基本素養 Basic Literacy

Technological and Cultural literacy

Environmental and Social Care

Ability to communicate effectively with others and work in a team with developed international perspective.

核心能力 Competence

Professional and interdisciplinary capacity

Innovative thinking as well as the ability to define and solve problems independently

Language and communication skills to coordinate the integration of interdisciplinary personnel

The ability to design, verify, and integrate with industrial implementations, and work together to promote industrial transformation and upgrading

Developed sense of self- improvement: International Perspective, Principle Literacy

課程概述 Course Description

This course introduces a basic theory of stochastic process, which provides a large number of modelling in natural sciences and engineering as well as in social sciences. Stochastic process is a mathematical modeling of time-dependent systems subject to random phenomena. Various probability techniques capture the random quantities in a mathematically sound way. Starting with a review of basic probability concepts, this course focuses on the theory of discrete and continuous Markov processes. The course also covers some most important types of stochastic processes (Poisson, Gaussian, queuing models). Real world application of the theory is emphasized on stochastic modelling arising in computer science, especially on stochastic transition systems. The application explains how to integrate computation into cyber physical systems in terms of concurrent and communicating systems.

課程學習目標 Course Objectives

• Markov Process
• Poisson Process and Application to Queueing Model
• Stochastic Modelling in Computer Science
• 課程進度 Progress Description

進度說明 Progress Description
1I. Probability Review (random variables and their characteristics, various distributions, independence and sums, etc)
2II. Markov Chains (discrete time) II-i State Spaces and Transition Matrices
3II-ii Classification of States
4II-iii Chapman Kolmogorov Equation
5II-iv Stationary Distributions: Detailed Balance and Reversibility
6II-v Algorithm to Check Reversibility
7II-vi Limit Behavior (Convergence to Equilibrium)
8II-vii Ergodic Theorem
9III. Stochastic Modelling in Computer Science I (stochastic automata)
10IV. Poisson Processes IV-i Continuous Time Stochastic Processes, Exponential Distributions
11IV-ii Limit Theorem (the Law of Rare Events)
12 V. Markov Processes (continuous time) V-i Transition Rate Matrices and Their Exponentials
13V-ii Kolmogorov Forward and Backward Equations
14V-iii Time Reversal
15VI. Stochastic Modelling in Computer Science II (stochastic petri nets)
16VII. Queueing Systems
17VIII. Brownian Motion and Gaussian Processes
18IX. OPTIONAL Markov Decision Process Simulation Algorithm (Markov Chain Monte Carlo)
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

課程是否與永續發展目標相關調查 Survey of the conntent relevant to SDGs

本課程與SDGs相關項目如下：
This course is relevant to these items of SDGs as following:
• 就業與經濟成長 (Decent work and Economic growth)
• 工業、創新與基礎建設 (Industry Innovation and infrastructure)

有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No
3.本課程是否可歸認為學術倫理課程? 否
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
4.本課程是否屬進入社區實踐課程? 否
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged? No