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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
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This starts by finishing the simple overview of statistics
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Covering Gaussian Random Numbers, Numerical Generation of Random Numbers both sequentially and in parallel
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Then we describe the central limit theorem which underlies Monte Carlo method
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Then it returns to Numerical Integration with the first part of discussion of Monte Carlo Integration
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This mixed presentation uses parts of the following base foilsets which can also
be looked at on their own!
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
CPS615-95D CPS615 Foils -- set D: Statistics and
Random Numbers (In preparation for
Monte Carlo)
CPS615NI95 CPS615 Numerical Integration Module
CPS 615 Lectures 1996 Fall Semester -- October 22
CPS615Master96 069 001 Delivered Lectures for
CPS615 -- Base Course for
the Simulation Track of
Computational Science
Fall Semester 1996 --
Lecture of October 22 - 1996
CPS615Master96 075 002 Abstract of Oct 22 1996
CPS615 Lecture
Last Part of Random Number Discussion
CPS615-95D 010 003 Generation of Gaussian
Distributions
CPS615-95D 011 004 How do computers get random
numbers?
CPS615-95D 012 005 Simple Random Number
Generator
CPS615-95D 013 006 More on Generation of Random
Numbers Numerically
CPS615-95D 014 007 An Illustration of Dangers
of Correlations!
CPS615-95D 015 008 Parallel Random Numbers
CPS615-95D 016 009 The Law of Large Numbers or
the Central Limit Theorem.
CPS615-95D 017 010 Shapes of Probability
Distributions in Central
Limit Theorem
CPS615-95D 018 011 Central Limit Theorem for
Functions
CPS615-95D 019 012 Error in Central Limit
Averaging
CPS615-95D 020 013 Simpson and Trapezoidal Rule
Integrations
CPS615-95D 021 014 Newton-Cotes and Iterated
Rules
CPS615-95D 022 015 Gaussian and Monte Carlo
Integration
Start of Monte Carlo Integration
CPS615NI95 033 016 33:Why Monte Carlo Methods
Are Best in
Multidimensional Integrals
CPS615NI95 034 017 34:Best Multidimensional
Integration Formulae
CPS615NI95 035 018 35:Distribution of Points
in Two-dimensional Integral
Done by Newton-Cotes Style
Formulae
CPS615NI95 036 019 36:Distribution of Points
in Two-dimensional Integral
Done by Monte Carlo
CPS615NI95 037 020 37:Use of Bounding Boxes to
Calculate --- I
CPS615NI95 038 021 38:Use of Bounding Boxes to
Calculate --- II
CPS615NI95 039 022 39:Use of Bounding Boxes in
Complicated Geometries ---
I
CPS615NI95 040 023 40:Use of Bounding Boxes in
Complicated Geometries ---
II
CPS615NI95 041 024 41:IMPORTANCE Sampling
Basic Theory
CPS615NI95 042 025 42:Choice of Importance
Sampling Weight Function
--- I
CPS615NI95 043 026 43:Choice of Importance
Sampling Weight Function
--- II
CPS615NI95 044 027 44:Monte Carlo Approach to
Discrete Integrals
CPS615NI95 045 028 45:Why Use Monte Carlo for
Summations?
CPS615NI95 046 029 46:Example of using Monte
Carlo for Summations
CPS615NI95 047 030 47:The Wrong Way to Perform
Multiple Monte Carlo
CPS615NI95 048 031 48:Stock Market Example of
Multiple Monte Carlos --- I
List of Foils Used as they occur
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
69 75
CPS615-95D CPS615 Foils -- set D: Statistics and
Random Numbers (In preparation for
Monte Carlo)
10 11 12 13 14 15 16 17 18 19 20 21 22
CPS615NI95 CPS615 Numerical Integration Module
33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
Sorted List of Foils Used
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
69 75
CPS615-95D CPS615 Foils -- set D: Statistics and
Random Numbers (In preparation for
Monte Carlo)
10 11 12 13 14 15 16 17 18 19 20 21 22
CPS615NI95 CPS615 Numerical Integration Module
33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
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