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Science and technology forum - Undergraduate - mihai.secasiu@nixdoc.netmihai.secasiu@nixdoc.netMon, 21 Apr 2014 07:12:39 GMTUndergraduate :: Business Stats II
http://sci4um.com/post-325564.html#325564
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16612" target="_blank">LMG</a><br />
Subject: Business Stats II<br />
Posted: Wed Aug 16, 2006 4:45 pm (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">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?"
</span><br />
Undergraduate :: Curve integral - correct or not?
http://sci4um.com/post-324999.html#324999
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16517" target="_blank">Daniel Nierro</a><br />
Subject: Curve integral - correct or not?<br />
Posted: Thu Jul 20, 2006 2:47 pm (GMT 0)<br />
Topic Replies: 2<br /><br />
<span class="postbody">Hi!
<br />
If one would like to calculate the curve integral of the function f(x,y,z) =
<br />
x^2 + y^2 over the curve C: r(t) = (e^t cos(t), e^t sin(t), t) where t goes
<br />
from 0 to 1, what would the result be?
<br />
The curve is clearly somewhat spiral-shaped with a radius increasing with t,
<br />
and the problem should be easily solvable using cylindrical coordinates.
<br />
I'm wondering, does e^(2t) sqrt(e^(2t) + 1) sound like a reasonable answer?
<br />
<br />
Cheers,
<br />
Doug <img src="http://sci4um.com//images/smiles/icon_smile.gif" alt="Smile" border="0" />
</span><br />
Undergraduate :: A Combinatorics/Graph Theory Question
http://sci4um.com/post-324691.html#324691
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=345" target="_blank">mathlover</a><br />
Subject: A Combinatorics/Graph Theory Question<br />
Posted: Wed Jul 19, 2006 11:30 pm (GMT 0)<br />
Topic Replies: 1<br /><br />
<span class="postbody">Hi every body,
<br />
<br />
There is a problem I have exposed to but, though being badly in need of
<br />
an answer, I have not yet been able to solve it. I am not quite sure if
<br />
it is better classified as a graph theory problem or a combinatorial
<br />
one; anyway, here is the problem:
<br />
<br />
Assume we have a bipartite graph with X and Y as its two parts. X has
<br />
"n" vertices and Y has C(k,n) vertices where "k" is a natural number
<br />
less than "n" and by C(k,n) I denote the number of k-element subsets of
<br />
an n-element set. The edges of the graph are formed as below: we
<br />
correspond each k-element subset of X with a vertex in Y and put an
<br />
edge between that vertex of Y and each member of the corresponding
<br />
k-element subset of X.
<br />
<br />
Now it is clear that for every vertex of X there are C(k-1, n-1)
<br />
vertices in Y that have an edge to that vertex. That is every vertex in
<br />
X has exactly C(k-1, n-1) number of neighbors in Y. Now the problem is
<br />
as follows: assuming "r" is a natural number not larger than C(k-1,
<br />
n-1) (I am specially interested in the case r=2) determine the minimum
<br />
number "p" (or at least a non-trivial upper bound on it) such that for
<br />
every p-element subset, like S, of Y the following property holds: for
<br />
every node in X, like "v", it has at least "r" neighbors which are
<br />
members of S.
<br />
<br />
Any help or clues are greatly appreciated.
<br />
<br />
Thanks.
</span><br />
Undergraduate :: Math Help Available
http://sci4um.com/post-324589.html#324589
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16530" target="_blank">at361@yahoo.com</a><br />
Subject: Math Help Available<br />
Posted: Wed Jul 19, 2006 8:44 pm (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">we're a group of mathematics graduates who have tutored,
<br />
taught,provided math help and researched in mathematics at various
<br />
levels and in different parts of the world.
<br />
We've formed this tutoring/consulting service mainly for the purpose of
<br />
solving university problems (homework assignments/specific questions),
<br />
but we're also open to general problems that may arise in other fields.
