= 27d567bc2d48d9f40e9ccc20ea370b15)
Qiaochu_Yuan comments on Open Thread, February 1-14, 2013 - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (282)
So, I mentioned here that I might write a "(pure) mathematics for rationalists" post. Would other people be interested in such a post, and if so, what sort of concerns would you want it to address? If there are lots of LWers trying to learn mathematics I would also like to know what their goals are in doing so.
(Edit, 2/10: Thanks for the responses, everyone. I'm in the process of writing this.)
I'm interested in heuristics for assembling or specific suggestions for a ruthless course aimed for giving a well-rounded math education (that doesn't trade thorough understanding of a diverse set of tools for better expertise in any particular area).
For example, I find the following techniques useful:
What makes specific recommendations valuable for me:
And these features make recommendations far less useful:
These are all good ideas and I would be happy to write a post in this direction.
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.
Goals: Deeper understanding of mathematics as a discipline, learning of useful formal concepts in mathematics, preferably with day-to-day applications such as probability theory.
Request: If possible, find a good balance between overly technical and overly practical presentation. Probability theory introduction usually suffer from the latter, more abstract concepts more from the former.
Useful for what purposes?
Well, I was thinking practically useful, e.g. geometry. Not general abstract nonsense.
My expertise happens to be largely concentrated in general abstract nonsense (which I think has a bad rap it doesn't deserve; to me it's the analogue of using a high-level programming language instead of a low-level one) but I'll see what I can do. It's worth mentioning that I gave the title as "(pure) mathematics..." instead of "mathematics..." because I don't have any particular expertise in applied mathematics.
Well, try this: Show how general abstract nonsense could be relevant to a rationalist in his day to day life or in his general understanding of the world. Or try an introduction to general abstract nonsense that does not leave the reader with the feeling that it is, well, general abstract nonsense.
I'm not sure about "day-to-day life", but this application of general abstract nonsense certainly did make my day better when I read it: link
So, in mathematics general abstract nonsense has a more specific meaning than this. It specifically refers to certain kinds of arguments in category theory.
That is quite amusing. Of course mathematicians have defined "general abstract nonsense" to mean something specific. :P