99jhgk$[EMAIL PROTECTED]">I'd like to think that 'intuition' is what is commonly developed by graduate students, or employed graduates who use this stuff on a regular basis. That would fit with experience educating engineers, learning theory, etc.,e tc.In article [EMAIL PROTECTED]"><[EMAIL PROTECTED]>,
Vadim Marmer <[EMAIL PROTECTED]> wrote:I have tried a number of textbooks but I still cannot find one that
combines intuition with mathematical rigour in a satisfactory way. The
best I have seen so far is 'Probability and Measure" by Billingsley,
and the last one I have tried is "Probability for Statisticians" by
Shorack which is great and provides a lot of details but too dry,
and does not care much about developing intuition .What's your favorite textbook on Probability Measure Theory?
It is verbose, but Loeve has considerable advantages.
One criticism which has been made of it is that it uses the
"cafeteria" style of theorems, namely, only the necessary
conditions are used. I consider this to be an advantage,
as special cases allow proofs which conceal the concepts.
In proving a general version of a theorem, one usually is
forced to come dowm to the essentials.
As for developing intuition, this does not seem to be done
in any book on any subject.
Then I could concentrate on developing said intution as part of the student-instructor interaction in class. Whether that interaction can be expressed or developed in a textbook, a fundamentally one-way communication, might be a subject for debate.
Jay
-- Jay Warner Principal Scientist Warner Consulting, Inc. 4444 North Green Bay Road Racine, WI 53404-1216 USA
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