<br />
<br />
At the present time we can provide math help in :
<br />
<br />
* calculus
<br />
* vector calculus
<br />
* integral calculus
<br />
* rings/fields
<br />
* group theory
<br />
* discrete math
<br />
* lie groups
<br />
* linear algebra
<br />
* complex analysis
<br />
* basic statistics
<br />
<br />
GOTO
<br />
<a href="http://www.angelfire.com/biz/mathconsultants" target="_blank">www.angelfire.com/biz/mathconsultants</a>
</span><br />
Undergraduate :: jordan decomposition and generalized eigenvectors
http://sci4um.com/post-323981.html#323981
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=525" target="_blank">Jeremy Watts</a><br />
Subject: jordan decomposition and generalized eigenvectors<br />
Posted: Tue Jul 18, 2006 6:49 pm (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">ok, firstly excuse the length of this post and the fact that it is cross
<br />
posted.... (i really didnt know the most appropriate NG to send it to....)
<br />
<br />
anyway, i am using an algorithm to perform a jordan decomposition taken from
<br />
'schaums outlines for matrix operations'. the algorithm states on p.82 that
<br />
to form a canonical basis (this being the first step in forming a jordan
<br />
decomposition) , then :-
<br />
<br />
Step 1. Denote the multiplicity of lambda as m , and determine the
<br />
smallest positive integer p for which the rank of (A - lambda I )^p equals
<br />
n-m , where n denotes the number of rows (and columns in A), lambda denotes
<br />
an eigenvalue of A and I is the identity matrix.
<br />
<br />
Step 2. For each integer k between 1 and p, inclusive, compute the
<br />
'eigenvalue rank number Nk' as :-
<br />
Nk = rank(A - lambda I)^(k-1) - rank(A - lambdaI)^k
<br />
Each Nk is the number of generalized eigenvectors of rank k that will appear
<br />
in the canonical basis
<br />
<br />
Step 3. Determine a generalized eigenvector of rank p, and construct the
<br />
chain generated by this vector. Each of these vectors is part of the
<br />
canonical basis.
<br />
<br />
Step 4. Reduce each positive Nk (k = 1,2,...,p) by 1. If all Nk are zero
<br />
then stop; the procedure is complete for this particular eigenvalue. If not
<br />
then continue to Step 5.
<br />
<br />
Step 5. Find the highest value of k for which Nk is not zero, and determine
<br />
a generalized eigenvector of that rank which is linearly independent of all
<br />
previously determined generalized eigenvectors associated with lambda. Form
<br />
the chain generated by this vector, and include it in the basis. Return to
<br />
Step 4.
<br />
<br />
<br />
Now, the matrix I am using the above procedure on is :-
<br />
<br />
<br />
0 0 1 0 i
<br />
0 -9+6i 0 1 0
<br />
A = 0 0 8 i 1
<br />
0 0 0 8 0
<br />
0 2i 0 -9 8
<br />
<br />
<br />
Now the eigenvalues and multiplicities are :-
<br />
<br />
-9+6i with multiplicity 1
<br />
8 with multiplicity 3
<br />
0 with multiplicity 1
<br />
<br />
Starting with -9+6i and going through the procedure then i make the value of
<br />
p in step 1 as p = 5. This immediately arouses my suspicions as it looks too
<br />
high, as Step 3 not only fails to find a generalized eigenvector of rank 5,
<br />
but also even if it existed, the vector plus its chain would be of length 5,
<br />
and so fill the entire canonical basis with the vectors generated by just
<br />
the first eigenvalue .
<br />
<br />
By the way I am using the definition of a 'generalized eigenvector' as the
<br />
one given in the same book, on the same page in fact as the above procedure,
<br />
which is :-
<br />
<br />
"A vector Xm is a generalized eigenvector of rank m for the square matrix A
<br />
and associated eigenvalue lambda if :-
<br />
<br />
(A - lambda I)^m Xm = 0 but (A - lambda I)^(m-1)Xm =/= 0
<br />
<br />
So, firstly does anyone agree that a generalized eigenvector of rank 5
<br />
cannot exist for the matrix A with the eigenvalue -9+6i , and if so what is
<br />
going wrong here generally?
<br />
<br />
<br />
thanks
</span><br />
Undergraduate :: Can you count?
http://sci4um.com/post-323880.html#323880
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=6152" target="_blank">Alexander Blessing</a><br />
Subject: Can you count?<br />
Posted: Tue Jul 18, 2006 4:03 pm (GMT 0)<br />
Topic Replies: 5<br /><br />
<span class="postbody">Let n denote the number of digits of a natural number.
