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#71
03-31-2012, 04:43 PM
 AAABBBCCC Member Join Date: Feb 2012 Posts: 1,329

Quote:
 Originally Posted by joni308 That's right. Do you know how often this stuff appears everywhere in all areas of mathematics. Or how on Earth will you be able to get into Measure Theory later if you never took basic Probability? Apparently Harvard has a different opinion. I was looking at the Degree Requirements and it looks like there are no required courses. They give their babies full freedom to choose between Probability, Calculus, Spanish or Dancing (maybe this is an exaggeration but is it?)
Probability theory \subset Measure theory. You dont need probability theory to take measure theory. It is more the converse.
#72
03-31-2012, 04:45 PM
 AAABBBCCC Member Join Date: Feb 2012 Posts: 1,329

They actually dont teach MGF per say... E(e^(itX)) =characteristic function is a better tool.
#73
03-31-2012, 04:46 PM
 AAABBBCCC Member Join Date: Feb 2012 Posts: 1,329

Quote:
 Originally Posted by xiaoxin I was talking about stuff like beta distributions and Markov chains. Then again I agree it is pathetic if a mathematician weren't good with the stuff you mentioned.
A lot of mathematicians dont know probability theory. Trust me on this one... Even some very good mathematicians.
#74
03-31-2012, 05:34 PM
 joni308 Member CAS SOA Join Date: Jun 2011 Posts: 2,122

Quote:
 Originally Posted by AAABBBCCC Probability theory \subset Measure theory. You dont need probability theory to take measure theory. It is more the converse.
You are probably talking about advanced Prob Theory but even then none is a prerequisite of the other in the strict sense. They are just related. What I meant, however, is how and why would you expect someone to take a measure theory class if you did not think it's necessary to teach them basic probability first that considers the most basic set function, probability?
__________________
Q. What do I do next?
A. List all options. Pick one randomly. You'll almost surely be much better off this way than by following an "expert"'s advice.
#75
03-31-2012, 05:37 PM
 joni308 Member CAS SOA Join Date: Jun 2011 Posts: 2,122

Quote:
 Originally Posted by AAABBBCCC A lot of mathematicians dont know probability theory. Trust me on this one... Even some very good mathematicians.
Again, you are talking about very advanced probability or you are very generous with the term "good" let alone "very good".

I know of no serious mathematician who does not know probability.
__________________
Q. What do I do next?
A. List all options. Pick one randomly. You'll almost surely be much better off this way than by following an "expert"'s advice.
#76
03-31-2012, 06:18 PM
 MasterChief Member Join Date: Oct 2009 College: University of Chicago Posts: 243

Quote:
 Originally Posted by joni308 Again, you are talking about very advanced probability or you are very generous with the term "good" let alone "very good". I know of no serious mathematician who does not know probability.
What are you talking about you dont need to know probability theory to know measure theory. To get a deep understanding of probability theory then you will need to study measure theory. Take a look at books that math departments use to study measure theory they assume no knowledge of probability theory
#77
03-31-2012, 06:31 PM
 AAABBBCCC Member Join Date: Feb 2012 Posts: 1,329

Quote:
 Originally Posted by joni308 You are probably talking about advanced Prob Theory but even then none is a prerequisite of the other in the strict sense. They are just related. What I meant, however, is how and why would you expect someone to take a measure theory class if you did not think it's necessary to teach them basic probability first that considers the most basic set function, probability?
it is not necessary. Probabilty theory is just the study of finite measure spaces (just normalize). Measure theory studies any measurable space even ones with complex measures.
#78
03-31-2012, 06:38 PM
 deathfrombelow Member Join Date: Jul 2008 Posts: 1,622

I have a graduate degree in stats, took measure theory, phd analysis, etc., and you guys are boring the crap out of even me. Take the math "measurement" contest to mathgeekoutpost.com.
__________________
Troll the trolls.
#79
03-31-2012, 07:01 PM
 xiaoxin Member SOA Join Date: Jun 2011 Studying for C College: '11 Favorite beer: Hoegaarden Posts: 491

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P, FM, MLC, MFE, C
Econ, Stat, Finance
#80
03-31-2012, 07:10 PM
 AAABBBCCC Member Join Date: Feb 2012 Posts: 1,329

I can do better. I have directed the mathoverflow folks to this thread...

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