1. Algebra History

2. Overview

3. Mostly based on the Rhind papyrus written at about 1650B.C.
Can solve problems with one unknown now called the “method of false position”
Rhetorical-problems are stated and solved verbally
Can solve some problems with two unknowns.
However, the Egyptian Algebra was slowed down by their troublesome unit fractions
1.Egyptian Algebra
Mostly based on the Rhind papyrus written at about 1650B.C.
Can solve problems with one unknown now called the “method of false position”
Rhetorical-problems are stated and solved verbally
Can solve some problems with two unknowns.
However, the Egyptian Algebra was slowed down by their troublesome unit fractions
a+7=30 a= =23
2.Babylonian Algebra
B.C.
More advanced than Egypt
had a general procedure similar to solving quadratic equations
dealt with the equivalent of two equations in two unknowns
considered some problems which involve more than two unknowns
Also consider equations of higher degree.
Some symbols but still rhetorical
Taught through examples( no reasons given)
3.Greek Geometrical Algebra
Represent quantities as geometrical magnitudes
In content only slightly beyond the
Babylonians but little practical value as it was in geometrical form
This approach had also slowed down the progress in Algebra for several centuries

4. 6.Arabic Algebra
improved the Hindu number symbols
worked freely with irrationals
Unlike the Hindu, they rejected negative numbers
The word “Algebra” comes from Arab textbook
entirely rhetorical
4.Diophantine Algebra
Ended the Geometrical Algebra
introduced the syncopated style of writing equations but still rhetorical
5.Hindu Algebra
took zero as a number and discussed operations and involve this number
introduced negative numbers to represent debts
developed correct procedures for operating with irrational numbers.
Again, only examples, no reasons or proof
7.European Algebra after 1500
Negative numbers were known but not fully accepted
mostly rhetorical
made many important improvements in symbolism
Symbolic algebra started at only 1637
By end of 17 century, symbolism was used deliberately (previously was just accidental)
8.Modern Algebra
scope of algebra was expanded to the its form and structure and not limited to ordinary systems of numbers
developed non-commutative algebras
demonstrated that complex numbers could be expressed as a formal algebra

5. Algebra
Long long ago, the world developed 7 forms of algebra (Egyptian, Babylonian, Greek Geometrical, Diophantine, Hindu, Arabic and European algebra)
Greek Geometrical Algebra
invented during classical period
Avoided irrational numbers
Geometrical magnitudes
Egyptian Algebra
Based on Rhind Papyrus
Method of false position
Mainly rhetorical-stated and solved verbally
Babylonian Algebra
High developed algebra
Dealt with equivalent of systems
Right now we combined all the different algebra and improve a little to create…
Abstract Algebra
Used now all over the world
Summary

6. CREDITS Heng Teng Hiang Lee Wen Sin jAnice Soo Mona Tan Class: Mo7102
Finalized on:20/3/07