<br />
Now, how many natural numbers with n digits are there which contain all
<br />
digits from 0 to 9 in their 10-adic expansion?
<br />
<br />
Any idea guys?
</span><br />
Undergraduate :: NEED HELP ONCE AGAIN
http://sci4um.com/post-322292.html#322292
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16074" target="_blank">Missy</a><br />
Subject: NEED HELP ONCE AGAIN<br />
Posted: Sun Jul 16, 2006 2:16 am (GMT 0)<br />
Topic Replies: 5<br /><br />
<span class="postbody">Please help I need to know how to solve each of the following
<br />
step-by-step:
<br />
<br />
1. Daria can wash and detail 3 cars in 2 hours. Larry can wash and
<br />
detail the same 3 cars in
<br />
1.5 hours. About how long will it take to wash and detail the 3
<br />
cars if Daria and Larry worked
<br />
together?
<br />
<br />
<br />
<br />
2. 100 people will attend the theatre if tickets cost $40 each. For
<br />
each $5 increase in price, 10
<br />
fewer people will attend. what price will deliver the maximum
<br />
dollar sales?
<br />
<br />
<br />
<br />
3. How many 3-person groups can be formed in a club with 8 people?
</span><br />
Undergraduate :: Finite # of subgroups -> Finite group
http://sci4um.com/post-322270.html#322270
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16450" target="_blank">tppytel@gmail.com</a><br />
Subject: Finite # of subgroups -> Finite group<br />
Posted: Sun Jul 16, 2006 1:47 am (GMT 0)<br />
Topic Replies: 9<br /><br />
<span class="postbody">Hello,
<br />
<br />
I'm working my way through some group theory on my own, and was looking
<br />
for advice on the following proof. I think my approach works, but it
<br />
seems like there must be an easier way. This problem is in the chapter
<br />
of the text on cyclic subgroups, so that's what I'm trying to use.
<br />
<br />
Given: Group G with a finite number of subgroups
<br />
Prove: Group G is finite
<br />
<br />
I will prove the contrapositive - if G is infinite, then we can
<br />
generate an infinite number of distinct subgroups from it.
<br />
<br />
Choose a in G where a != e. (G is infinite, so this a must exist.)
<br />
</span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>Quote:</b></span></td> </tr> <tr> <td class="quote">From a we can construct the cyclic subgroup <a>.
<br />
</td> </tr></table><span class="postbody">
<br />
Case 1: <a> is finite
<br />
(Is this case really valid? Can I get a finite cyclic subgroup other
<br />
than {e} out of an infinite group?)
<br />
<br />
Choose b in G such that b is not in <a>. This b must exist because G is
<br />
of infinite order, while <a> is finite. Then we have a new subgroup <b>
<br />
distinct from <a>. This process can be continued so long as we keep
<br />
generating finite cyclic subgroups.
<br />
<br />
Case 2: <a> is infinite
<br />
Then we can construct a new subgroup <a^2>. a is not in <a^2>, because
<br />
if it were then there would be an n in Z such that
<br />
<br />
(a^2)^n = a
<br />
a^2n = a
<br />
a^(2n-1) = e
<br />
<br />
But that would mean that <a> is finite, which is a contradiction. Thus
<br />
a is not in <a^2>, so <a^2> is distinct from <a>. By the same
<br />
reasoning, <a^3> is distinct from either <a^2> or <a>, and so on...
<br />
<br />
Therefore, from an infinite group G, we can generate an infinite number
<br />
of subgroups.
<br />
And the contrapositive also holds, that if a group G has a finite
<br />
number of subgroups, then G itself must be finite.
<br />
<br />
<br />
Valid, I think, but kind of messy. There must be an easier way...
