Transcript Mohammed ibn Musa al-Khwarizmi

Abu Ja’far Muḥammad
ibn Mūsā al-Khwārizmī
(780-850AD)
‫محمد بن موسى الخوارزمي‬
Developed by
Ivan 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
variables, numbers, and at least one operation.
3x + 4
Variable
Constant
Coefficient
of
Essential Vocabulary
Variables
A variable is a symbol that represents a number.
Constants
Fixed values, like 2, 7 or p.
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
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.
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This presentation is developed by Ivan Seneviratne © 2006
purely for personal use.
[email protected]