A Graduate Course in Probability
暫譯: 研究生機率課程

Liviu I Nicolaescu

相關主題

商品描述

This book grew out of the notes for a one-semester basic graduate course in probability. As the title suggests, it is meant to be an introduction to probability and could serve as textbook for a year long text for a basic graduate course. It assumes some familiarity with measure theory and integration so in this book we emphasize only those aspects of measure theory that have special probabilistic uses.The book covers the topics that are part of the culture of an aspiring probabilist and it is guided by the author's personal belief that probability was and is a theory driven by examples. The examples form the main attraction of this subject. For this reason, a large book is devoted to an eclectic collection of examples, from classical to modern, from mainstream to 'exotic'. The text is complemented by nearly 200 exercises, quite a few nontrivial, but all meant to enhance comprehension and enlarge the reader's horizons.While teaching probability both at undergraduate and graduate level the author discovered the revealing power of simulations. For this reason, the book contains a veiled invitation to the reader to familiarize with the programing language R. In the appendix, there are a few of the most frequently used operations and the text is sprinkled with (less than optimal) R codes. Nowadays one can do on a laptop simulations and computations we could only dream as an undergraduate in the past. This is a book written by a probability outsider. That brings along a bit of freshness together with certain 'naiveties'.

商品描述(中文翻譯)

這本書源自於一個學期的基本研究生課程的筆記。正如書名所示,它旨在介紹機率,並可以作為一年制基本研究生課程的教科書。它假設讀者對測度理論和積分有一定的熟悉度,因此本書僅強調那些在機率上有特殊用途的測度理論方面。本書涵蓋了成為一名有抱負的機率學家所需的文化主題,並受到作者個人信念的指導,即機率是一個由範例驅動的理論。範例是這個主題的主要吸引力。因此,本書專門用於收錄各種範例,從古典到現代,從主流到「異國情調」。文本中還附有近200道練習題,其中不少是非平凡的,但所有題目都旨在增強理解並擴大讀者的視野。在本科和研究生階段教授機率時,作者發現了模擬的啟發性力量。因此,本書包含了一個隱晦的邀請,鼓勵讀者熟悉程式語言 R。在附錄中,有一些最常用的操作,文本中也穿插了(不太理想的)R 代碼。如今,人們可以在筆記本電腦上進行模擬和計算,而這在過去的本科生時期我們只能夢想。這是一本由機率外行撰寫的書,帶來了一些新鮮感以及某種「天真」。