That's very useful, thanks!

when is b+1 prime

hey ptmx just saw that now, thanks for the effort anyways

gonna post another one in a couple minutes, gonna take some time though since i have to translate it to english

K is a subfield of a field L

V is an L-Vector space

x1,x2,...,xn (1,2,..,n are subscripts) is a generating system(i hope thats the right translation) of V as an L-Vector space


α1,α2,...,αm (1,2,..,m are subscripts) (those are alphas) is a generating system of L as a K-Vector space


show: the products αixj (i,j are subscripts) with i=1,2,...,m and j=1,2,...,n form a generating system of V as an K-Vector space

heureka and nevermind!

writing it down in another language condensed to the bare minimum kinda helped!

I doubt this will work but does anybody have a better errata list for Lang's Algebra text than the well known Berkeley one? I've found a couple of things not listed there and now have doubts about something else that is either wrong or that I don't get.

I have not seen one, but if you post or PM, I'd be glad to look at it, and I'm sure several others would also.

I actually figured out my mistake, but I may take you up on that offer if I get stuck again. Its a wonderful book, but pretty dense as i am sure you know. There are a few topics at the end that i have never learned and this still isn't exactly a text that I can breeze through,

The angles of elevation of the top H of a vetical pole HO are observed to be x and y from points P and Q due east and due south of the pole. Distance PQ = d. Show the height of the post is

d
---------------
sqrt of (cot^2 x + cot^2 y)

I'd be interested in this too.

You should be aware that when you multiply two complex numbers you multiply their modulii and add their angles (or phases). eg. multiplying by a complex number with modulii 1 (a point on the unit circle) amounts to a rotation. I struggled quite a while with complex numbers before I realized this.

i has moduli 1 and angle pi/2. So if you want a cube root of i you want a point in the plane with modulii 1 and angle 1/3 of pi/2 (mod 1/3 of 2pi). You should understand this up front and then be able to follow how this is formally happening in Wyman's solution. Wyman's formalism is much more powerful of course and allows you to solve more general problems.


PairTheBoard

Yeah this was how I did it. It's so beautiful.

Ok i have a nother one for u guys:

K is a field, n∈ with n>1, is a K-vector space

and:
:={x∈ : + ... + = 0}
:={x∈ : - + -... + = 0 }

show: and are subspaces and compute the dimension of and

1) Show 0 is in U.
2) Show that if x and y are in U, then x+y is in U.
3) Show that if x is in U, cx is also in U.

[You will have to do this both for U = U_1 and U=U_2.]

As for dimension: intuitively, there is one linear constraint here, so the dimension should be n-1. In your case, you might want to show that the dimension is n-1 by providing a basis.

For U1, a basis is {e_i-e_(i+1): i=1,2,...,n-1}
For U2, a basis is {e_i+e_(i+1): i=1,2,...,n-1}

I'll leave it to you to show that any x satisfying the linear constraint can be (uniquely) written as a linear combination of the appropriate basis vectors.

d^2 = P^2 + Q^2
P tan (x) = Q tan(y) = H

how do you do this question without guess n check

sq root of (5.25 + 3 x (sq root of 3)) = x + (sq root of y)

x+y could be:

a) 11/3
b) 9/2
c) 22/5
d) 21/4
e) 15/4

Square both sides, then match terms inside the sqrt, then see what x makes everything work.

Okay -- for solving DE's using the Frebonius method (when there is a x^n term in front of the y term) which gives me C(k-2)=f(k)C(k) in this particular example when there was a x^2 term in front of the y term [where k-2 and k are subscripts of C].

How do I solve from here?

I don't think I quite understand the method completely and might have done something wrong up until this point.

Hi forum, been lurking her for a month. Help would be appreciated.

Question from Introduction to the Economics and Mathematics of Financial Markets

Chapter 5. Problem 1.

Consider two investors who care only about the means and variances of their investments. Investor A is indifferent between portfolio 1 with expected return of 10% and stdev of 15% and portfolio 2 with expected return of 18% and stdev of 20%. Investor B is indifferent between portfolio 3 with expected return of 12% and portfolio 4 with expected return of 15%, where the stdev of portfolios 3 and 4 are the same as of portfolios 1 and 2, that is, equal to 15% and 20%, respectively. Which of the two investors would you say is more risk-averse ?

Thanks in advance

short question, are those 2 equations aquivalent?




im slightly confused by the sums

No. The second sum includes the i=j term, where the first does not.

edit: wow, actually a lot more here is totally wrong -- misread the first time. Posting something meaningful in a sec.

For notation's sake, let Q = the double sum in the 2nd eqn; i.e.
Q = (a11 * x1) + (a12*x1 + a22*x2) + (a13*x1 + a23*x2 + a33*x3) + ...
These equations say:

top
y1 = x1
y2 = x2 + (a12*x1)
y3 = x3 + (a13*x1) + (a23*x2)
y4 = ...

bottom
y1 = x1 + Q
y2 = x2 + Q
y3 = x3 + Q
y4 = ...

not sure if this deserves its own thread so i'll post it here, but i'm writing a scholarship application and would love if someone was would be willing to read it. the prompt is based around the idea of prospective research interests and i am writing about biomimetic robotics. i'd love it if someone would critique my first draft and give me an idea how to better get my point across.

it is only a 2 page application (a little under actually, still need some sort of conclusion) but it would be great to get someone scientifically literate to tell me if it makes sense.

The sum of the x and y values of one of the four ordered pairs of integers that make the following two equations true is
a) -4
b) 4
c) -7
d) 5
e) -6

The two equations:
3x^2 + 4xy - 2y^2 = 12
x^2 - 4xy + 2y^2 = 4

Add the 2 equations together, solve for x, use the originals to solve for y.