A Solution provided for the 1st series of homework, Computer Simulation course, 40634 Sharif UT, Spring 2023 (course page).
The provided notebook resolves the following five problems,
- Using Monte Carlo's method, Find an approximation (numerical solution) for π. A recommended topology is provided on this Wikipedia page.
- Provide a convergence diagram (to exact π) of multiple setups for your proposed method.
- Run two more simulations for approximation of π with the same inputs that were used in part 1. Compare the results with the previous ones.
- What probability distributions were used in part a? Are there any other options for the probability distributions that are used in the model?
- Use the Monte Carlo method for estimating the area of an ellipse with the following equation,
$$5x^2-6xy+5y^2-32=0$$ See the notebook for the solutions and more information.
The official problem set (from the first series of computer simulation homework) is also provided here. However, since it is in Farsi it may not be preferable for all.