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CPS615-End of Basic Overview of Random Numbers and First Part of Monte Carlo Integration

Given by Geoffrey C. Fox at Delivered Lectures of CPS615 Basic Simulation Track for Computational Science on 22 October 96. Foils prepared 12 November 1996

This starts by finishing the simple overview of statistics
Covering Gaussian Random Numbers, Numerical Generation of Random Numbers both sequentially and in parallel
Then we describe the central limit theorem which underlies Monte Carlo method
Then it returns to Numerical Integration with the first part of discussion of Monte Carlo Integration

This mixed presentation uses parts of the following base foilsets which can also be looked at on their own!
Master Set of Foils for 1996 Session of CPS615
CPS615 Foils -- set D: Statistics and Random Numbers (In preparation for Monte Carlo)
CPS615 Numerical Integration Module

Table of Contents for CPS615-End of Basic Overview of Random Numbers and First Part of Monte Carlo Integration

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CPS 615 Lectures 1996 Fall Semester -- October 22
1 Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1996 --
Lecture of October 22 - 1996
2 Abstract of Oct 22 1996 CPS615 Lecture
Last Part of Random Number Discussion
3 Generation of Gaussian Distributions
4 How do computers get random numbers?
5 Simple Random Number Generator
6 More on Generation of Random Numbers Numerically
7 An Illustration of Dangers of Correlations!
8 Parallel Random Numbers
9 The Law of Large Numbers or the Central Limit Theorem.
10 Shapes of Probability Distributions in Central Limit Theorem
11 Central Limit Theorem for Functions
12 Error in Central Limit Averaging
13 Simpson and Trapezoidal Rule Integrations
14 Newton-Cotes and Iterated Rules
15 Gaussian and Monte Carlo Integration
Start of Monte Carlo Integration
16 33:Why Monte Carlo Methods Are Best in Multidimensional Integrals
17 34:Best Multidimensional Integration Formulae
18 35:Distribution of Points in Two-dimensional Integral Done by Newton-Cotes Style Formulae
19 36:Distribution of Points in Two-dimensional Integral Done by Monte Carlo
20 37:Use of Bounding Boxes to Calculate --- I
21 38:Use of Bounding Boxes to Calculate --- II
22 39:Use of Bounding Boxes in Complicated Geometries --- I
23 40:Use of Bounding Boxes in Complicated Geometries --- II
24 41:IMPORTANCE Sampling Basic Theory
25 42:Choice of Importance Sampling Weight Function --- I
26 43:Choice of Importance Sampling Weight Function --- II
27 44:Monte Carlo Approach to Discrete Integrals
28 45:Why Use Monte Carlo for Summations?
29 46:Example of using Monte Carlo for Summations
30 47:The Wrong Way to Perform Multiple Monte Carlo
31 48:Stock Market Example of Multiple Monte Carlos --- I
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