sci4um.com Undergraduate Forum

Undergraduate :: Business Stats II

Author: LMG
Subject: Business Stats II
Posted: Wed Aug 16, 2006 4:45 pm (GMT 0)
Topic Replies: 0

I am in need of some help with this question. I had a three-fold question and figured out the other two parts but couldn't figure this one out. Please help!! "When we discuss tests like Goodness of Fit, Independence, ANOV, why are other distributions introduced?"

Undergraduate :: Curve integral - correct or not?

Author: Daniel Nierro
Subject: Curve integral - correct or not?
Posted: Thu Jul 20, 2006 2:47 pm (GMT 0)
Topic Replies: 2

Hi!
If one would like to calculate the curve integral of the function f(x,y,z) =
x^2 + y^2 over the curve C: r(t) = (e^t cos(t), e^t sin(t), t) where t goes
from 0 to 1, what would the result be?
The curve is clearly somewhat spiral-shaped with a radius increasing with t,
and the problem should be easily solvable using cylindrical coordinates.
I'm wondering, does e^(2t) sqrt(e^(2t) + 1) sound like a reasonable answer?

Cheers,
Doug

Undergraduate :: A Combinatorics/Graph Theory Question

Author: mathlover
Subject: A Combinatorics/Graph Theory Question
Posted: Wed Jul 19, 2006 11:30 pm (GMT 0)
Topic Replies: 1

Hi every body,

There is a problem I have exposed to but, though being badly in need of
an answer, I have not yet been able to solve it. I am not quite sure if
it is better classified as a graph theory problem or a combinatorial
one; anyway, here is the problem:

Assume we have a bipartite graph with X and Y as its two parts. X has
"n" vertices and Y has C(k,n) vertices where "k" is a natural number
less than "n" and by C(k,n) I denote the number of k-element subsets of
an n-element set. The edges of the graph are formed as below: we
correspond each k-element subset of X with a vertex in Y and put an
edge between that vertex of Y and each member of the corresponding
k-element subset of X.

Now it is clear that for every vertex of X there are C(k-1, n-1)
vertices in Y that have an edge to that vertex. That is every vertex in
X has exactly C(k-1, n-1) number of neighbors in Y. Now the problem is
as follows: assuming "r" is a natural number not larger than C(k-1,
n-1) (I am specially interested in the case r=2) determine the minimum
number "p" (or at least a non-trivial upper bound on it) such that for
every p-element subset, like S, of Y the following property holds: for
every node in X, like "v", it has at least "r" neighbors which are
members of S.

Any help or clues are greatly appreciated.

Thanks.

Undergraduate :: Math Help Available

Author: at361@yahoo.com
Subject: Math Help Available
Posted: Wed Jul 19, 2006 8:44 pm (GMT 0)
Topic Replies: 0

we're a group of mathematics graduates who have tutored,
taught,provided math help and researched in mathematics at various
levels and in different parts of the world.
We've formed this tutoring/consulting service mainly for the purpose of
solving university problems (homework assignments/specific questions),
but we're also open to general problems that may arise in other fields.

At the present time we can provide math help in :

* calculus
* vector calculus
* integral calculus
* rings/fields
* group theory
* discrete math
* lie groups
* linear algebra
* complex analysis
* basic statistics

GOTO
www.angelfire.com/biz/mathconsultants

Undergraduate :: jordan decomposition and generalized eigenvectors

Author: Jeremy Watts
Subject: jordan decomposition and generalized eigenvectors
Posted: Tue Jul 18, 2006 6:49 pm (GMT 0)
Topic Replies: 0

ok, firstly excuse the length of this post and the fact that it is cross
posted.... (i really didnt know the most appropriate NG to send it to....)

anyway, i am using an algorithm to perform a jordan decomposition taken from
'schaums outlines for matrix operations'. the algorithm states on p.82 that
to form a canonical basis (this being the first step in forming a jordan
decomposition) , then :-

Step 1. Denote the multiplicity of lambda as m , and determine the
smallest positive integer p for which the rank of (A - lambda I )^p equals
n-m , where n denotes the number of rows (and columns in A), lambda denotes
an eigenvalue of A and I is the identity matrix.