</span><br />
Undergraduate :: embedding problem
http://sci4um.com/post-322006.html#322006
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=5371" target="_blank">winshum</a><br />
Subject: embedding problem<br />
Posted: Sat Jul 15, 2006 5:24 pm (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">a cylindrically symmetric manifold is described by the line element
<br />
ds^2=4e^(2ar)dr^2+r^2d@^2
<br />
now the manifold is embedded into 3-D flat space, with Euclidean coordinates x,y,z where
<br />
r=sqrt(x^2+y^2)
<br />
z=h(r)
<br />
Find a differential equation satisfied by h(r)
<br />
and also how to solve h(r)
<br />
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!
</span><br />
Undergraduate :: JSH: My research, a roadmap
http://sci4um.com/post-321670.html#321670
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=11112" target="_blank">jstevh@msn.com</a><br />
Subject: JSH: My research, a roadmap<br />
Posted: Sat Jul 15, 2006 2:04 am (GMT 0)<br />
Topic Replies: 29<br /><br />
<span class="postbody">My research speaks for itself.
<br />
<br />
I have given a definition of mathematical proof:
<br />
<br />
<a href="http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html" target="_blank">http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html</a>
<br />
<br />
Figured out the key properties that define rings that are like the ring
<br />
of integers:
<br />
<br />
<a href="http://mymath.blogspot.com/2005/03/object-ring.html" target="_blank">http://mymath.blogspot.com/2005/03/object-ring.html</a>
<br />
<br />
Found my own prime counting function, which unlike any other known
<br />
relies on summing a partial difference equation, which is also why it
<br />
finds primes on its own, unlike any other known:
<br />
<br />
<a href="http://mymath.blogspot.com/2005/06/counting-primes.html" target="_blank">http://mymath.blogspot.com/2005/06/counting-primes.html</a>
<br />
<br />
Fighting mathematicians who have done their best to ignore my research
<br />
I wrote the first prime counting function article for the Wikipedia,
<br />
where my latest version is now found in the history of the current
<br />
page:
<br />
<br />
<a href="http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old..." target="_blank">http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old...</a>
<br />
<br />
There readers can see my prime counting function in its fully
<br />
mathematicized "pure" form, and see how it is a summation, so they can
<br />
make the leap to understanding how it relates to a partial differential
<br />
equation and an integration.
<br />
<br />
I had a paper published in a formally peer reviewed mathematical
<br />
journal--and then the editors withdrew it after sci.math pressure
<br />
against it:
<br />
<br />
<a href="http://www.emis.de/journals/SWJPAM/vol2-03.html" target="_blank">http://www.emis.de/journals/SWJPAM/vol2-03.html</a>
<br />
<br />
Link is to a site mirror as the electronic journal DIED a few months
<br />
later.
<br />
<br />
That paper covered some pioneering research advancing modular algebra
<br />
or the algebra of congruences, extending on the work started by Gauss:
<br />
<br />
<a href="http://mymath.blogspot.com/2005/07/tautological-spaces-factoring.html" target="_blank">http://mymath.blogspot.com/2005/07/tautological-spaces-factoring.html</a>
<br />
<br />
Which is a line of attack I used to find a short proof of Fermat's Last
<br />
Theorem:
<br />
<br />
<a href="http://mymath.blogspot.com/2006/03/proof-of-fermats-last-theorem.html" target="_blank">http://mymath.blogspot.com/2006/03/proof-of-fermats-last-theorem.html</a>
<br />
<br />
But I've even considered problems in logic and set theory, handling
<br />
supposed contradictions:
<br />
<br />
<a href="http://mymath.blogspot.com/2005/06/three-valued-logic.html" target="_blank">http://mymath.blogspot.com/2005/06/three-valued-logic.html</a>
<br />
<br />
and
<br />
<br />
<a href="http://mymath.blogspot.com/2005/05/logical-formedness-axioms.html" target="_blank">http://mymath.blogspot.com/2005/05/logical-formedness-axioms.html</a>
<br />
<br />
and
<br />
<br />
<a href="http://mymath.blogspot.com/2005/06/3-logic-more-basics.html" target="_blank">http://mymath.blogspot.com/2005/06/3-logic-more-basics.html</a>
<br />
<br />
Even some of my minor research is significant, as I talked about a
<br />
simple way to find primes using quadratic residues:
<br />
<br />
<a href="http://mymath.blogspot.com/2006/04/method-for-quickly-finding-primes...." target="_blank">http://mymath.blogspot.com/2006/04/method-for-quickly-finding-primes....</a>
<br />
<br />
The only explanation given the breadth of my research, and dramatic
<br />
events like a math journal imploding after publishing then retracting a
<br />
paper of mine is that it is so huge that mathematicians who are living
<br />
in a political society today--where their word is more important than
<br />
their research--are fighting a war to deny acceptance of any of it.
