MandrakeRoot

I think this system has been abandoned a long time ago. Like degrees, they are not used in scientific circles. Mandrake

The best beginning is maybe to simply follow some advanced courses. Once you are into the way of thinking you will easily learn new stuff. IT is surely worth putting lots of effort in in the beginning i think. Mandrake

Yeah i think the beginning would be the most hard with maths. Once you get the hang of it, it is easy to self study and continue improving your skills. But if you have never seen a definition, theorem or lemma of your life and dont know what is the difference then it would be quite a challenge to learn that alone. I would say that it is not impossible but you need some serious perseverence !! => What is the best text book is also quite ambiguous, what one finds a great book others dont like it at all. I personally hate books with lots of exemples, but not everybody would think the same way. Why not study the philosophy of mathematics early on ? I dont see any harm in that, though the "reasons why it is like so" might escape you if you never did a lot of math i guess ? Mandrake

It is the equation that does the trick. [math]x^2 + y^2 = 1[/math] is a nice circle right ? [math]x^2 + y^2 + z^2= 1[/math] would be a ball So well [math]\sum_{i=1}^n x_i^2= 1[/math] would be the n-dimensional ball (hyperball if you like). Mandrake

There are at least infinitely many solutions. Try fixing y to a real number and solving for z complex. You will see that almost all the complex axis is a solution (parametrized by y) except for a small part in the center of it. Mandrake

That is not really a valid reason now is it ? That reminds me an old post of some guy that cracked his neck so hard that he felt a tingling sensation in his body for several minutes. If you would come to that point it is better to stop => Better a soft nutter than a hard nutter in a wheelchair right ? Mandrake

I think sex was always practices like crazy, why do you think we are 6 miljard now I think most healthy people can pretty much control their sex drive. The sex drive doesnt seem to be at the same level as eating or drinking i would say ? Why would the sexual pattern evolve over time when it seems to work for what it is for : reproduce ? Mandrake

I have no idea if they do it for real or not, though the image seems pretty commonplace. I dont think that cracking your knuckles will do all that much harm. Why do you want to crack your neck ? If it doesnt naturally why do it ? Mandrake

I used to crack my fingers but stopped doing it. It is pretty hard to stop since the first couple of days you have the feeling having lost flexibiilty. This feeling goes away after some days though. Since most parts of the body seem to crack naturally i dont think there is any harm in cracking your knuckles deliberately either. Though without proper research there is no way of being sure and why take the risk ? Mandrake

ah ok then. Mandrake

Or discrete with infinite (but countable) values, needing infinite sums. Mandrake

I think the trick behind it is confusing conditional probability with probability. In this example the probability of being gay knowing you are black is not the same as when you are white. 5% of the workforce hired is gay which reflect the community proportion. => the company constituted its workforce using conditional probabilities; The complaints are done not using the non-conditional probablities. Hence the difference. Ergo the complaints are not grounded. What kind of exercise is this anyway ? Mandrake

Sum of probabilities should be one. Since you have only 6 possible values for x the equation you have to solve is : k + 4k + 9k + k(7 - 4)^2 + k(7 - 5)^2 + k(7 - 6)^2 = 1 which would be 28k = 1, making k = 1/28 Mandrake

To whom are you wondering that ? Mandrake

Yeah but it is whole theory more general than just FMT. The FMT is just a consequence of whole the theory set up by the guy. There are actually people understanding all of this theory since they pointed out an error in the original reasoning and helped to repair it. In any case it is not like on the first page you see proof : and then 250 pages further you see QED or something like that. It is an entire theory with many results. Mandrake If i remember correctly it was Andrew Wiles who proved FMT in 1994 and corrected his proof in 1995.

Maybe a complex circle ? It is rather hard to imagine such higher dimensional circles and it depends on what you call a circle too. In any case there are no real solutions and many many complex ones. You could for exemple assume that y is real and z is complex and let y parametrize z. You will find that the solutions of your equation are situated on the imaginary axis covering almost all except for the part in between -i and i. You could decompose y and z in imaginary and real parts and obtain 2 (non linear) equations with 4 variables. The thing is you need 4 dimensions to show the collection of all points satisfying your equation. Mandrake

It will probably take more time than that Mandrake

I would say that the problem of doing someones exercises for them would be that they learn nothing. The whole point of such exercises (as the one above) is to get comfortable with definitions and simple application of such definitions. Mandrake

What kind of questions ? You could try to prove Riemann's hypothesis. It will keep you occupied for quite some time Mandrake

How about routing schedules, shortest path determination etc.... This is often used in computer games such as the war games (C&C stuff, whatever). It could allow you to implement a simple AI and stuff like that. Mathematicians rarely use numbers in fact. You will be surprised to see how much you can do without once using a number Mandrake

You havent defined P and an infinite sum is a limit of the partial sums by definition. Since for what i understood of your argument you were using the fact that polynomials are continuous, writing a function f as an infinite sum (a power series) and then taking the limit and wanting to apply your argumentation would involve interchanging two limits. Or the use of arguments of the type that you can get the tail uniformly small or whatever. Mandrake

I think the easiest way is to use the inverse function theorem like says dave. Show that the functions sine etc. satisfy the requirements and conclude that the functions arcsine etc are also continuous. Joe => It is impossible to use the derivatives of the arcsine functions to show continuity since they can only exists if your functions is continuous, making your arguementation circular. Gauss => A taylor series is not a polynomial ! showing that polynomials are continuous is easily done using epsilon-delta definition. But your step 3 involves changing two limits ! (that of the partial sums and that of x tending to c) which can be rather tricky.... Mandrake

Say the second question, why dont you arrive to solve it ? Tell me what you tried to do in order to find the solution and maybe someone can help you find out what is missing in your argumentation ? Mandrake