只推荐Girardin, V.; Limnios, N. (2022). Applied Probability: From Random Experiments to Random Sequences and Statistics这本法国人的书, 足够精简也足够现代, 在初等的动机和计算与高等的严格和恰切之间达到了很好的平衡; 初学者有一定数学成熟度的话也可以直接上手.
虽然国内数学系概率论入门书没一个能打的, 张颢那本面向工科(尽管是清华)的概率论也不是很值得花力气读. 想学现代应用没必要在本应该是概念导向的书中学, 个人所知比较合适的选择有
- Dmitry Panchenko (2019) Introduction to Probability Theory 用此书作课本的一门课说”We will not dwell on definitions and standard techniques too much (which means you will have to digest them quickly), and will try to learn important ideas through examples from computer science, random graphs, statistics, geometry, and number theory.”
- Lange, K. (2010). Applied Probability 去掉中间随机过程相关依然内容丰富, 有独到的计算和优化的观点.
- M. Mitzenmacher & E. Upfal (2017) Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis 面向信科的离散概率教科书, 副标题挺长所以顾名思义即可; 说个题外话, 离散概率其实比较容易追上前沿而且时下颇为火热, 有兴趣了解的话建议参照这个课来学.
当然最后还是建议能学高等概率论就直接去学, 何必在初等高等衔接处扭扭捏捏的呢?(͡° ͜ʖ ͡°)