Step 2. For each integer k between 1 and p, inclusive, compute the
'eigenvalue rank number Nk' as :-
Nk = rank(A - lambda I)^(k-1) - rank(A - lambdaI)^k
Each Nk is the number of generalized eigenvectors of rank k that will appear
in the canonical basis

Step 3. Determine a generalized eigenvector of rank p, and construct the
chain generated by this vector. Each of these vectors is part of the
canonical basis.

Step 4. Reduce each positive Nk (k = 1,2,...,p) by 1. If all Nk are zero
then stop; the procedure is complete for this particular eigenvalue. If not
then continue to Step 5.

Step 5. Find the highest value of k for which Nk is not zero, and determine
a generalized eigenvector of that rank which is linearly independent of all
previously determined generalized eigenvectors associated with lambda. Form
the chain generated by this vector, and include it in the basis. Return to
Step 4.

Now, the matrix I am using the above procedure on is :-

0 0 1 0 i
0 -9+6i 0 1 0
A = 0 0 8 i 1
0 0 0 8 0
0 2i 0 -9 8

Now the eigenvalues and multiplicities are :-

-9+6i with multiplicity 1
8 with multiplicity 3
0 with multiplicity 1

Starting with -9+6i and going through the procedure then i make the value of
p in step 1 as p = 5. This immediately arouses my suspicions as it looks too
high, as Step 3 not only fails to find a generalized eigenvector of rank 5,
but also even if it existed, the vector plus its chain would be of length 5,
and so fill the entire canonical basis with the vectors generated by just
the first eigenvalue .

By the way I am using the definition of a 'generalized eigenvector' as the
one given in the same book, on the same page in fact as the above procedure,
which is :-

"A vector Xm is a generalized eigenvector of rank m for the square matrix A
and associated eigenvalue lambda if :-

(A - lambda I)^m Xm = 0 but (A - lambda I)^(m-1)Xm =/= 0

So, firstly does anyone agree that a generalized eigenvector of rank 5
cannot exist for the matrix A with the eigenvalue -9+6i , and if so what is
going wrong here generally?

thanks

Undergraduate :: Can you count?

Author: Alexander Blessing
Subject: Can you count?
Posted: Tue Jul 18, 2006 4:03 pm (GMT 0)
Topic Replies: 5

Let n denote the number of digits of a natural number.
Now, how many natural numbers with n digits are there which contain all
digits from 0 to 9 in their 10-adic expansion?

Any idea guys?

Undergraduate :: NEED HELP ONCE AGAIN

Author: Missy
Subject: NEED HELP ONCE AGAIN
Posted: Sun Jul 16, 2006 2:16 am (GMT 0)
Topic Replies: 5

Please help I need to know how to solve each of the following
step-by-step:

1. Daria can wash and detail 3 cars in 2 hours. Larry can wash and
detail the same 3 cars in
1.5 hours. About how long will it take to wash and detail the 3
cars if Daria and Larry worked
together?

2. 100 people will attend the theatre if tickets cost $40 each. For
each $5 increase in price, 10
fewer people will attend. what price will deliver the maximum
dollar sales?

3. How many 3-person groups can be formed in a club with 8 people?

Undergraduate :: Finite # of subgroups -> Finite group

Author: tppytel@gmail.com
Subject: Finite # of subgroups -> Finite group
Posted: Sun Jul 16, 2006 1:47 am (GMT 0)
Topic Replies: 9

Hello,

I'm working my way through some group theory on my own, and was looking
for advice on the following proof. I think my approach works, but it
seems like there must be an easier way. This problem is in the chapter
of the text on cyclic subgroups, so that's what I'm trying to use.

Given: Group G with a finite number of subgroups
Prove: Group G is finite

I will prove the contrapositive - if G is infinite, then we can
generate an infinite number of distinct subgroups from it.

Choose a in G where a != e. (G is infinite, so this a must exist.)

