617-141 Scientific Programming and Simulation

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Objectives:

On completion of this subject, students should:

Comprehend:

• the syntax of a programming language;

• the terminology of probability and the principles of probability modelling.

Have developed:

• the ability to read, write and adapt computer programs;

• skills in reformulation of problems in a form suitable for computer solution;

• the ability to use established numerical methods;

• the ability to carry out probability calculations using standard distributions;

• the ability to make an appropriate choice of model for standard situations;

• the ability to write programs to simulate simple probability models.

Appreciate:

• the structure of a programming language, its potential and limitations;

• the application of probability modelling in describing the real world;

• the concept of randomness.

Content:

Introduction to programming: algorithms, simple data types, assignment, conditionals, iteration, functions and procedures, complex data types, array processing. Numerical methods: number representation, errors, numerical integration, solution of linear and nonlinear equations. Probability: basic probability theory, conditional probability and independence, law of total probability and Bayes' theorem. Elementary distribution theory: cumulative distribution function and quantiles; probability mass function and probability density function. Discrete and continuous distributions - using binomial and normal distributions as examples. Uniform number generators. Simulation of observations on a given distribution. Simulation of probability models. Application of the computer to simulation.

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