Introduction to Probability with R

Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R.

This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers.

The book has an accompanying website with more information.

基於麻省理工學院已故教授Gian-Carlo Rota的一門熱門課程，並新增了許多新的主題，《使用R進行概率介紹》提供了R程式和動畫，以直觀而嚴謹的方式來建模自然現象的概率觀點。儘管R程式的長度較短，但它們和其他語言中的較長程式一樣複雜且強大。這種簡潔使學生能夠輕鬆掌握R。

這本以微積分為基礎的介紹圍繞著關鍵主題組織材料。其中一個最重要的主題是將概率視為觀察世界的一種方式，幫助學生以概率思考和推理。本書還展示了如何結合和連接隨機過程以形成更複雜的過程，這些過程更能成為自然現象的模型。此外，它還介紹了使用熵和信息來建立基本隨機過程的統一處理，以及從不同觀點介紹馬爾可夫鏈。每章都包括一個有關概率理論貢獻者的簡短傳記，練習題和選擇性答案。

本書附帶有一個相應的網站，提供更多信息。