bloodhound

ill just do the given question for an example we have F(x,y,z,lamda)=x^2+y^2+z^2 - lamda*(x^2-yz-5) finding the four partial derivatives and equating them to 0 we get 4 simultaneous equations. 2x-2lambda*x=0 which gives us lambda = 1 partial dev wrt y gives us 2y+lambda*z=0 since lambda = 1 we get 2y+z=0 partial dev wrt z gives us 2z+lambda*y=0 since lambda = 1 we get 2z+y=0 therefore from the last two equations , the only solution is y=0,z=0 Now, Partial Dev wrt lambda gives us 5-x^2=0 which gives us x=plus.minus(sqrt(5)) Therefore (x,y,z)=(+-sqrt(5),0,0) minimises the distance from the origin given =0 But if we look at x^2+y^2+z^2 we see that its nonnegative and not bounded above there fore the points(+-sqrt(5),0,0) minimises the distance

Hi, me and my mate were talking about uni and stuff. he does computer science at imperial. and this came up. its the famous eight queen problem "All you have to do is put eight queens on a chess board so that none of them are attacking each other." sounds easy rite. but believe me, i can manage only 7. apparently he had to write a program to find a solution to this problem. and yes there are solutions. So now, I dont want anyone to cheat or look it up on the web. I would just like to know how a mathematician would go about solving this. I was thinking about using matrices. a 8by8 matrice. but then i dont know what to do with it. anyway if anyone can find a solution, post it. and tell us how u went about finding it. cheers. ill have more go at it.

for general questions like this, u can use the method of lagrange multipliers. basically if u are given a function f and u have to minimise or maximise the value of f given a condition that another function g=0 then if u form another function F(x,y,z,lamda)=f(x,y,z)-lamda*g(x,y,z) and then u find the partial derivatives , Fx,Fy,Fz,Flamnda, and solve Fx=Fy=Fz=Flamnda=0 , then those values of (x,y,z) will minimise the value of f(x,y,z) with the condition that g(x,y,z)=0 In this case we are minimising (x^2+y^2+z^2)^(1/2) which is the same as minimising(x^2+y^2+z^2) set that = f(x,y,z) . also we are given the condition that g(x,y,z)=x^2-yz-5=0 now take F(x,y,z,lamda)=f(x,y,z)-lamda*g(x,y,z) =x^2+y^2+z^2 - lamda*(x^2-yz-5) so now find all the partial derivatives. equate them to 0 and solve them. that is ur values which will minimise ur function This method can be applied to function of as many variables as u like with as many conditions eg. minimise f(r,s,t,v) given g(r,s,t,v)=0 and h(r,s,t,v)=0 u create F(r,s,t,v,lambda, mu)=f(r,s,t,v)-lambda*g(r,s,t,v) - mu*h(r,s,t,v) u find the partial derivatives of F w.r.t r,s,t,v, lambda and mu and equate them to 0 and solve them. Those valuesof (r,s,t,v) minimises or maximises the function f(r,s,t,v) and so it can be extended to functions of as many variables as u like

dont know about MatLab but Maple is Wicked

well, for me maths and sciences were easy. but they way they teach english and other subjects here are totally different. I just managed to get a C is english language and another C is literature. Apparently thats whats need to be able to do a levels

do u have to use maple. and have u got it?

ok. ill have a go then.

yeah. same here. analysis is wicked. followed probably by calculus

so whos gonna give em the word

so whats ur fav module rite now then

so whos the main man round here?

try textpad. http://www.textpad.com . its really good. really simple. opens as quick as notepad. has compiler. can write java etc etc . download it .

lol. i am from nepal. but came here in 1999. done gcses and a level here. good thing. cos the SLC which is similar to GCSE here. is way way way harder, and i was lucky not to have done it

is that a bad thing sayonara?

Its new year in nepal rite now. year 2061. we are way ahead of u guys. hehe

gravity wouldn't be affected as gravitational field depends on the mass of the object. on the other hand it also depends on the distance from the centre of mass so if u walk on the now empty oceans then probably u would observe a slightly(tiny tiny tiny) increase in the gravitational force.

Everyone. lets get on the bandwagon while its going. Can i seel my story to a tabloid for 200,000 quid?

or just create new subforums like. Analytical Mathematics := i presume it would involve calculus, number theory, abstract algebra and Practical Mathematics: probably Stats and geometry

usually when i want to print some proper mathematics, i just use mathtype , save it as an image. upload it to my ftp and link it to the post. saves all this syntax nonsense

once u get into larger numbers. the proof by contradiction that they are irrational of rational gets quite confusing. you have to use the fact that any number can be expressed as multiple or prime numbers. and this combination is unique. i am still quite baffled. have to revise really badly

i hope i wont have to do any essays. are u doing a MMath course? apparently the whole 4th year we spend doing a thesis. phew. ill probably do it the night before

the reason its quicker is that the error involved decreases as a square rather than linearly in the other method. we havent been introduced properly wolfson:)

i am too lazy to work it out myself. someone do it for me

Toshiba Sattelite A30 2.3Ghz 512MB RAM 64MB integrated graphics 40 Gigs 15"TFT CDRW/DVD Wireless PCMCIA card. Sony Vaio Desktop AMD athlon 2200+ 256 ram g4 mb gforce 4 MX460 a cdrw and a dvd bay 40GB

yeah. its pretty relaxed. love it. i think the second year goin to be tough.