<br />
<br />
If any piece of my research is acknowledged as important from my
<br />
definition of mathematical proof to my ideas about finding primes then
<br />
they have to fear that the world will realize what they are doing, so
<br />
the math wars as I call them are political ones.
<br />
<br />
It is a fight of group power against mathematical truth.
<br />
<br />
<br />
James Harris
</span><br />
Undergraduate :: probability and statistics
http://sci4um.com/post-321388.html#321388
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16420" target="_blank">Akilah Seecharan</a><br />
Subject: probability and statistics<br />
Posted: Fri Jul 14, 2006 6:09 pm (GMT 0)<br />
Topic Replies: 2<br /><br />
<span class="postbody">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:
<br />
u=[xf(x)dx] from 0<x<1?
</span><br />
Undergraduate :: Loose connectivity, factoring and residues
http://sci4um.com/post-320079.html#320079
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=11112" target="_blank">jstevh@msn.com</a><br />
Subject: Loose connectivity, factoring and residues<br />
Posted: Thu Jul 13, 2006 1:13 am (GMT 0)<br />
Topic Replies: 26<br /><br />
<span class="postbody">The factoring problem can be easily approached using simple algebra.
<br />
<br />
Start with
<br />
<br />
x^2 - y^2 = S - 2*x*k
<br />
<br />
where all are integers, as notice then you trivially have
<br />
<br />
x^2 + 2*x*k + k^2 = y^2 + S + k^2
<br />
<br />
so
<br />
<br />
x+k = sqrt(y^2 + S + k^2)
<br />
<br />
and finding y is just a matter of factoring (S+k^2)/4.
<br />
<br />
Now with just the explicit equation you end up with nothing but
<br />
trivialities, but turning to congruences, you can now simply let
<br />
<br />
x^2 - y^2 = 0 mod T
<br />
<br />
which--this is important--now forces
<br />
<br />
S - 2*x_res*k = 0 mod T
<br />
<br />
where I put in x_res to emphasize that now it's congruences, so there
<br />
is loose connectivity and an explicit value of x is not needed--just a
<br />
residue.
<br />
<br />
But now I can just solve for k, assuming 2, S and x are
<br />
coprime to T:
<br />
<br />
k = S*(2*x_res)^{-1} mod T
<br />
<br />
where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.
<br />
<br />
That the modular inverse makes an appearance is critical, but more
<br />
importantly I now have a way to find all the variables!!!
<br />
<br />
That can be done by simply picking a residue for x_res and then picking
<br />
S, like x_res = 1, and S =1, to get k.
<br />
<br />
For instance if T=35, and I use x_res=S=1, then k = 18 mod 35, and k=18
<br />
will suffice.
<br />
<br />
Then y is found by factoring (1+18^2)/4 and then you have x as well.
<br />
<br />
Of course there will exist and x and y such that
<br />
<br />
x^2 - y^2 = 0 mod T
<br />
<br />
for any x_res you choose, which is trivial to prove, as that is
<br />
equivalent to
<br />
<br />
x^2 - y^2 = kT
<br />
<br />
where k can be any integer.
<br />
<br />
So an equation that is useless explicitly becomes quite powerful with
<br />
modular algebra--introducing loose connectivity--leading to a general
<br />
method for factoring.
<br />
<br />
<br />
James Harris
</span><br />
Undergraduate :: A new one - Please explain
http://sci4um.com/post-320027.html#320027
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16074" target="_blank">Missy</a><br />
Subject: A new one - Please explain<br />
Posted: Thu Jul 13, 2006 12:10 am (GMT 0)<br />
Topic Replies: 2<br /><br />
<span class="postbody">1. What in the world is a Chi-squared Distribution? I looked it up on
<br />
the internet and still do not have a clue.
