Abu Ja’far Mu ḥ ammad ibn Mūsā al-Khwārizmī (780-850AD) محمد بن موسى...

Abu Ja’far Muḥammad ibn Mūsā al-Khwārizmī

(780-850AD)

محمد بن موسى الخوارزمي

Developed byIvan Seneviratne

Father of Algebra

Al-Khwarizmi was a Persian mathematician, astronomer, astrologer and geographer born around 780, in either Khwarizm or Baghdad, and died around 850.

His systematic and logical approach gave shape to the discipline of algebra.

He also made major contributions to the fields of trigonometry, astronomy, astrology, geography and cartography.

Kitab Al-Jabr wal Muqabala

Written by al-Khwarizmi in 9th century, this was the first book on systematic solution of linear and quadratic equations.

The word ‘Algebra’ is a part of the title of this textbook which was translated into Latin in Europe.

Algorithmus is a Latin transcription of his name.

What is Algebra?

• Algebra is a branch of Mathematics that describes the relationships between things that vary over time.

• Variables are denoted by letters and symbols.

• Algebra is a study in logic a practical system for solving problems.

• "al-jabr" means "completion", it is the process of removing negative terms from an equation.

Algebraic Expression

• An algebraic expression is a combination of variables, numbers, and at least one operation.

43 x

CoefficientCoefficient

VariableVariable

ConstantConstant

Essential Vocabulary

Variables

A variable is a symbol that represents a number.

Constants

Fixed values, like 2, 7 or .

Coefficients

Constant factors that multiply a variable or powers of a variable.

Like Terms

Same variables

Laws of Algebra

• Distributive: x(y+z) = xy+xz, (x+y)z = xz+yz

• Associative: (x+y)+z = x+(y+z)

(xy)z = x(yz)

• Commutative: x+y = y+x

xy = yx

• Identity: x+0 = 0+x = x x 1 = 1x = x

• Inverse: x+(-x) = (-x)+x = 0

x(x-1) = (x-1)x = 1

Placement Rule

Always write the variable after the number.

b x 6 write 6b

Using parentheses

b ( 6 ) write 6b

6 ( b ) write 6b

9

Let’s Think & Discuss

Give an example of an expression that is algebraic.

Give an example of an expression that is not

algebraic.

Compare the two expressions: how are the same

and how are they different.

This presentation is developed by Ivan Seneviratne © 2006 purely for personal use.ivanthexplorer@yahoo.co.uk