This has been a fantastic introduction to Monte Carlo methods

Great tutorial. It made a lot of theoretical concepts clear for me when implementing. I really wish that you make more videos on Monte Carlo Simulations. I read that these were first used to solve atomic simulations. I am not connected to the physics world, and it would be great to learn more about that. Once again, great job

@Andrew Dotson , I don't know if you read comments on older videos, but I just wanted to thank you. I missed the lecture on Monte Carlo and understood nothing of the example code we were given. I already subscribed to you for the awesome skits, but this was the perfect video for me. You explain the concept and what each part of the code does, without going too slow. (I am a noob at programming, ngl.) Thank you, and greetings from Finland.

This was so much better than my lecturer's explanation. Nice and concise and some coding thrown in too. Good job. Thanks Andrew!

I'm not sure if threads exist in Python, but in C there is a concept called threading, where you can run multiple functions at the same time, and in this case you'd be able to split the N operations among M threads, where M threads are computing N/M operations at the same time, which would result in a faster runtime. After a quick google search, it seems that Python does have threads, I'd recommend learning them so that you can optimize your code runtime whenever creating a new program, especially in a field such as physics where you would have situations in which you'd have to compute 10000+ points sometimes.

I've never been introduced to Monte Carlo integration this way. Thanks!

I've been meaning to learn this technique. Great introduction!!

Good video, straight into it, with results! Others would have dragged this out.

Hi! Thanks a lot for this video, this Python example helped me get a better idea of how to approach solving problems in Python. In my research, I have to calculate entrainment rates (the rate dry air mixes with clouds to dissipate them) in cloud fields and observe how these rates affect cloud size distributions. Dealing with atmospheric processes, most of my data is in 4 dimensional arrays, so I've been slowly getting acquainted with those. Though your example was general, showing how to solve that integral helped give me a couple of good ideas of how I can approach solving a couple of my unknown variables. Thanks again for the video, I wish you the best of luck in your QCD research! Keep up the awesome videos! -From an elightened Python noob 😊😜

Great tutorial. Cleared my concept on MC integration. I was looking for this topic on KZfaq and found your video very helpful .

This was actually very very helpful! I mainly watch the comedic side of your channel, but this was just a great video.

Excellent video. In 1 video i learnt the basics of how to plot a histogram, generate random numbers, write for loops and use arrays in python. Excellent. Thanks! Please make more of such videos using python

This is my first video on Monte Carlo integration. Loved your explanation :) Thank you :)

Thanks, Andrew. Helped me a ton with understanding my lab on Monte Carlo Integration.

Hey Andrew! I just wanna say thank you for this video. I made a monte carlo maximum successive scattering simulator out of it and the program did work as intended.

Wha... thats absolutely genius! I was struggling to understand this but now its just clicked!

many thanks! you are helping a lot of programmers around the world... (I´m from Brazil!)

Great production in this video 👏👏 thanks for the content

Hi Andrew, thank you very much for this explanation. Now I know how to propose the solution for my project. I feel like I'm going to have a lot of fun applying this method!

Thanks Andrew, I'm just getting into my calculus courses at my college. I'm trying to pick up programming along with it and this video is quite helpful. I haven't taken any statistic courses as my degree plan doesn't require them and so my question is, have you taken any statistic courses and if so which ones? Keep up the great work we all appreciate it.

What a fantastic and helpful video... Thanks a lot. You really made it very simple and easy to understand.

As a person who has trouble with math terminology and symbols, bless you for doing this in code.

This is great thank you! The way you teach is very clear!

Title: Monte Carlo Integration In Python For Noobs : : : First words: "What's goin' on smart people!" Great video, sub and respect (:

Nice Explanation bro, Need more stuffs like this.

I first watched this in my 1st year in college thinking oh this is non of my business. I did not know I would need this video so bad. Thank you for your hardwork into making this video. luv it

Great, straight to the point wonderful tutorial!

Good introductory video for Montecarlo!

it was a good and simple intro to Monte Carlo Integration. helped a lot!!

Superb content sir 😎

Hey andrew, this is really nice !

clear to the point very good video.

Ahuyet! Thanks Andrew that was very cool!

Fantastic video!

Thank you for publishing such a great video.

Amazing Video! Thank you

Great video!

clicked because I am a noob, suddenly called "Smart People", subscribed.

Eyyy lmao, I'm gonna take a class on Monte Carlo Methods!

I needed this last week and KZfaq didn't recommend it when I googled it. Unlucky

Thank you for this tutorial! Very understandable and easy, while looking for smth simmilar in internet is so complexed(

really interesting stuff!

Great explanation, thank you

Loved it!

love me some Monte Carlo!

These videos are really interesting to watch. Seeing you suss things out in real-time with a not-so-super-fast entry into python is awesome. Out of interest, does the script break anywhere for different A's, B's or func(x)?

This is great, thank you very much!

i love you bro. you saved my butt. i owe you. edit: subbed

I actually started to get away from python but this video gave me life hahahaha, thanks!

nice one. Yeah, np arrays are way faster than lists. Interesting about the convergence for single variable functions. Got any recommendations for books on numerical methods in general (and Python in particular)?