Quote:

From a we can construct the cyclic subgroup <a>.

Case 1: <a> is finite
(Is this case really valid? Can I get a finite cyclic subgroup other
than {e} out of an infinite group?)

Choose b in G such that b is not in <a>. This b must exist because G is
of infinite order, while <a> is finite. Then we have a new subgroup <b>
distinct from <a>. This process can be continued so long as we keep
generating finite cyclic subgroups.

Case 2: <a> is infinite
Then we can construct a new subgroup <a^2>. a is not in <a^2>, because
if it were then there would be an n in Z such that

(a^2)^n = a
a^2n = a
a^(2n-1) = e

But that would mean that <a> is finite, which is a contradiction. Thus
a is not in <a^2>, so <a^2> is distinct from <a>. By the same
reasoning, <a^3> is distinct from either <a^2> or <a>, and so on...

Therefore, from an infinite group G, we can generate an infinite number
of subgroups.
And the contrapositive also holds, that if a group G has a finite
number of subgroups, then G itself must be finite.

Valid, I think, but kind of messy. There must be an easier way...

Undergraduate :: embedding problem

Author: winshum
Subject: embedding problem
Posted: Sat Jul 15, 2006 5:24 pm (GMT 0)
Topic Replies: 0

a cylindrically symmetric manifold is described by the line element
ds^2=4e^(2ar)dr^2+r^2d@^2
now the manifold is embedded into 3-D flat space, with Euclidean coordinates x,y,z where
r=sqrt(x^2+y^2)
z=h(r)
Find a differential equation satisfied by h(r)
and also how to solve h(r)
i haven't study differential geometry and it is a problem about general relativity, could anyone gives me any ideas of this problem and also what does "Manifold" really mean? thanks!

Undergraduate :: JSH: My research, a roadmap

Author: jstevh@msn.com
Subject: JSH: My research, a roadmap
Posted: Sat Jul 15, 2006 2:04 am (GMT 0)
Topic Replies: 29

My research speaks for itself.

I have given a definition of mathematical proof:

http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html

Figured out the key properties that define rings that are like the ring
of integers:

http://mymath.blogspot.com/2005/03/object-ring.html

Found my own prime counting function, which unlike any other known
relies on summing a partial difference equation, which is also why it
finds primes on its own, unlike any other known:

http://mymath.blogspot.com/2005/06/counting-primes.html

Fighting mathematicians who have done their best to ignore my research
I wrote the first prime counting function article for the Wikipedia,
where my latest version is now found in the history of the current
page:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old...

There readers can see my prime counting function in its fully
mathematicized "pure" form, and see how it is a summation, so they can
make the leap to understanding how it relates to a partial differential
equation and an integration.

I had a paper published in a formally peer reviewed mathematical
journal--and then the editors withdrew it after sci.math pressure
against it:

http://www.emis.de/journals/SWJPAM/vol2-03.html

Link is to a site mirror as the electronic journal DIED a few months
later.

That paper covered some pioneering research advancing modular algebra
or the algebra of congruences, extending on the work started by Gauss:

http://mymath.blogspot.com/2005/07/tautological-spaces-factoring.html

Which is a line of attack I used to find a short proof of Fermat's Last
Theorem:

http://mymath.blogspot.com/2006/03/proof-of-fermats-last-theorem.html

But I've even considered problems in logic and set theory, handling
supposed contradictions:

http://mymath.blogspot.com/2005/06/three-valued-logic.html

and

http://mymath.blogspot.com/2005/05/logical-formedness-axioms.html

and

http://mymath.blogspot.com/2005/06/3-logic-more-basics.html

Even some of my minor research is significant, as I talked about a
simple way to find primes using quadratic residues:

http://mymath.blogspot.com/2006/04/method-for-quickly-finding-primes....

The only explanation given the breadth of my research, and dramatic
events like a math journal imploding after publishing then retracting a
paper of mine is that it is so huge that mathematicians who are living
in a political society today--where their word is more important than
their research--are fighting a war to deny acceptance of any of it.

