Online courses directory (2)
6.00.2x will teach you how to use computation to accomplish a variety of goals and provides you with a brief introduction to a variety of topics in computational problem solving . This course is aimed at students with some prior programming experience in Python and a rudimentary knowledge of computational complexity. You will spend a considerable amount of time writing programs to implement the concepts covered in the course. For example, you will write a program that will simulate a robot vacuum cleaning a room or will model the population dynamics of viruses replicating and drug treatments in a patient's body.
Topics covered include:
- Advanced programming in Python 3
- Knapsack problem, Graphs and graph optimization
- Dynamic programming
- Plotting with the pylab package
- Random walks
- Probability, Distributions
- Monte Carlo simulations
- Curve fitting
- Statistical fallacies
The motion of falling leaves or small particles diffusing in a fluid is highly stochastic in nature. Therefore, such motions must be modeled as stochastic processes, for which exact predictions are no longer possible. This is in stark contrast to the deterministic motion of planets and stars, which can be perfectly predicted using celestial mechanics.
This course is an introduction to stochastic processes through numerical simulations, with a focus on the proper data analysis needed to interpret the results. We will use the Jupyter (iPython) notebook as our programming environment. It is freely available for Windows, Mac, and Linux through the Anaconda Python Distribution.
The students will first learn the basic theories of stochastic processes. Then, they will use these theories to develop their own python codes to perform numerical simulations of small particles diffusing in a fluid. Finally, they will analyze the simulation data according to the theories presented at the beginning of course.
At the end of the course, we will analyze the dynamical data of more complicated systems, such as financial markets or meteorological data, using the basic theory of stochastic processes.