THANKS BRO I GOT IT CLEARED IN 5 minutes IN!!!

yaaaas, thank you for the video!

Thank you Sir...from India....

thank you!!!so helpful

dude, thank you!

Thank you bro for this video nice content

, how can I find the area inside a curve? I have data points for a hysteresis loop and I want to calculate the area inside the curve

Great presentation. It works well. You said it will become a delta function, but you probably mean a Gaussian distribution, since it yields an average and a standard deviation.

Great video. Do have a tutorial for phyton installation?

So is there a way to turn this into something to show growth of investment portfolios? Like with the average growth and standard deviation?

Hi Andrew. if I look a mean for a cost. what formula apply?

Nice and impressive demonstration...the x axis should not be labeled as expected value instead of area?

nice explanation❤❤❤❤❤❤❤❤❤❤

Thx, that helped me!

You, sir, are a fucking gangster for this tutorial!!! Exactly what I was after. #Sauce

Thank You very much!

How I put dots in required area.want to know the command in python for plotting

Thank you so much!

Two questions, first I notice that the histogram of the integrals looks like the normal distribution. Is this because of the central limit theorem? Also, there are two places where sampling occurs where the first is sampling for estimating the integral and the other is sampling integral calculations for taking the average. My question is about how each of these parameters impacts the result. For example what if I only used 100 samples for calculating a single integral but took the average of 10000 integrals?

hey andrew, can you make a vedio showcasing what all compuatational work you do in your research in theoretical nuclear physics?

Thoroughly disturbed by the way you write a.

super nice video

I'm using Monte Carlo to model electron transport through water for my thesis, nice to see some Monte-Carlo!

Do you think you could show to take the gradient of a scalar field in python? Recently discovered your channel and love your videos!

Thank you very much.

How do you do it for 2 dimension or higher integral? Like let's say Sqrt(x + y)

Lol where was this last semester when I was working on this for my computational physics course?

Nice introduction. Can you show a tutorial for monte carlo simulation of a honeycomb Ising lattice?

Nice idea with the histogam. Looks a bit low-slanted, though. Hard to include the last x-value in the x domain, as that interval is semi-open. But wonderful example, thank You!

Great explaination but I have one doubt like if they give two circles and told to find the intersection area whose radius is r1 = 2, r2 = 2. And random sampling is n = 100000. Then how to print estimated area? I am getting error while implementing this? Please someone help. Thank you.

one question why do i have to use random numbers. shouldnt it work if i use equdistant values in my integralinterval as well ?

I don't understand however why it is better to use random samples (even for higher dimensions). Wouldn't a sample of uniformily spaced values be basically as good as a uniform distribution as it can get since the order doesn't matter. So for example for a one dimensional integral you can choose numbers from a and then increment by a small delta untill you get to b, and for a bidimensional integral do something similar but in 2 dimensions (of course making shure that you keep the points evenly spaced). For some integrals it might be easier to just take random samples i get that but when it is easier to just increment by a delta my question is if that would yield as good a result as with random numbers?

can you please explain monte carlo method for multidimensional integration

How do you apply the trapezoidal rule to a dataframe instead of a function?

Thanks Andrew

Could you help me with a monte carlo assignment I have for a more complex equation by any chance :(

Hey Andrew , please make a video on how to read a research paper and what research paper can an undergraduate can read.

Great work bro... 2 questions here... If anyone can help... 1) when you wrote the very first expression of , I think it should mean that avg of f(x) for x in [a, b]... And not for any value of X. 2) while we carry out the experiment of randomly generating value of x and then, finding f(x), we should not be bias and should pick any value of x in the domain [a, b]. But, I think, Random no generator will only generate numbers randomly between 0 and 1, and not 0 to pi. Not sure though how the result is perfect.

''Very nice out of 10'' got me laughing

Very nice / 10

Great video! How would you solve for an integral with infinite limits though?

Hey Andrew can you tell me about your python journey?

Wouldn't the end distribution of areas end up approximating a normal distribution instead of the delta function as a result of the central limit theorem?

Only one thing is wrong. The distribution will never be a Dirac's delta. Because of the central limit theorem, the width of the normal distribution will grow as sqrt(N). (You can check the x tics with N=1000 and N=10000 and see the width is greater in the later).What will decrease as sqrt(N) is the standard deviation of the mean. Great video tho👍

What will the Julia equivalent of this code be?

THANK YOU!!

Do you know if there's a scenario where using Monte Carlo's method would be preferable over other numerical integration methods (such as trapezoidal rule or simpson's rule)? I ask this because, like you said, seems like a lot of computational effort to generate random numbers and then feed them into a function.

Wolverine is teaching map its cool!

What is the difference between taking the average of 1000 integration results each having N=10000 random points, and just 1 integration with N=1000*10000? Is the point of doing this just visualization with histograms?

didn't know to use the same variable e.g. i for index in nested for loops several times