If any piece of my research is acknowledged as important from my
definition of mathematical proof to my ideas about finding primes then
they have to fear that the world will realize what they are doing, so
the math wars as I call them are political ones.

It is a fight of group power against mathematical truth.

James Harris

Undergraduate :: probability and statistics

Author: Akilah Seecharan
Subject: probability and statistics
Posted: Fri Jul 14, 2006 6:09 pm (GMT 0)
Topic Replies: 2

I'm having a problem finding the mean (U) of this distribution function, f(x) = x to the 4, 0<x<1 How would you solve this problem using the formula:
u=[xf(x)dx] from 0<x<1?

Undergraduate :: Loose connectivity, factoring and residues

Author: jstevh@msn.com
Subject: Loose connectivity, factoring and residues
Posted: Thu Jul 13, 2006 1:13 am (GMT 0)
Topic Replies: 26

The factoring problem can be easily approached using simple algebra.

Start with

x^2 - y^2 = S - 2*x*k

where all are integers, as notice then you trivially have

x^2 + 2*x*k + k^2 = y^2 + S + k^2

so

x+k = sqrt(y^2 + S + k^2)

and finding y is just a matter of factoring (S+k^2)/4.

Now with just the explicit equation you end up with nothing but
trivialities, but turning to congruences, you can now simply let

x^2 - y^2 = 0 mod T

which--this is important--now forces

S - 2*x_res*k = 0 mod T

where I put in x_res to emphasize that now it's congruences, so there
is loose connectivity and an explicit value of x is not needed--just a
residue.

But now I can just solve for k, assuming 2, S and x are
coprime to T:

k = S*(2*x_res)^{-1} mod T

where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.

That the modular inverse makes an appearance is critical, but more
importantly I now have a way to find all the variables!!!

That can be done by simply picking a residue for x_res and then picking
S, like x_res = 1, and S =1, to get k.

For instance if T=35, and I use x_res=S=1, then k = 18 mod 35, and k=18
will suffice.

Then y is found by factoring (1+18^2)/4 and then you have x as well.

Of course there will exist and x and y such that

x^2 - y^2 = 0 mod T

for any x_res you choose, which is trivial to prove, as that is
equivalent to

x^2 - y^2 = kT

where k can be any integer.

So an equation that is useless explicitly becomes quite powerful with
modular algebra--introducing loose connectivity--leading to a general
method for factoring.

James Harris

Undergraduate :: A new one - Please explain

Author: Missy
Subject: A new one - Please explain
Posted: Thu Jul 13, 2006 12:10 am (GMT 0)
Topic Replies: 2

1. What in the world is a Chi-squared Distribution? I looked it up on
the internet and still do not have a clue.

Undergraduate :: -Word Problems-

Author: Alex111
Subject: -Word Problems-
Posted: Wed Jul 12, 2006 9:05 pm (GMT 0)
Topic Replies: 8

Hello! I would just like some answers and information to these topics. I really need help. And any information would be accepted. Please help me in the following:

1. Anne leaves town A traveling by bike to town B along a certain path at sunrise. Bart leaves town B travelling by bike to town A along the same path as Anne. They travel at a constant speed, and do not stop biking towards their final destinations. The cross each other's paths at noon. Anne gets to town B at 5:00pm and Bart gets to town A at 11:15pm. At what time was sunrise?

2. Show that there is no perfect square whose digits sum of to 2006. (7 points)

3. Two natural numbers, x and y, are taken such that their sum is less than 100. (x + y < 100) Both x and y are greater than 1. Sam is told the sum of the numbers (x + y) and Pam is told the product of the numbers (xy). Neither of them knows the original two numbers, x and y. They have the following conversation:

Pam: I cannot determine the sum of the numbers.
Sam: I know.
Pam: Now, I know their sum.
Sam: Now, I know their product.

Determine x and y.

PLEASE help me with whatever you can! Thank you!

Undergraduate :: Advice on messy integral?

