Al-Khawarizmi

Muḥammad ibn Mūsā al-Khwārizmī was a Persian[1] Islamic mathematician, astronomer, astrologer and geographer. He was born around 780 in Khwārizm[2] (now Khiva, Uzbekistan) and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.

His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra,[3] a title he shares with Diophantus. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the 12th century.[4] He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book. The words algorism and algorithm stem from Algoritmi, the Latinization of his name.[5] His name is also the origin of the Spanish word guarismo[6] and of the Portuguese word algarismo, both meaning digit.

meaning optimization problem

In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.

Assignment 3

LOGIC

-What is proporsition
Sentences considered in propositional logic are not arbitrary sentences but are the ones that are either true or false, but not both.


-What is truth table
This relationship of the value of a proposition and those of its constituent variables can be represented by a table. It tabulates the value of a proposition for all possible values of its variables and it is called a truth table.

-What is logical connectives
NOT, AND, OR, IMPLIES, IF AND ONLY IF

-What is variable
A symbolic representation used to denote a quantity or expression. In mathematics, a variable often represents an "unknown" quantity that has the potential to change.

coding for calculating gpa

import javax.swing.*;
public class Calculator{
public static void main (String [] args)
{ String gred, ulang, input;
int count, kredit;
double points, point1, point2, totalkredits, GPA, totalPoints;
do
{
gred = JOptionPane.showInputDialog( "Enter your letter grade" );
points = 0.00;
totalPoints = 0.00;
totalkredits = 0.00;
do {
input = JOptionPane.showInputDialog( "Enter your number of kredits? 1-6" );
kredit = Integer.parseInt( input );
if ((kredit<1)>6)) {
JOptionPane.showMessageDialog( null, "-----------------------------------------------------------------\nERROR\n\n----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----\nYOU MUST ENTER A NUMBER FROM 1 TO 6"); } }
while ((kredit<1)>6));
{ if (gred.equalsIgnoreCase("A"))
points = 4.00 * kredit;
} { if (gred.equalsIgnoreCase("A-"))
points = 3.75 * kredit;
} { if (gred.equalsIgnoreCase("B+"))
points = 3.50* kredit;
}{ if (gred.equalsIgnoreCase("B"))
points = 3.00 * kredit;
}{ if (gred.equalsIgnoreCase("B-"))
points = 2.75 * kredit;
}{ if (gred.equalsIgnoreCase("C+"))
points = 2.50 * kredit;
}{ if (gred.equalsIgnoreCase("C"))
points = 2.00 * kredit;
}{ if (gred.equalsIgnoreCase("C-"))
points = 1.75 * kredit;
} { if (gred.equalsIgnoreCase("D"))
points = 1.00 * kredit;
}{ if (gred.equalsIgnoreCase("F"))
points = 0.00 * kredit;
} totalPoints += points;
totalkredits += kredit;
ulang = JOptionPane.showInputDialog("Would you like to enter another class grade? Yes or NO"); }while (ulang.equalsIgnoreCase("YES"));
if (ulang.equalsIgnoreCase("NO")) {
GPA = totalPoints/totalkredits;
JOptionPane.showMessageDialog( null, (" You have a GPA of " + GPA));
System.exit(0); }
} }

assignment

-What is Discrete?
Word discrete comes from the 15th Century Latin word discretus which means separate

-What is Structures?
Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities.

-What is Discrete Structures (DS)?
Discrete Structures: “The abstract mathematical structures used to represent discrete objects and relationships between these objects

-Why is DS important?
These structures form the conceptual basis for many of the data structures that we use as programmers. To use ds as abstract models for use in solving problems and developing algorithms.

-How do we apply DS?
Discrete structures include sets, permutations, relations, trees, graphs and finite-state machines

Assignment 2

Assignment 2

We assume :
-have computers = 221 = C
-have programming books = 159 = B
-have both = 87 = T

Answers :

c + 87 = 221
c = 221-87 = 134

B + 87 = 159
B = 159-87 = 72

T = C + B +87
T = 134 + 72 + 87
T = 293

Find percentage (%) of student who :

a) have at least one computers and programming books
= C + B
= ((C/293) * 100) + ((B/293) * 100)
= ((134/293) * 100) + ((72/293) * 100)
= 45.73% + 24.57%
= 70.3%

b) have only computers
=((134/293) * 100)
=45.73%

c) have only programming books
=((72/293) * 100)
=24.57%

d) have both computers and programming books
have both we assume as T
T = 293
T/100 = 293/100
T = 29.3

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