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Oct
31
comment Motivation behind study of martingales
Thanks to your help thus far, I guess I can now articulate my question better. How do you tell in general whether a given process will be a martingale. I mean what are the tell tale signs attached with a process that send you some strong intuitive signals and push you towards trying to understand whether there is some martingale business going on. I guess, I would like to understand at an operation level, how do you use the theory of martingales as a tool.
Oct
31
comment Motivation behind study of martingales
Thanks again. I meant no offence [:-)] -- apologize if it came across that way. I have an engg background and I was looking for an explanation which I felt maybe more suitable for someone in my position. Btw, just a final request. Do you have some other suggestions that might help me internalize martingale properties better (besides the std and correct suggestion of more practice)? I mean maybe some playful example that you are aware of where martingale is a very natural way to attack the problem. I apologize if I am being too demanding.
Oct
30
comment Motivation behind study of martingales
Thanks. This is useful
Oct
30
comment Motivation behind study of martingales
Thanks I find your answer really helpful. I think of myself as more of a theory person but I guess I need many examples to appreciate why some theory is needed I really like your answer -- it delivers the high level overview that I think I need to begin exploring some mathematical area. Just wanted to request if you know of some other big picturish motivation behind martingales which you can share? I mean suppose you are trying to get some average engg undergraduate student interested in martingales. What will be your pitch I apologize if you find this inconvenient. Thanks in advance though
Oct
30
accepted Motivation behind study of martingales
Oct
30
asked Motivation behind study of martingales
Jul
2
awarded  Curious
Mar
27
awarded  Good Question
Mar
21
comment two probability questions (related to lower bounding error probability)
@AndreNicolas Hi Andre, I am not sure I follow. Can you please elaborate a little more?
Mar
19
asked two probability questions (related to lower bounding error probability)
Apr
24
comment Basic Question about linearity of expectation
you can work out the values and see that $pr(I_j = 1) = 7/22$ in all the cases. does that help?
Apr
24
awarded  Critic
Mar
30
comment History of Conic Sections
Thanks for the book by Coolidge.
Mar
30
comment History of Conic Sections
Thanks for your response. Like you said, I am not sure if that is historically correct as it seems somewhat unnatural to my untrained mathematical senses. Assuming it is, I am wondering how earthshaking would it have been to realize that these curves can be obtained by cutting a cone. Really, WOW!
Mar
29
comment History of Conic Sections
[cont'd] Things like circles and lines were also probably once abstract. But I find ellipses, parabolas and hyperbolas fancier (and more so when I stand in 200 BC). Is there something else, that I am missing which historians of math can help with? In case I am being too demanding in which case I apologize.
Mar
29
comment History of Conic Sections
@BrentJ Thanks for your suggestion. Following your lead, I have something I need to study over the weekend I was wondering if you could suggest something else I could go through. As for the motivation part, I find the curiosity a surprising reason (one, i respectfully find myself disagreeing with). Given my limited experience with math, I have difficulties accepting that a mathematician will cut a cone (why just cone, go cut up some more fancy objects) and then study the figures obtained. I agree that they do create abstract objects.
Mar
29
asked History of Conic Sections
Jun
13
awarded  Popular Question
Jan
12
awarded  Teacher
Jan
12
revised How many ways can $b$ balls be distributed in $c$ containers with no more than $n$ balls in any given container?
made some corrections