Author: David1132
Subject: Advice on messy integral?
Posted: Tue Jul 11, 2006 7:06 pm (GMT 0)
Topic Replies: 8

I'm struggeling with a weird triple integral:

z / (1 + x^2 + y^2) dxdydz

over the volume defined as x^2 + y^2 + z^2 <= 1 and z >= sqrt(x^2 + y^2)
(Which is the volume that is inside the unit sphere, and also inside the
upside-down flipped cone with the pointy end at origo and it's base at
z=1/sqrt(2) )

I've tried to approach this in several ways, but every time i end up with
_really_ messy solutions, like integrating complex ln functions to hell when
I try cylindrical coordinates and even worse situations with spherical
coordinates.

How would I do to solve this problem in the best, nicest and simplest way?
I really hope anyone can help... I would be very grateful for advice.

/ David

Undergraduate :: PLEASE explain this problem

Author: Missy
Subject: PLEASE explain this problem
Posted: Mon Jul 10, 2006 11:42 pm (GMT 0)
Topic Replies: 6

Like i have mentioned before I have not had math for some time now and
would like some assistance every now and again. would someone please
explain this problem to me.

4!/(2! � 2!)

Undergraduate :: test - ignore

Author: matt271829-news@yahoo.co.
Subject: test - ignore
Posted: Mon Jul 10, 2006 10:32 pm (GMT 0)
Topic Replies: 1

test - ignore

Undergraduate :: sat prep question

Author: Travis
Subject: sat prep question
Posted: Mon Jul 10, 2006 5:09 am (GMT 0)
Topic Replies: 18

If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9

I want to say the answer is 6 but I dont know why

Undergraduate :: Irreducibility of a Polynomial over Q

Author: Ohad Kammar
Subject: Irreducibility of a Polynomial over Q
Posted: Sat Jul 08, 2006 5:57 pm (GMT 0)
Topic Replies: 2

Hello,
I was wondering whether the next polynomial is irreducible over the rational
field Q:
1 + x^(p^k) + x^(2p^k) + x^(3p^k) + ... + x^((p-1)p^k)) = (x^(p^(k+1)) -
1)/(x^(p^k) - 1)
Where p is prime and k is a non-negative integer.

Thanks in advance,
Ohad.

Undergraduate :: Call for Papers: Graphs, Mappings and Combinatorics at the Minnesota State Fair

Author: EdV
Subject: Call for Papers: Graphs, Mappings and Combinatorics at the Minnesota State Fair
Posted: Thu Jul 06, 2006 2:07 am (GMT 0)
Topic Replies: 0

Leonardo's Basement (www.leonardosbasement.org) a Minneapolis based
school for Art, Science, Mathematics and Technology has been most
honorably charged with the assignment of "do some math stuff for us" by

the Minnesota State Fair Organizing Committee. To this end we are
issuing a call for papers on the topic of "Graphs, Mappings and
Combinatorics at the Minnesota State Fair". Papers submitted need not

pertain specifically to the Minnesota State Fair but should generally
embrace the topic of a state fair for example:

1 - animal sizes
2 - crowd movement
3 - corndog consumption
4 - are people having fun?
5 - hypotheses on why some amusement rides do not exist
6 - puzzle challenges
7 - puzzle solutions
8 - anything having to do the SOMA Cube Puzzle, because we are making a

huge one (it is kind of how we got the gig)

Dissertations that are tongue in cheek, completely unprovable,
incomprehensible or just plain funny to read out loud, are of course
most welcome. Please submit by August 1, 2006. Selected papers will
be presented on top of the world's largest SOMA Cube Puzzle (assembled
from 4ftx4ftx4ft cubes) on September 4, 2006. Presentation preference
will be shown to participants who:

1 - submit
2 - can show up
3 - have an appetite for the absurd

At this time we are not able to reimburse travel or lodging expenses.
However if you have a truly gonzo mathematics presentation I will be
most encouraged to figure something out.

Please send your submission to my special no spam email:

epvnospam-nospam1@yahoo.com

If you need to snail mail please contact me at the above email address
and I will provide a mailing address.

