Thank you for the references, Cuchulainn. I have followed those up and added them to the "queue". I agree that MT itself rarely gets a look-in directly into C++ implementations, but it is surely implicit in the theory of modern probability and numerical methods, which is being implemented.Nice trefoil!

DCH, I think Paul is saying that you are being naive in your assumptions about why people write books.Think about their incentives, unless you are Hull writing for a general readership, is it in your interests to simplify the subject?Or is it more beneficial to you professionally and financially to make it seem as arcane and difficult as possible?I get the impression from most of the textbooks that someone has delivered a lecture course for a few years, have got their lecture notes hammered into shape and decide to publish them for a bit of name recognitionThe more people pick up the book, flick through it and swear under their breath about how difficult it looks the betterI don't think they're worried about sales of the book because it's a small field in the grand scheme of things so even if the book is a relatived 'success'they won't sell many copiesMark Joshi wrote a very 'successful' introductory book (a good one too imo) but he calculated it came out at less than minimum wage for the time he put inEven if you get a couple of quid per copy, how many copies are sold? A few thousand maybe (if you're lucky)It's more important to be able to say you published the book, and then claim it's the 'standard text' in that areaAnd write it in a such a way that the other mathematicians won't look down on you at the Christmas party.The point about 'filler' is very relevant, you'll discover when you start researching any area of finance such as term structure models that when you readthe dissertations from Fin Math students, that they all start off the same way, the first 30 or so pages is the same waffle about sigma algebras, filtrations etcI've even seen Phd theses which derive BS using Ito. That's madness, imagine a Phd in numerical analysis or fluid dynamics describing the chain ruleAt some point you have to be able to take the standard results as given, and concentrate on when they're appropriateFiltrations etc are just a straightfoward case of a barrier to entry imo. Economics 101 really.

QuoteMT [..] is surely implicit in [..] numerical methodsUnfortunately, no. Take any book on numerical methods, I bet you will not find anything on MT. Even in the approximation of SDEs using finite differences no mention of MT is needed/used, but rather random variables which contains measure implicitly. In fact, most numerical methods use the Riemann integral.The books by 1) Bharucha-Reid 2) Tsokos/Padgett on Random equations I like because their methods are computable (they use a branch of maths called Functional Analysis) and nowhere is the word 'measure' to be found in the index. BTW I find FA much more practical than MT because you can do so much with it. In other areas as well, like engineering and industry I can tell you for a fact that MT is also not a job prerequisite.hth

QuoteTake any book on numerical methods, I bet you will not find anything on MT. How much do you want to bet?Quote ...no mention of MT is needed/used, but rather random variables which contains measure implicitly. My point precisely!

hmmm, I was expecting a bit more depth It is not a Christmas pantomine.

QuoteOriginally posted by: TinManDCH, I think Paul is saying that you are being naive in your assumptions about why people write books.Gosh, you're a pretty good mindreader! Next time I lose something, I might employ your psychic skills ;-)QuoteThink about their incentives, unless you are Hull writing for a general readership, is it in your interests to simplify the subject?Or is it more beneficial to you professionally and financially to make it seem as arcane and difficult as possible?I get the impression from most of the textbooks that someone has delivered a lecture course for a few years, have got their lecture notes hammered into shape and decide to publish them for a bit of name recognitionThe more people pick up the book, flick through it and swear under their breath about how difficult it looks the betterWhile what you say maybe true in a few rare cases (i.e. writers deliberately obfuscating), I think there is a much more widespread problem which has the same effects. This is the problem of not being able to communicate properly, despite a desire to do so. In fact to communicate difficult subjects like mathematics well seems to be a very rare skill. Many books suffer because either:i) The writer is mentally unable to put themselves into the shoes of someone who is new to a subject (and thereby able to formulate text which is meaningful to such persons).ii) Writers are too used to delivering their work to other specialists.iii) They don't take enough time or effort to explain fundamental principles properly.iv) They don't lay out their arguments in a coherent or presentable manner....(this list could be added to)It's a sad fact that mathematicians don't have the best reputation when it comes to communication skills. The maths book that it an exemplary tome of clarity of exposition is certainly the exception not the rule. Mathematics can be presented in pictures, numbers, words and symbols and yet it is another sad fact that the first two of these are so frequently dispensed with in "advanced" books. The more "advanced" the mathematics book gets, the worse the problem gets. The mathematician is often so keen to get everything right and all the technical details correct that she so often forgets her audience.

I still think you're being naive, I don't think it's a problem of communication, it's a problem of motivation.There's an apt quote in Brigo & Mercurio:"Our paper became a monograph. When we had completed the details, werewrote everything so that no one could tell how we came upon our ideasor why. This is the standard in mathematics." -- David Berlinski, "Black Mischief" (1988)

I think we're in agreement here, really. Here's a quote to match yours from an excellent textbook on linear algebra by Carl Meyer, which has a picture of an egyptian needle covered in scaffolding on the front cover:Quote"Scaffolding. Reacting to criticism concerning the lack of motivation in his writings Gauss remarked that achitects of great cathedrals do not obscure the beauty of their work by leaving the scaffolding in place after the construction has been completed. His philosphy epitomized the formal presentation and teaching of mathematics throughout the nineteenth and twentieth centuries, and it is still found in mid-to-upper-level mathematics textbooks. The inherent efficiency and natural beauty of mathematics are compromised by strying too far from Gauss's viewpoint. But, as with most things in life, appreciation is generally preceded by some understanding seasoned with a bit of maturity, and in mathematics this comes from seeing some of the scaffolding."silenoz said that Shreve has a clear discussion on filtrations and picking Shreve up again I find I agree. Here we have an author who is clear in their discussion, and who leaves a lot of the scaffolding in place. Paul I presume is suggesting that writers put MT in unnecessarily (and you would say deliberately for academic kudos), but that doesn't mean that it is entirely redundant - it means that MT is itself scaffolding to supporting arguments. You could view this stuff as unnecessary, but if you understand it, it might actually help, and in some situations it might actually be needed.

Polya, how to solve it

We all have to relax, sometimes so here is a lighter post from me. It's about scaffolds and a castle. Good analogy?QuoteHiding a needle in a haystack is easy enough.But Robert Fidler kept something much bigger concealed among the piles of straw down on his farm... a castle. Hay presto! Farmer unveils the 'illegal' mock-Tudor castle he tried to hide behind 40ft hay bales

QuoteOriginally posted by: silenozShreve explains the ideas quite nice in his book "Stochastic calculus for finance II".I'm a student in financial math as well and this book is brillant. It's good mix of intuition and technical details.