Monte Carlo Integration Books for Senior Undergrads

In summary, the conversation discussed a request for a good book to learn Monte Carlo Integration at a senior undergraduate level. The user apologized for posting in the wrong subforum and requested to move the thread to the appropriate forum. Suggestions for books were given, including Numerical Mathematics and Computing by Cheney & Kincaid, Statistical Mechanics: Algorithms and Computations by W. Krauth, and An Introduction to Computer Simulation Methods: Applications to Physical Systems by Gould/Tobochnik. The user also mentioned signing up for a course on Coursera that uses the first book.
  • #1
Hercuflea
596
49
First let me say I apologize for posting in the wrong subforum. But for some reason I am not allowed to post in Math and Science Learning materials, maybe a glitch? Please move this thread there if possible.

I am looking for a good book that will teach me Monte Carlo Integration at a senior undergraduate level. I am in a second course in numerical analysis, and I would like to learn Monte Carlo Integration for one of my projects. Does anyone know of a good source that will teach me this method at an undergraduate level? All of the books I have seen it in are graduate textbooks and a little over my head.
 
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  • #2
Hercuflea said:
First let me say I apologize for posting in the wrong subforum. But for some reason I am not allowed to post in Math and Science Learning materials, maybe a glitch? Please move this thread there if possible.

The Learning Materials forums are for actual online materials written for PF, or for links to such materials on other sites; not for requests for them, or discussion about them.

This is the appropriate forum to ask about books.
 
  • #3
The book Numerical Mathematics and Computing by Cheney & Kincaid contains a basic introduction to Monte Carlo methods.
 
  • #4
Statistical Mechanics: Algorithms and Computations by W. Krauth

or
An Introduction to Computer Simulation Methods: Applications to Physical Systems by Gould /Tobochnik
 
  • #5
jesse73 said:
Statistical Mechanics: Algorithms and Computations by W. Krauth

or
An Introduction to Computer Simulation Methods: Applications to Physical Systems by Gould /Tobochnik

Interesting, I just signed up for a course on coursera that uses that first book. We'll see how it goes.
 

1. What is Monte Carlo integration?

Monte Carlo integration is a numerical method used to approximate the value of a complex mathematical function by randomly sampling points within its domain and calculating their average. It is particularly useful for high-dimensional integrals that are difficult or impossible to solve analytically.

2. How does Monte Carlo integration work?

Monte Carlo integration works by randomly selecting points within the domain of a function and evaluating the function at those points. The average of these evaluations is then multiplied by the volume of the domain to approximate the integral. As more points are sampled, the accuracy of the approximation improves.

3. What are the advantages of using Monte Carlo integration?

One major advantage of Monte Carlo integration is its ability to handle high-dimensional integrals that are challenging for other methods. It also does not require any prior knowledge about the function being integrated, making it a versatile tool for a wide range of applications. Additionally, the error in the approximation decreases as more points are sampled, allowing for greater precision.

4. What are some common applications of Monte Carlo integration?

Monte Carlo integration has many applications in science and engineering, including in computational physics, finance, and computer graphics. It is often used to solve problems involving complex systems, such as in simulating physical phenomena, optimizing processes, and estimating probabilities in statistical analysis.

5. Are there any limitations or potential drawbacks to using Monte Carlo integration?

While Monte Carlo integration is a powerful tool, it does have some limitations. It can be computationally expensive, especially for high-dimensional integrals, and the accuracy of the approximation depends on the number of points sampled. Additionally, it may not be the most efficient method for some types of integrals, such as those with smooth and well-behaved functions.

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