Undergraduate :: ode textbook

Author: mark snyder
Subject: ode textbook
Posted: Wed Jul 05, 2006 10:37 pm (GMT 0)
Topic Replies: 0

Hi,

I will be teaching a junior-level course in ode in the fall, and am looking for a textbook for the course. I would be interested in a textbook that has some links with MAPLE. Does anyone have any textbooks they would recommend? Thanks

Undergraduate :: what's the concept of "Newton gradient"? Thanks

Author: gaolgifer
Subject: what's the concept of "Newton gradient"? Thanks
Posted: Wed Jul 05, 2006 5:16 am (GMT 0)
Topic Replies: 0

what's the concept of "Newton gradient"? Thanks

Undergraduate :: Factoring idea

Author: jstevh@msn.com
Subject: Factoring idea
Posted: Wed Jul 05, 2006 2:10 am (GMT 0)
Topic Replies: 4

After years of effort with lots of failures I noticed something
remarkably simple, and this time the math is all worked out, and there
are few places for errors to hide.

Was doodling, playing around with some simple equations and noticed
that with

x^2 - a^2 = S + T

and

x^2 - b^2 = S - k*T

I could subtract the second from the first to get

b^2 - a^2 = (k+1)*T

which is, of course, a factorization of (k+1)*T:

(b - a)*(b+a) = (k+1)*T

with integers for S and T, where T is the target composite to factor,
so you have to pick this other integer S, and factor S+T.

Really simple.

But how do you find all the variables?

Well, if you pick S, and have a T you want to factor, then using

f_1*f_2 = S+T

it must be true that

a = (f_1 - f_2)/2

And

x=(f_1 + f_2)/2

so, you need the sum of factors of (S-k*T)/4 to equal the sum of the
factors of (S+T)/4, so I introduce j, where

S - k*T = (f_1 + f_2 - j)*j

and now you solve for k, to get

k = (S - (f_1 + f_2 - j)*j)/T

so you also have

S - (f_1 + f_2 - j)*j = 0 mod T

so

j^2 - (f_1 + f_2)*j + S = 0 mod T

and completing the square gives

j^2 - (f_1 + f_2)*j + (f_1 + f_2)^2/4 = ((f_1 + f_2)^2/4 - S) mod T

so

(2*j - (f_1 + f_2))^2 = ((f_1 + f_2)^2 - 4*S) mod T

so you have the quadratic residue of ((f_1 + f_2)^2 - 4*S) modulo T, to
find j, which is kind of neat, while it's also set what the quadratic
residue is, so there's no search involved.

The main residue is a trivial result that gives k=-1, but you have an
infinity of others found by adding or subtracting T.

And then you can find b, from

b^2 = x^2 - S + kT

and you have the factorization:

(b-a)*(b+a) = (k-1)*T.

It is possible to generalize further using

j = z/y

and then the congruence equation becomes

(2*z - (f_1 + f_2)y)^2 = ((f_1 + f_2)^2*y^2 - 4*S*y^2) mod T.

If you're skeptical you may consider the question of finding k when you
already have the factorization of T.

James Harris

Undergraduate :: Please explain the empty relation

Author: TOMERDR
Subject: Please explain the empty relation
Posted: Mon Jul 03, 2006 9:44 am (GMT 0)
Topic Replies: 4

1.What exactly is an empty relation?
(no one in relation with other,or a relation on empty set?)
2.Why is it both symetric and anti symetric according to the definition
of symetric and anti symetric

Thanks in advance.

Undergraduate :: Where can i find problems in relations and equivalence relations?

Author: TOMERDR
Subject: Where can i find problems in relations and equivalence relations?
Posted: Mon Jul 03, 2006 7:11 am (GMT 0)
Topic Replies: 2

Hi,
I am looking for problems with answers regarding relations and
equivalence Relations.

for example a good question can be:

"Is there a relation which is reflexive symetric and antisymmetric"

Btw my strategy to solve such problems is to write the definition
and using operation on sets and de morgan law to simplify it..is this a
good method?

Thanks in advance.