https://smile.amazon.com/gp/product/B00G3L6JQ4/
Not so much notes as a glowing recommendation. There’s nothing new in here if you already have a mathematical background, but it’s a beautiful example of how to actually ground mathematics in real-world examples. It’s very probability/statistics heavy, which I much prefer to the existing triangle-heavy school syllabus. All the ideas are introduced using concrete, realistic examples.
There are a lot of books that try to do this, but I find the vast majority of them unconvincing. I think what this one does right is rather than focus on interesting puzzles or on engineering tools, it focuses on contentious historical debates - topics that are familiar to everyone but are genuinely unintuitive, and that required the de velopment of powerful tools to solve.
For example, one chapter looks at the debate in the 80s on whether smoking causes lung cancer. It uses this to talk about correlation vs causation, non-transitivity of correlation, using expected lives saved/lost to make policy decisions, frequentist vs bayesian interpretations of probability, selection bias in statistical studies and more. It does this in a way that seems to actually convey understanding as opposed to just the appearance of understanding - I expect that many readers would actually be able to correctly apply some of the intuition, even if they can’t produce an exact definition or a rigorous proof.
It’s very focused on intuition over rigour, to the point of often not using mathematical notation at all. I really like this as an approach for introducing subjects, providing framing and motivation before generalizing to a precise theory. I’d be really interested to see someone try teaching a course based around this book - following up each chapter with theory, exercises and case studies to ground the intuition that is developed by the examples.