QuoteOriginally posted by: albertmillsQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: PaulQuoteOriginally posted by: CuchulainnMathematics is not a science IMO, but it is historically a part of Philosophy.Yes. And it's not easy to be a mathematician unless you did maths as an undergrad degree, and in your youth.PAbsolutey.They say that one is best (original) at 24/25, then it is downhill after that.It is mind-boggling doing a MSc/MFE and not having this mathematical background, e.g. measure theory ... I did group theory at school when 17 (using Arnold analogy of geometric transformation, not Bourbaki); my teacher has a PhD from Uni London in number theory) but learing this stuff when in one's 30's ++ is painful. The brain cells just can't handle the abstraction, anymore. It is possible to do Fourier series and Laplace transforms well into your 60's.years ago i got into a good MFE program. I was preparing myself for the program by reading the recommended book on stochastic calculus by shreve (including measure theory) in finance...it was very rough going for someone who had a technical background, but had never seen that kind of math before, and was working a full time job. I did well in my math classes at school, but they had hadn't covered this.You are not the first person to have aired such views on this topic. If we take the SDE as the middle ground to understand initially then the prerequisites IMO are nothing less than measure, Lebesgue, (functional) analysis and probability, even some PDE otherwise the symbols mean nothing. Having got to SDE, then the applicatons get discussed but much of the theory tends to be devoid of hands-on examples. Not having numerical methods and computational approach certainly does not help. At the end of the day it's about number-crunching I suppose.I am not in academia, but is seems to me that the cart is being put before the horse. It's cruel. And kind of ad-hoc. //Even, how do you compute a Lebesque integral approximately, similar to Riemann.
Last edited by Cuchulainn
on January 12th, 2014, 11:00 pm, edited 1 time in total.