A review of probability theory(terrytao.wordpress.com)
terrytao.wordpress.com
A review of probability theory
http://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/
3 comments
Well, the hacker news feature a lot of programming-related stuff that is certainly 'above' the (average) blog post level (in the whole blogosphere). I know of no better meta-filter than hacker news for blog entries attracting a hacker's mindset. Certainly, the appreciation for mathematical thinking as well as mathematical methods plays a big role in this (analytic) mind set.
While the novice programmer might not get (the content and purpose of) python vs. ruby comparisons and the like, readers with a weak background in math will not find this probability entry useful (or too 'difficult').
However, for a certain subset of all hacker news readers, which are looking to dig deeper, it is a very nice resource.
Hacker news, to me, is especially useful since it provides links which are well distributed in terms of this 'entry level'.
While the novice programmer might not get (the content and purpose of) python vs. ruby comparisons and the like, readers with a weak background in math will not find this probability entry useful (or too 'difficult').
However, for a certain subset of all hacker news readers, which are looking to dig deeper, it is a very nice resource.
Hacker news, to me, is especially useful since it provides links which are well distributed in terms of this 'entry level'.
I think a better way is needed to teach probability.
Perhaps something more visual and involving interactivity (like visual programming).
What percentage of students after having passed a probability course can define a random variable?
Perhaps something more visual and involving interactivity (like visual programming).
What percentage of students after having passed a probability course can define a random variable?
> What percentage of students after having passed a probability course can define a random variable?
In a typical probability theory course, all of them, hopefully. I found random variables to be a crucial part of my probability theory class, being used in almost all (if not all) topics after the first month.
There are certainly other approaches to learning probability theory (though perhaps not what you were thinking.) I understand that E.T. Jaynes' book on probability theory, which I have not yet read, does not go the route of random variables.
In a typical probability theory course, all of them, hopefully. I found random variables to be a crucial part of my probability theory class, being used in almost all (if not all) topics after the first month.
There are certainly other approaches to learning probability theory (though perhaps not what you were thinking.) I understand that E.T. Jaynes' book on probability theory, which I have not yet read, does not go the route of random variables.
Students can still solve many sorts of problems without a good understanding of foundations.
They may use random variables frequently without being able to define them.
They may use random variables frequently without being able to define them.
I understand that E.T. Jaynes' book on probability theory, which I have not yet read, does not go the route of random variables.
Jaynes' book is excellent but is more about the philosophy of the Bayesian interpretation of probability than mathematics.
His problem with "random variables" is not so much the concept (although he wasn't a fan of measure theory), but the "random" in the name.
Jaynes' book is excellent but is more about the philosophy of the Bayesian interpretation of probability than mathematics.
His problem with "random variables" is not so much the concept (although he wasn't a fan of measure theory), but the "random" in the name.
A better question would be: what percentage understand what a random variable is and will be able to apply this understanding later. See http://www.youtube.com/watch?v=WwslBPj8GgI for exploration of the difference by a Harvard physics professor who realized a few years into his teaching career that most of his into physics students weren't learning very much, although they were able to apply all the appropriate mathematical recipes to all the standard type homework and exam questions.
I think your point is true when it comes to teaching introductory probability or perhaps even a second and third course in probability. However, at some point, it becomes necessary to dive into things formally.
This blog entry is meant for a review for a graduate level course, so it makes sense that it runs through a lot of formal definitions.
This blog entry is meant for a review for a graduate level course, so it makes sense that it runs through a lot of formal definitions.
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I was able to read only part 1: Foundations, and these are my impressions. Definitely goes into my Bookmarks, so that I can read the rest...
Edit: The title was changed from "Probability Theory 101 (by Fields medallist Terry Tao)".