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#1 2008-08-17 05:48:18

Starschild
Guest

where to begin?

hi,
let me start saying that this is a brilliant forum. i've seen tons of interesting stuff
i am a masters student studying business economics. i've always been highly fascinated by math, and quite gifted when compared to my average class-mate... wich is not much, as my courses never had much math content :x
the next year i will be able to choose a course (named something like "mathematics applied to management and finance", the course is taken in french) and i see it as a big personal challange i want to take.
the course is obliviously above my level and the teacher is not very kind but i am highly motivated. i would like to fill the gap with self-study

the problem is that i am not sure of what i should be looking at!

i will try to translate the contents of the course (in french yikes ) so maybe you could help me making a list of what to look at:

1st and 2nd session:
real variable functions (quick review), solving the equation f(x) = 0  (numerical methods, application on Excel), multiple real variables functions.
cobb-douglas function, utility function

session 3, 4 and 5
optimization (with and without constraints). matrix calculations, simmetric matrix, hessien's matrix, lagrange's. (application on excel)
matrix of variance and co-variance, risk modeling of a portfolio.
article: reading and analyzing markowitz's "a portfolio selection"
article: reading and analyzing Stigler's "the adoption of the marginal utility theory"

session 6 and 7
integral calculus, multiple integrals
financial calcoulations with compounded rates

session 8
probabilities, the big laws of continuing probabilities, moments calculus

session 9 and 10
introduction to stochastic models. brownian movement
article: reading and analyzing Black & Scholes "the pricing of options and corporate liabilities"

what would be the contents list? could you build it as a tree? (i.e. algebra, pre-calculus, calculus, etc)

#2 2008-08-17 06:28:54

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: where to begin?

real variable functions (quick review), solving the equation f(x) = 0  (numerical methods, application on Excel), multiple real variables functions.
cobb-douglas function, utility function

This is introductory numerical analysis.  If you have a solid background in algebra and introductory calculus (even pre-calculus may be enough), you should be fine.  Familiarity with programming of some sort is probably needed as well (looks like you're using Excel mostly).

optimization (with and without constraints). matrix calculations, simmetric matrix, hessien's matrix, lagrange's. (application on excel)
matrix of variance and co-variance, risk modeling of a portfolio.

This is more advanced numerical analysis.  I would suggest having a course in linear algebra under your belt for this, as well as the above.

integral calculus, multiple integrals
financial calcoulations with compounded rates

It's hard to say, but going off the above, this looks like numerical analysis combined with integral calculus.  Typically for such, you would need two courses of single variable calculus and a course in multivariable calculus.  The "compounded rates" makes it look like there will be differential equations in there too.

probabilities, the big laws of continuing probabilities, moments calculus

This seems to be introductory continuous statistics, but based on the below it might be much deeper.  I would recommend having a good understanding of several different distributions and how to use them (Normal, Weibull, Possion are three common ones at least in engineering).  Moments calculus should not be hard to pick up on the fly, and should have been covered in earlier calculus courses.  Not sure why they are included here.

introduction to stochastic models. brownian movement

Stochastic models are a rather large area of study, and since it's the end of course I have a feeling that it is only supposed to be a brief introduction to.  You probably won't get to the meat of the subject.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2008-08-17 11:42:09

starschild
Guest

Re: where to begin?

thanks a lot!

i will try to make a list of books, could i come back when i get it to see wether i'm missing something huge?

#4 2008-08-18 04:26:30

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: where to begin?

Certainly.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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