Introduction

I am currently working on an emergency license for math. I am trying to pass the Math Praxis 0061 to receive my certification. Need some help on some of the questions.

Thanks,
karies4083

Hi! I am relatively new as well - what is an emergency license for maths? I have never heard of it, but it sounds kind of unusual!

I am a teacher working on an additional licensure. .. . I am currently certified to teach in one area .. and working on another subject area.

Hope this helps

Oh I see - well good luck with it!

Dear team
Good afternoon.....
recently i have completed my BBA>.
now am planning for IAS officer..
so here i just want to clear my all concept of Maths

Well, the only way we can help is if you post specific problems. What kind of problems do you have difficulty with?

Hello, I have graduated from math -uhm- maybe 20 years ago and now, after some turmoil in ICT field, I have scrubbing a job from here and there (part time teaching and re-warming the research career.)

My current problem is this: Given a unit hypersphere S_3 (in R^4) and four normalized vectors n1,n2,n3,n4 (ni<>nj), how to calculate the -uhm- space angle defined by the vectors (subvolume of the sphere)?

I am familiar of the normal unit sphere S_2 which have a space angle Phi defined by 3 vectors n1,n2,n3 as: Phi= a12+a23+a31 -pi where a_{ij} = cos^{-1}(ni . nj). (E.g. the familiar rectangular corner slice of the sphere which has the area Phi = 3 pi/2 -pi = 4pi / 8 .)

Is there a nice equation for S_3 case? Preferably one using a_{ij} angles. Or a recursive one? Actually my hunger goes up to S_11 (12 vectors in R^12), so I need references if the problem is
not trivial. The intended use is non-commercial, so I am not trying to milk you for my profit.

Problem (almost) solved. I stumbled upon Heinz Hopf, Selected Chapters of Geometry, 1940, which answers my problem with the first incoming breeze. (Let's see if the computation is too expensive next... And I had a mistake in the definition of cos -terms, have to snip away the components along nk from ni and nj... )