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Based on Papers that published :

  1. University of Tehran
  2. Sharif University of Technology
  3. Amirkabir University of Technology
  4. Iran University of Science and Technology
  5. Shiraz university
  6. Isfahan University of Technology
  7. Ferdowsi University of Mashhad: Third University
  8. University of Tabriz
  9. K. N. Toosi University of Technology
  10. Shahid Beheshti University
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Based on Papers that published :

  1. University of Tehran
  2. Sharif University of Technology
  3. Amirkabir University of Technology
  4. Iran University of Science and Technology
  5. Shiraz university
  6. Isfahan University of Technology
  7. Ferdowsi University of Mashhad: Third University
  8. University of Tabriz
  9. K. N. Toosi University of Technology
  10. Shahid Beheshti University
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Answering questions about the rank of a university has always been a difficult and sometimes controversial task, and answers might differ widely depending on the ranking criteria. If the measure for ranking universities is the quality of education in undergrad level (as opposed to, for instance, the number of journal papers published by the faculty), probably the best way to rank the Iranian universities is to talk to different universities' students, and try to find out what graduate schools they are admitted to for their higher education. Have the students decided not to enter graduate school, one must observe which companies have hired them.

In terms of quality of education, K.N.Toosi is, without a doubt, one of the top engineering schools in Iran. I myself am a class 82 graduate of the K.N.Toosi University of Technology, and many of my classmates got admitted to good universities in USA, Canada, Australia, and Europe. I personally know K.N.Toosi graduates who have been admitted to Purdue, Stanford, Michigan, Waterloo etc. Currently (as of February 2010), I am a graduate student in a reputable university in the US, and with the background and knowledge that I have acquired at K.N.Toosi, I can easily compete with Americans.

As a person who had been involved with Iranian Universities for 6 years, I rank public Engineering schools in Iran as the following (in terms of quality of education as described above):

1. Sharif University of Technology

2. Tehran University

3. Amir-Kabir University of Technology

4. Iran University of Science and Technology

5. K. N. Toosi University of Technology

5. Shiraz University

5. Isfahan University of Technology

6. Ferdowsi University of Mashad

7. Shahid Beheshti University

Note that this ranking reflects my personal opinion, with which I believe many students at my level would agree. Please also be advised that this is just about Engineering Schools only, and does NOT apply to medical sciences. As far as I know, Shahid Beheshti University has a medical school, which is one of the top ones in the Nation.

Regards,

S.E.P.

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n(n+1)/2

You can see this from the following:

Let x=1+2+3+...+n

This is the same as x=n+(n-1)+...+1

x=1+2+3+...+n

x=n+(n-1)+...+1

If you add the corresponding terms on the right-hand side of the two equations together, they each equal n+1 (e.g., 1+n=n+1, 2+n-1=n+1, ..., n+1=n+1). There are n such terms. So adding the each of the left-hand sides and right-hand sides of the two equations, we get:

x+x=(n+1)+(n+1)+...+(n+1) [with n (n+1) terms on the right-hand side

2x=n*(n+1)

x=n*(n+1)/2

A more formal proof by induction is also possible:

(1) The formula works for n=1 because 1=1*2/2.

(2) Assume that it works for an integer k.

(3) Now show that given the assumption that it works for k, it must also work for k+1.

By assmuption, 1+2+3+...+k=k(k+1)/2. Adding k+1 to each side, we get:

1+2+3+...+k+(k=1)=k(k+1)/2+(k+1)=k(k+1)/2+2(k+1)/2=(k(k+1)+2(k+1))/2=((k+2)(k+1))/2=(((k+1)+1)(k+1))/2=((k+1)((k+1)+1)/2

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#include<stdio.h>

#include<stdlib.h>

#include<math.h>

#include<conio.h>

void main(void)

{

int K, P, C, J;

double A[100][101];

int N;

int Row[100];

double X[100];

double SUM, M;

int T;

do

{

printf("Please enter number of equations [Not more than %d]\n",100);

scanf("%d", &N);

} while( N > 100);

printf("You say there are %d equations.\n", N);

printf("From AX = B enter elements of [A,B] row by row:\n");

for (K = 1; K <= N; K++)

{

for (J = 1; J <= N+1; J++)

{

printf(" For row %d enter element %d please :\n", K, J);

scanf("%lf", &A[K-1][J-1]);

}

}

for (J = 1; J<= N; J++) Row[J-1] = J - 1;

for (P = 1; P <= N - 1; P++)

{

for (K = P + 1; K <= N; K++)

{

if ( fabs(A[Row[K-1]][P-1]) > fabs(A[Row[P-1]][P-1]) )

{

T = Row[P-1];

Row[P-1] = Row[K-1];

Row[K-1] = T;

}

}

if (A[Row[P-1]][P-1] 0)

{

printf("The matrix is SINGULAR !\n");

printf("Cannot use algorithm --- exit\n");

exit(1);

}

X[N-1] = A[Row[N-1]][N] / A[Row[N-1]][N-1];

for (K = N - 1; K >= 1; K--)

{

SUM = 0;

for (C = K + 1; C <= N; C++)

{

SUM += A[Row[K-1]][C-1] * X[C-1];

}

X[K-1] = ( A[Row[K-1]][N] - SUM) / A[Row[K-1]][K-1];

}

for( K = 1; K <= N; K++)

printf("X[%d] = %lf\n", K, X[K-1]);

getch();

}

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n=1 a(1) = 0.001

n=2 a(2) = 0.012

n=3 a(3) = 0.144

n=4 a(4) = 1.728

n=5 a(5) = 20.736

....

n=k a(k) = (12^(k-1))/1000

let n = k+1

a(k+1) = 12^(k)/1000

12(ak) = a(k+1)

12(12^k-1)/1000 = 12^k/1000

the 12 gets absorbed here.

12^(k-1+1)/1000 = 12^k/1000

Valid for k and k+1

therefore our equation

A(n) = 12^(n-1)/1000, n(greater than or equal to) 1

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