## Algebra:Linear Thinking and Solving First Degree Eqationsby: Juan Pablo GutiĆ©rrez, Santiago Mendoza and Samuel Camacho

### What is Algebra?

Algebra is the branch of mathematics that studies the combination of elements of abstract structures according to certain rules. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols.

### Two Great Mathematicians of Algebra: al-Khwarizmi and Diophantus of Alexandria

Diophantus of Alexandria and al-Khwarizmi were known as "the fathers of algebra". Diophantus of Alexandria wrote a series of books called "Arithmetica" which was a series of algebraic problems that helped to create and develop the number theory. The number theory is the series of patterns between numbers. Like composite-prime, even-odd, or negative-positive. The other "father of algebra" was al Khwarizmi. He was born in 780 A.D. He worked on The House of Wisdom in Baghdad. What did he do? He wrote Algebra in words, but al-Khwarizmi's most important contribution was the idea of "completing the square". He introduced his method with the equation x^2+10x=39.

Step 1: Assume "ax^2+bx+c"

Step 2: Take "b/2" and square it ("w")

Step 3: Add "w" to "c"

Step 4: Square root ("w")

Step 5: Subtract "b/2" from "w"

Step 6: Square that value to complete the square

### History of Algebra

The roots of algebra can be traced to the ancient Babylonians, at 2000 before Christ, who developed an advanced arithmetical system with which they were able to do calculations in an algorithmic fashion. The Babylonians developed formulas to calculate solutions for problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations. Algebra was basically made by Babylonians and Egyptians, and algebra has been changing and improving since it was made, until nowadays, where we learn algebra and mathematicians teach and still try to improve even more algebra.

### The Four Main Events of Algebra

There are some events in the history of Algebra that were important, like Egyptian algebra, Babylonian Algebra, Greek Algebra, Arabic Algebra, Hindu Algebra, Dipohantine Algebra, European Algebra after 1500, and Abstract Algebra. But probably the four main events of algebra would be Egyptian Algebra, Babylonian Algebra, Diophantine Algebra and Abstract Algebra. Egyptian Algebra was were algebra started. They created algebra and the equations that contains. Babylonian algebra was where algebra was improved with new equations. Dipohantine Algebra was when Dipohantus of Alexandria, a "father of Algebra", improved algebra by the number theory and wrote a book called "Arithmetica". Finally, Abstract Algebra, because that is present day Algebra, so that is the algebra we know today and the algebra mathematicians still try to improve.

Algebra Timeline: file:///Users/juanpablogutierrezmunoz/Documents/Algebra%20Timeline.pdf

Credits:

Created with images by ericfleming8 - "mathematics math abstract algebra"

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