</span><br />
Undergraduate :: -Word Problems-
http://sci4um.com/post-319931.html#319931
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=11680" target="_blank">Alex111</a><br />
Subject: -Word Problems-<br />
Posted: Wed Jul 12, 2006 9:05 pm (GMT 0)<br />
Topic Replies: 8<br /><br />
<span class="postbody">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:
<br />
<br />
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?
<br />
<br />
2. Show that there is no perfect square whose digits sum of to 2006. (7 points)
<br />
<br />
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:
<br />
<br />
Pam: I cannot determine the sum of the numbers.
<br />
Sam: I know.
<br />
Pam: Now, I know their sum.
<br />
Sam: Now, I know their product.
<br />
<br />
Determine x and y.
<br />
<br />
PLEASE help me with whatever you can! Thank you!
</span><br />
Undergraduate :: Advice on messy integral?
http://sci4um.com/post-319074.html#319074
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=9933" target="_blank">David1132</a><br />
Subject: Advice on messy integral?<br />
Posted: Tue Jul 11, 2006 7:06 pm (GMT 0)<br />
Topic Replies: 8<br /><br />
<span class="postbody">I'm struggeling with a weird triple integral:
<br />
<br />
z / (1 + x^2 + y^2) dxdydz
<br />
<br />
over the volume defined as x^2 + y^2 + z^2 <= 1 and z >= sqrt(x^2 + y^2)
<br />
(Which is the volume that is inside the unit sphere, and also inside the
<br />
upside-down flipped cone with the pointy end at origo and it's base at
<br />
z=1/sqrt(2) )
<br />
<br />
I've tried to approach this in several ways, but every time i end up with
<br />
_really_ messy solutions, like integrating complex ln functions to hell when
<br />
I try cylindrical coordinates and even worse situations with spherical
<br />
coordinates.
<br />
<br />
How would I do to solve this problem in the best, nicest and simplest way?
<br />
I really hope anyone can help... I would be very grateful for advice.
<br />
<br />
/ David
</span><br />
Undergraduate :: PLEASE explain this problem
http://sci4um.com/post-318436.html#318436
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16074" target="_blank">Missy</a><br />
Subject: PLEASE explain this problem<br />
Posted: Mon Jul 10, 2006 11:42 pm (GMT 0)<br />
Topic Replies: 6<br /><br />
<span class="postbody">Like i have mentioned before I have not had math for some time now and
<br />
would like some assistance every now and again. would someone please
<br />
explain this problem to me.
<br />
<br />
<br />
4!/(2! × 2!)
</span><br />
Undergraduate :: test - ignore
http://sci4um.com/post-318408.html#318408
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=6953" target="_blank">matt271829-news@yahoo.co.</a><br />
Subject: test - ignore<br />
Posted: Mon Jul 10, 2006 10:32 pm (GMT 0)<br />
Topic Replies: 1<br /><br />
<span class="postbody">test - ignore
</span><br />
Undergraduate :: sat prep question
http://sci4um.com/post-317782.html#317782
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=4550" target="_blank">Travis</a><br />
Subject: sat prep question<br />
Posted: Mon Jul 10, 2006 5:09 am (GMT 0)<br />
Topic Replies: 18<br /><br />
<span class="postbody">If T represents an operation that
<br />
includes addition and subtraction.
<br />
Ex) 5 T 3 = 6, 4 T 1 = 2.
<br />
What is the value of 7 T 3?
<br />
A. 5
<br />
B. 6
<br />
C. 7
<br />
D. 8
<br />
E. 9
<br />
<br />
<br />
I want to say the answer is 6 but I dont know why
</span><br />
Undergraduate :: Irreducibility of a Polynomial over Q
http://sci4um.com/post-316971.html#316971
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16241" target="_blank">Ohad Kammar</a><br />
Subject: Irreducibility of a Polynomial over Q<br />
Posted: Sat Jul 08, 2006 5:57 pm (GMT 0)<br />
Topic Replies: 2<br /><br />
<span class="postbody">Hello,
<br />
I was wondering whether the next polynomial is irreducible over the rational
<br />
field Q:
<br />
1 + x^(p^k) + x^(2p^k) + x^(3p^k) + ... + x^((p-1)p^k)) = (x^(p^(k+1)) -
<br />
1)/(x^(p^k) - 1)
<br />
Where p is prime and k is a non-negative integer.
