一、課程說明(Course Desc<x>ription)
<br>蒙特卡羅方法是一種以隨機抽樣(Random Sampling)技術為基礎的通用數值模擬方法，伴隨電腦計算能力的增進，其在各領域的應用日益多樣。本課程由淺而深逐步探究蒙特卡羅方法的理論與應用，內容主要涵蓋隨機變數、類比蒙特卡羅模擬與變異數降低技巧。蒙特卡羅本質上是一種數值計算方法，為了學以致用並增加理解，本課程期望學生能夠利用電腦實現課程所學的概念與方法，建議修課學生至少熟悉一種程式語言，例如C/C++/Fortran/Python/Matlab或其它。本課程特別強調蒙特卡羅方法在核工與輻射領域的應用，也就是如何描述輻射與物質作用和遷移的行為，課程內容包含下列主題：
<br>1. Introduction to Monte Carlo Method
<br>2. Random Variables
<br>3. Analog Monte Carlo Simulation
<br>4. Variance Reduction Techniques
<br>5. Applications
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<br>二、指定用書(Textbook)
<br>1. Lecture notes
<br>2. Monte Carlo Methods for Particle Transport, Second Edition, Alireza Haghighat, CRC Press (2021)
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<br>三、參考書籍(References)
<br>1. Monte Carlo Techniques for Nuclear Systems – Theory Lectures, F.B. Brown, LA-UR-16-29043 (2016)
<br>2. Statistical Methods in Radiation Physics, J.E. Turner, D.J. Downing, J.S. Bogard, Wiley-VCH (2012)
<br>3. Monte Carlo - Advances and Challenges, F.B. Brown, W.R. Martin, R.D. Mosteller, LA-UR-08-05891 (2008)
<br>4. An MCNP Primer, J.K. Shultis, R.E. Faw, Kansas State University (2008)
<br>5. A Monte Carlo Primer: A Practical Approach to Radiation Transport, S.A. Dupree and S.K. Fraley, KA/PP (2002)
<br>6. Fundamentals of Monte Carlo Method for Neutral and Charged Particle Transport, A.F. Bielajew, University of Michigan (2000)
<br>7. A Primer for the Monte Carlo Method, I.M. Sobol, CRC Press (1994)
<br>8. Google…
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<br>四、教學方式(Teaching Method)
<br>1. 授課(Lectures)
<br>2. 討論(Discussion)
<br>3. 專題與簡報(Project & Presentation)
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<br>五、教學進度(Syllabus)
<br>1. Introduction to Monte Carlo Method
<br>2. Random Number Generation
<br>3. Application in Particle Transport (Analog Monte Carlo)
<br>4. Mathematical Basis for Monte Carlo Particle Transport
<br>5. Particle Tracking and Flux Estimation
<br>6. Random Variables
<br>7. Random Sampling Methods
<br>8. Fundamentals of Statistics
<br>9. Variance Reduction Techniques
<br>10. Applications and Special Topics
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<br>六、成績考核(Evaluation)
<br>1. 作業 (30%) Homework
<br>2. 考試 (40%) Exam
<br>3. 專題 (30%) Project
<br>4. 出席與小考 (5%) Attendance & Quiz
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