PAI 的内容来自斯坦福面向计算机专业学生的概率课 CS109，改编成面向大众的版本。课程说，只要会代数就够了：能看懂 y = 2x + 1，就有足够的基础。

PAI is based on material from CS109, Stanford's probability course for computer scientists, rebuilt for the general public. The course says comfort with algebra is all you need: if you can make sense of y = 2x + 1, you have the background.

课程由斯坦福计算机系的两位教授 Chris Piech 和 Mehran Sahami 主讲，Kelly Cochran 担任课程主任。Chris 的研究是用机器学习理解人是怎样学习的；Mehran 还曾在 Google 担任研究科学家。

他们做过类似的事。2020 年，他们参与创办了 Code in Place，一门免费的编程入门课，第一期就迎来了一万多名学生。PAI 也用同样的方式来教。

The course is led by two Stanford computer science professors, Chris Piech and Mehran Sahami, with Kelly Cochran as the course director. Chris's research uses machine learning to understand how people learn. Mehran also worked as a research scientist at Google.

They have done this before. In 2020 they helped start Code in Place, a free introduction to coding that welcomed more than ten thousand students in its first offering. PAI is taught the same way.

做法很简单：每十名学生配一位志愿老师。教学团队相信，想教的人其实很多，也许和想学的人差不多；而教，是最好的学习方式。很多小组老师（section leader）当年也上过类似的课，后来回来把它传下去。

The model is simple: one volunteer teacher for every ten students. The teaching team's bet is that the number of people who want to teach is large, perhaps close to the number who want to learn, and that teaching is the best way to learn. Many section leaders took a course like this once and came back to pass it on.

进入学生页面后，有几个部分，各有分工：

• Home：把本周安排画成一条路线：要看的课、要做的项目，以及小组课。
• Lessons：课程视频，还有一个汇总了所有定义和规则的工具箱（Toolbox），以及课程教材。
• Puzzles：每天给全班一道新的概率题，另有一个可以把已发布题目全部练一遍的练习器。
• Portfolio：存放你做的所有项目。我的第一批作品是 Word Detective 和 Inference Time Calculator。
• Events：每周一和 Chris 的半小时线上活动，都会录像。
• Forums：全班和各小组交流的地方。

Once you are in, the student site has a few parts, each with a clear job:

• Home: the week's plan as a path: lessons to watch, something to build, and your section.
• Lessons: the lecture videos, plus a toolbox with every definition and rule in one place, and the course book.
• Puzzles: a new probability puzzle for everyone each day, and a trainer with every puzzle released so far.
• Portfolio: everything you build. My first projects are a Word Detective and an Inference Time Calculator.
• Events: a half-hour session with Chris every Monday, and it is recorded.
• Forums: where the whole class, and each section, talks.

我觉得这门课设计里最有意思的是小组课（section）。每周我和一位志愿小组老师、大约十位同学线上见面 50 分钟。老师先梳理这一周的内容，再带大家一起做题。小组课从周三到周五全天都有，不同时区都能找到合适的时间。

第一次的主题是“同一个提示，为什么答案不一样？”。这周是“帕尔帕廷民调”：当没人愿意公开说出来时，怎样知道有多少人暗中支持某个人？

✎ 阅读提示小组课也是课程确认“这是你自己在学”的方式：证书看的是每周的参与，而不是 AI 也能代做的线上作答。

For me the most interesting part of the design is the section. Each week I meet live for 50 minutes with a volunteer section leader and about ten other students. Our leader goes over that week's ideas, and we work through problems together. Sections run at all hours from Wednesday to Friday, so there is a time for every time zone.

Our first topic was "Same prompt, different answers?". This week it is the Palpatine poll: how do you find out how many people secretly support someone, when nobody wants to say so out loud?

✎ 阅读提示Section is also how the course knows you are doing your own work: the certificate depends on taking part each week, not on online answers that an AI could produce.

每周把一个概率概念和一个要动手做的项目配在一起：

课程最后是一个自己设计的期末项目，它会成为公开作品集的核心。

Each week pairs one idea from probability with something you build:

The course ends with a final project of your own design, which becomes the centrepiece of the public portfolio.

有两种方式：申请当学生，或者申请当志愿老师，带一个小组。申请每年开放一次。2026 年的申请已在九月底截止，课程于 10 月 9 日开始，所以下一次机会是明年在 pai.stanford.edu 的申请。

There are two ways in: apply to learn, or volunteer to teach a small group of learners. Applications open once a year. For 2026 they closed at the end of September, and class started on 9 October, so the next chance is next year's round on pai.stanford.edu.

我刚刚学完第一周，接下来会分享这一周的笔记。课程 FAQ 里有一句话让我印象很深：“不是学数学的料”，通常只是意味着“很久以前上过一堂糟糕的数学课”。它让我想到：如果我能早一点遇到这样的老师，也许会更喜欢数学和计算机科学。

I have just finished week one, and my notes from it come next. One line from the course FAQ has stayed with me: "not a math person" usually means "had one bad math class a while ago". It made me wonder whether I would have loved math and computer science even more if I had met teachers like these earlier.

• Probability for AI：课程首页、FAQ 和申请。
• Probability for AI 团队。
• Code in Place：以同样方式教学的斯坦福免费编程课。
• Chris Piech 与 Mehran Sahami 的斯坦福主页。

• Probability for AI: the course home page, FAQ and applications.
• The Probability for AI team.
• Code in Place: the earlier free Stanford course taught the same way.
• Chris Piech and Mehran Sahami: Stanford profiles.