley 2nd edition
Continuous system modeling, Francois Cellier. Springer Verlag 1991
Computer Simulations with Mathematica:  Explorations in Complex Physical and Biological Systems by
Richard J. Gaylord and Paul R. Wellin
Steven Keltner and Scott Sloan, University of Missouri-Rolla: Mathematica in Education
Volume 3 Number 1 Winter 1994
Weiss, George H. 1983. "Random Walks and Their Applications", American Scientist, 71(1), pp. 65-71
K.D. Stroyan, Calculus using Mathematica Academic Press 1993.

Introduction

Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means. --- Bertrand Russell
In this NoteBook you will look into Random Number Generation and the use in estimating integrals and modelling random processes.

Important  instructions  for  all students:
Each notebook  contains several questions that must be handed in. Theses questions are labeled accordingly:

Required: These questions must be done by all students.

Advanced:  These questions are considered to be more difficult and may be assigned by the instructor.

Optional:   These questions are optional  to all students  and will be counted towards   extra  marks.


 
     
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