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XiXiDu comments on What math is essential to the art of rationality? - Less Wrong
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Comments (62)
I am not sure about the prerequisites you need for "rationality" but take a look at the following courses:
(1) Schaum's Outline of Probability, Random Variables, and Random Processes:
(2) udacity's Intro to Artificial Intelligence:
(3) udacity's Machine Learning: Supervised Learning :
My suggestion is to use khanacademy.org in the following order: Precalculus->Differential calculus->Integral calculus->Linear Algebra->Multivariable calculus->Differential equations->Probability->Statistics.
If you prefer books:
Statistics comes last, here is why. Take for example the proof of minimizing squared error to regression line. You will at least need to understand how to solve partial derivatives and systems of equations.
(Note: Books 4-7 are based on my personal research on what to read. I haven't personally read those particular books yet. But they are praised a lot and relatively cheap and concise.)
Jaynes Draft of "Probability Theory:The Logic of Science". http://www-biba.inrialpes.fr/Jaynes/prob.html
Bretthorst's slightly edited version. http://thiqaruni.org/mathpdf9/(86).pdf
EDIT: If anyone knows how to fix that link, please ping me with a solution.
Although the link is broken, the file doesn't exist anymore. According to comments here Jaynes' publishers took the book down. For your edification, one would normally escape parentheses with "URL encoding" by replacing the opening parenthesis with %28 and the closing parenthesis with %29.
http://thiqaruni.org/mathpdf9/(86).pdf
That seems rather tedious for blog comments.
Why doesn't \ work as an escape character here?
This section in the FAQ about escapes and links just doesn't seem to work as advertised: http://wiki.lesswrong.com/wiki/FAQ#How_do_I_make_a_comment.3F
http://thiqaruni.org/mathpdf9/\(86\).pdf
http://thiqaruni.org/mathpdf9/(86\).pdf
[http://thiqaruni.org/mathpdf9/(86\).pdf] ( http://thiqaruni.org/mathpdf9/(86\).pdf)
Maybe if I put some text in between? The first one below is the same as the previous one above, where the text and url have a carriage return between them. The second removes the carriage return so it is all on one line. The third removes the backslash in the url portion.
[http://thiqaruni.org/mathpdf9/(86\).pdf] ( http://thiqaruni.org/mathpdf9/(86\).pdf)
<http://thiqaruni.org/mathpdf9/(86\>).pdf.pdf)
<http://thiqaruni.org/mathpdf9/(86>).pdf.pdf)
Yes, that does seem to work for me. I think you must be typing it wrong somehow. Or it's some crazy bug.
Edit: I see, the problem is when it looks for links to automatically promote them if you don't use Markdown syntax. I guess escaping the parenthesis doesn't work there.
Should look like this:
http://thiqaruni.org/mathpdf9/(86).pdf
You don't actually have to escape the close parenthesis in the "link text" park of the Markdown (in square brackets), only in the URL part (in parentheses).
Thank you. Having a ready made "course sequence" that I can then adapt, is really helpful.
I appreciate having Khan academy for looking up math concept that on which I need a refresher, but I've heard (or maybe just assumed?) that the higher level teaching was a bit mediocre. You disagree? I'm fully prepared to update on the estimates of people here.
What's the value of taking classes in math vs. teaching myself (or maybe teaching myself with the occasional help of a tutor)?
Comparing Khan Academy's linear algebra course to the free book that I recommended, I believe that Khan Academy will be more difficult to understand if you don't already have some background knowledge of linear algebra. This is not true for the calculus course though. Comparing both calculus and linear algebra to the books I recommend, I believe that Khan Academy only provides a rough sketch of the topics with much less rigor than can be found in books.
Regarding the quality of Khan Academy. I believe it is varying between excellent and mediocre. But I haven't read enough rigorous material to judge this confidently.
The advantage of Khan Academy is that you get a quick and useful overview. There are books that are also concise and provide an overview, often in the form of so called lecture notes. But they are incredible difficult to understand (assume a lot of prerequisites).
As a more rigorous alternative to Khan Academy try coursera.org.
I've never visited a class or got the help of a tutor. I think you can do just fine without one if you use Google and test your knowledge by buying solved problem books. There are a lot of such books:
Some massive open online courses now offer personal tutors if you pay a monthly fee. udacity.com is one example here.
I also want to add the following recommendations to my original sequence, since you specifically asked about Bayesian statistics:
Thanks!