<br />
<br />
Thanks in advance,
<br />
Ohad.
</span><br />
Undergraduate :: Call for Papers: Graphs, Mappings and Combinatorics at the Minnesota State Fair
http://sci4um.com/post-315241.html#315241
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16130" target="_blank">EdV</a><br />
Subject: Call for Papers: Graphs, Mappings and Combinatorics at the Minnesota State Fair<br />
Posted: Thu Jul 06, 2006 2:07 am (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">Leonardo's Basement (www.leonardosbasement.org) a Minneapolis based
<br />
school for Art, Science, Mathematics and Technology has been most
<br />
honorably charged with the assignment of "do some math stuff for us" by
<br />
<br />
the Minnesota State Fair Organizing Committee. To this end we are
<br />
issuing a call for papers on the topic of "Graphs, Mappings and
<br />
Combinatorics at the Minnesota State Fair". Papers submitted need not
<br />
<br />
pertain specifically to the Minnesota State Fair but should generally
<br />
embrace the topic of a state fair for example:
<br />
<br />
1 - animal sizes
<br />
2 - crowd movement
<br />
3 - corndog consumption
<br />
4 - are people having fun?
<br />
5 - hypotheses on why some amusement rides do not exist
<br />
6 - puzzle challenges
<br />
7 - puzzle solutions
<br />
8 - anything having to do the SOMA Cube Puzzle, because we are making a
<br />
<br />
huge one (it is kind of how we got the gig)
<br />
<br />
<br />
Dissertations that are tongue in cheek, completely unprovable,
<br />
incomprehensible or just plain funny to read out loud, are of course
<br />
most welcome. Please submit by August 1, 2006. Selected papers will
<br />
be presented on top of the world's largest SOMA Cube Puzzle (assembled
<br />
from 4ftx4ftx4ft cubes) on September 4, 2006. Presentation preference
<br />
will be shown to participants who:
<br />
<br />
<br />
1 - submit
<br />
2 - can show up
<br />
3 - have an appetite for the absurd
<br />
<br />
<br />
At this time we are not able to reimburse travel or lodging expenses.
<br />
However if you have a truly gonzo mathematics presentation I will be
<br />
most encouraged to figure something out.
<br />
<br />
Please send your submission to my special no spam email:
<br />
<br />
<a href="mailto:epvnospam-nospam1@yahoo.com">epvnospam-nospam1@yahoo.com</a>
<br />
<br />
If you need to snail mail please contact me at the above email address
<br />
and I will provide a mailing address.
</span><br />
Undergraduate :: ode textbook
http://sci4um.com/post-315124.html#315124
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16148" target="_blank">mark snyder</a><br />
Subject: ode textbook<br />
Posted: Wed Jul 05, 2006 10:37 pm (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">Hi,
<br />
<br />
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
</span><br />
Undergraduate :: what's the concept of "Newton gradient"? Thanks
http://sci4um.com/post-314577.html#314577
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=16120" target="_blank">gaolgifer</a><br />
Subject: what's the concept of "Newton gradient"? Thanks<br />
Posted: Wed Jul 05, 2006 5:16 am (GMT 0)<br />
Topic Replies: 0<br /><br />
<span class="postbody">what's the concept of "Newton gradient"? Thanks
</span><br />
Undergraduate :: Factoring idea
http://sci4um.com/post-314531.html#314531
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=11112" target="_blank">jstevh@msn.com</a><br />
Subject: Factoring idea<br />
Posted: Wed Jul 05, 2006 2:10 am (GMT 0)<br />
Topic Replies: 4<br /><br />
<span class="postbody">After years of effort with lots of failures I noticed something
<br />
remarkably simple, and this time the math is all worked out, and there
<br />
are few places for errors to hide.
<br />
<br />
Was doodling, playing around with some simple equations and noticed
<br />
that with
<br />
<br />
x^2 - a^2 = S + T
<br />
<br />
and
<br />
<br />
x^2 - b^2 = S - k*T
<br />
<br />
I could subtract the second from the first to get
<br />
<br />
b^2 - a^2 = (k+1)*T
<br />
<br />
which is, of course, a factorization of (k+1)*T:
<br />
<br />
(b - a)*(b+a) = (k+1)*T
<br />
<br />
with integers for S and T, where T is the target composite to factor,
<br />
so you have to pick this other integer S, and factor S+T.
