Monte Carlo Methods: A Hands-On Computational Introduction Utilizing Excel

This book is intended for undergraduate students of Mathematics, Statistics, and Physics who know nothing about Monte Carlo Methods but wish to know how they work. All treatments have been done as much manually as is practicable. The treatments are deliberately manual to let the readers get the real feel of how Monte Carlo Methods work.

Definite integrals of a total of five functions ��(��), namely Sin(��), Cos(��), e��, loge(��), and 1/(1+��2), have been evaluated using constant, linear, Gaussian, and exponential probability density functions ��(��). It is shown that results agree with known exact values better if ��(��) is proportional to ��(��). Deviation from the proportionality results in worse agreement.

This book is on Monte Carlo Methods which are numerical methods for Computational Physics. These are parts of a syllabus for undergraduate students of Mathematics and Physics for the course titled Computational Physics.

Need for the book: Besides the three referenced books, this is the only book that teaches how basic Monte Carlo methods work. This book is much more explicit and easier to follow than the three referenced books. The two chapters on the Variational Quantum Monte Carlo method are additional contributions of the book.

Pedagogical features: After a thorough acquaintance with background knowledge in Chapter 1, five thoroughly worked out examples on how to carry out Monte Carlo integration is included in Chapter 2. Moreover, the book contains two chapters on the Variational Quantum Monte Carlo method applied to a simple harmonic oscillator and a hydrogen atom.

The book is a good read; it is intended to make readers adept at using the method. The book is intended to aid in hands-on learning of the Monte Carlo methods.

這本書是為數學、統計和物理的大學本科生而設計的，他們對蒙特卡羅方法一無所知，但希望了解它們的工作原理。所有的處理都盡可能地手動完成。這些處理故意手動進行，讓讀者真正感受到蒙特卡羅方法的工作方式。

使用常數、線性、高斯和指數概率密度函數對五個函數的定積分進行了評估，這五個函數分別是Sin(x)、Cos(x)、e^x、loge(x)和1/(1+x^2)。結果表明，如果概率密度函數與函數本身成比例，則結果與已知的精確值更接近。與比例關係偏離會導致結果更不準確。

這本書是關於蒙特卡羅方法的，這些方法是計算物理學的數值方法。這些方法是數學和物理學本科生計算物理學課程的一部分。

這本書的需求：除了參考的三本書之外，這是唯一一本教授基本蒙特卡羅方法工作原理的書。這本書比參考的三本書更加明確和易於理解。關於變分量子蒙特卡羅方法的兩章是本書的額外貢獻。

教學特點：在第一章對背景知識進行全面了解之後，第二章包含了五個詳細的實例，介紹如何進行蒙特卡羅積分。此外，本書還包含兩章關於變分量子蒙特卡羅方法應用於簡谐振子和氫原子的內容。

這本書很值得一讀，旨在使讀者熟練使用這種方法。這本書旨在幫助讀者實踐學習蒙特卡羅方法。