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This is a rather nice question that involves proving the irrationality of e and pi without the usual proof by contradiction. (a) Show that y=1+x/[(1!*a)]+(x^2)/[a(a+1)*2!]+... satisfies the differential equation xy''+ay'=y (b) Hence or otherwise, show that y/y' is irrational (c) Show that...

I'm doing a Commerce/Science degree majoring in actuarial studies and math but I'm concerned that this degree does no provide enough training in business related fields, with too much focus on maths (I enjoy maths, but am concerned that it doesnt lead anywhere in business) which may impact...

Im doing the B.Commerce/B.Science degree at UNSW, with the intention of majoring in actuarial studies and mathematics. However, I dont really like the recommended program that is on the unsw math department website for first year. I was wondering whether i am allowed switch the courses, MATH1081...

Hello Ive been giving my choice of preferences a great deal of thought lately, but cannot really decide on which course to place first; I really enjoy, and am decent at doing math and am considering a course in actuarial studies. Im not sure about whether to choose Macq or UNSW. I also heard of...

Let F₀(x)=x, and for each positive integer k, F_k(x)=k[∫₀^x(F_k-1(t)dt+x∫₀^-1(F_k-1(t)dt)] Prove that for each positive integer k, (a) F_k(-1)=F_k(0)=0 (b) Use induction to prove that (i)...

This is kinda off-syllabus, but i was wondering how one would go about this problem: (a) Let A be a 3x3 non-singular matrix, and I be the 3x3 identity matrix. Show that: det(A^-1-xI)=[-x³/det(A)][det(A-x^-1I)] (b) Let A= 0 1 0...

Anyone here take JLPT today? I took level 3.....stuffed choukai and bunpou (as expected...)........hopefully i can scrape a pass.....~.~ how did everyone else go?