<br />
<br />
Really simple.
<br />
<br />
But how do you find all the variables?
<br />
<br />
Well, if you pick S, and have a T you want to factor, then using
<br />
<br />
f_1*f_2 = S+T
<br />
<br />
it must be true that
<br />
<br />
a = (f_1 - f_2)/2
<br />
<br />
And
<br />
<br />
x=(f_1 + f_2)/2
<br />
<br />
so, you need the sum of factors of (S-k*T)/4 to equal the sum of the
<br />
factors of (S+T)/4, so I introduce j, where
<br />
<br />
S - k*T = (f_1 + f_2 - j)*j
<br />
<br />
and now you solve for k, to get
<br />
<br />
k = (S - (f_1 + f_2 - j)*j)/T
<br />
<br />
so you also have
<br />
<br />
S - (f_1 + f_2 - j)*j = 0 mod T
<br />
<br />
so
<br />
<br />
j^2 - (f_1 + f_2)*j + S = 0 mod T
<br />
<br />
and completing the square gives
<br />
<br />
j^2 - (f_1 + f_2)*j + (f_1 + f_2)^2/4 = ((f_1 + f_2)^2/4 - S) mod T
<br />
<br />
so
<br />
<br />
(2*j - (f_1 + f_2))^2 = ((f_1 + f_2)^2 - 4*S) mod T
<br />
<br />
so you have the quadratic residue of ((f_1 + f_2)^2 - 4*S) modulo T, to
<br />
find j, which is kind of neat, while it's also set what the quadratic
<br />
residue is, so there's no search involved.
<br />
<br />
The main residue is a trivial result that gives k=-1, but you have an
<br />
infinity of others found by adding or subtracting T.
<br />
<br />
And then you can find b, from
<br />
<br />
b^2 = x^2 - S + kT
<br />
<br />
and you have the factorization:
<br />
<br />
(b-a)*(b+a) = (k-1)*T.
<br />
<br />
It is possible to generalize further using
<br />
<br />
j = z/y
<br />
<br />
and then the congruence equation becomes
<br />
<br />
(2*z - (f_1 + f_2)y)^2 = ((f_1 + f_2)^2*y^2 - 4*S*y^2) mod T.
<br />
<br />
If you're skeptical you may consider the question of finding k when you
<br />
already have the factorization of T.
<br />
<br />
<br />
James Harris
</span><br />
Undergraduate :: Please explain the empty relation
http://sci4um.com/post-313297.html#313297
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=14600" target="_blank">TOMERDR</a><br />
Subject: Please explain the empty relation<br />
Posted: Mon Jul 03, 2006 9:44 am (GMT 0)<br />
Topic Replies: 4<br /><br />
<span class="postbody">1.What exactly is an empty relation?
<br />
(no one in relation with other,or a relation on empty set?)
<br />
2.Why is it both symetric and anti symetric according to the definition
<br />
of symetric and anti symetric
<br />
<br />
<br />
Thanks in advance.
</span><br />
Undergraduate :: Where can i find problems in relations and equivalence relations?
http://sci4um.com/post-313265.html#313265
Author: <a href="http://sci4um.com//profile.php?mode=viewprofile&u=14600" target="_blank">TOMERDR</a><br />
Subject: Where can i find problems in relations and equivalence relations?<br />
Posted: Mon Jul 03, 2006 7:11 am (GMT 0)<br />
Topic Replies: 2<br /><br />
<span class="postbody">Hi,
<br />
I am looking for problems with answers regarding relations and
<br />
equivalence Relations.
<br />
<br />
for example a good question can be:
<br />
<br />
"Is there a relation which is reflexive symetric and antisymmetric"
<br />
<br />
Btw my strategy to solve such problems is to write the definition
<br />
and using operation on sets and de morgan law to simplify it..is this a
<br />
good method?
<br />
<br />
Thanks in advance.
</span><br />