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paper-machine comments on Open Thread, February 1-14, 2013 - Less Wrong
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Comments (282)
Why reinvent the wheel? There are plenty of decent textbooks out there already, and no apparent reason why "pure mathematics for rationalists" is any different from "pure mathematics."
There are various meta-level questions left unanswered by textbooks, such as "how do I go about deciding which textbooks to read in a particular subject," "how do I go about deciding which subjects to study," "what resources other than textbooks are good for learning math," and "say, what's the big picture here, anyway?" The goal would not be to regurgitate the content of any particular textbook.
I also expect rationalists to be more goal-oriented than most people, so my recommendations for them would be different from my recommendations for people who just want to learn whatever math is cool and interesting. My recommendations would depend heavily on what those goals are, which is why I'd like to know what those goals are.
You probably know this anyway Qiaochu, given your involvement in the various math stackexchanges. But others here might find it useful.
This is my Google search string for mathematics textbooks on the stackexchanges:
Replace "coding theory" with the area you want to learn, and you end up getting a nice list.
You have overestimated the strength of my google-fu! That's a nice search string.
I would be very interested in something like this.
I hope you do write this. I'm trying to get comfortable with using math again and I'm pretty much starting from scratch with only my rusty half-forgotten high school algebra and pre calculus (I haven't even learned calculus. Should I? That's why I need your post).This kind of general guidance about what to focus on would likely be very helpful.
My goal (for now, unless I try and find out I really like some specific direction of study) is mainly just to learn whatever math gets me the most mileage in understanding the random grab bag of subjects I happen to like a bit more rigorously- I'm not sure what specific advice that would warrant, besides maybe some discussion on the math prereqs for various domains. Could that be something your post covers?
It could be if you list those domains, although I can't claim to be a domain expert in anything that isn't math.
I'm still working on deciding what I'm into; I was hoping for something like a general overview of the maths used in different fields (whichever ones you felt like writing about about). But since you're wanting examples, I'll list some things I might or might not read and would like to know what math would enable understanding them
Theory of Computation
Causality: Models, Reasoning and Inference
The Feynman Lectures on Physics
AI: A modern approach
Networks, Crowds, and Markets: Reasoning About a Highly Connected World
Chaitin's books on algorithmic information theory and the math of evolution
Highly Advanced Epistemology 101 for Beginners
or learning computational cognitive science
And are the math courses listed in Louie Helm's course recommendations everything I need to understand the rest of the courses in it?
I don't know! But I'll attempt to suggest untested heuristics for answering this question.