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The [course_title] course introduces you to the stochastic process through numerical simulations. In probability theory, a stochastic process is a time sequence representing the evolution of some system represented by a variable whose change is subject to a random variation.

Throughout the course, you will learn the basic theories of stochastic processes that will be followed by the lessons to develop python codes to perform numerical simulations of small particles diffusing in a fluid. Then, you will learn to analyse the simulation data based on the above theories.

Upon completion, you will be able to analyse the dynamical data of more complicated systems.

**Assessment**

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

**Certification**

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Course Credit: Kyoto University.

### Course Curriculum

Introduction | |||

Welcome! | 00:03:00 | ||

Lesson 1 | |||

Part 1 | Using Python, iPython, and Jupyter notebook | 00:09:00 | ||

Part 2 | Making graphs with matplotlib | 00:08:00 | ||

Part 3 | The Euler method for numerical integration | 00:11:00 | ||

Part 4 | Simulating a damped harmonic oscillator | 00:08:00 | ||

Lesson 2 | |||

Part 1 | Stochastic variable and distribution functions | 00:21:00 | ||

Part 2 | Generating random numbers with Gaussian/binomial/Poisson distributions | 00:13:00 | ||

Part 3 | The central limiting theorem | 00:15:00 | ||

Part 4 | Random walk | 00:13:00 | ||

Lesson 3 | |||

Part 1 | Basic knowledge of Stochastic process | 00:13:00 | ||

Part 2 | Brownian motion and the Langevin equation | 00:14:00 | ||

Part 3 | The linear response theory and the Green-Kubo formula | 00:11:00 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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