History of Algebra, Its Main Topics and Influence on Our Life

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Islam is a religion founded by Muhammad, a merchant from Mecca, in the 7th century. Muhammad started sharing his ideas, however it was very difficult because most of the people that lived in Mecca were polytheistic and he was teaching a monotheistic religion. Because of this he move to Medina and started teaching his beliefs. After being in Medina for a while he returned to Mecca with an army of 10,000 people, this was called the Hijrah. He became a military, political and religious leader in Mecca, he converted Mecca in the center of expansion of Islam. Muhammad’s revelations said that he was the last prophet and that Allah was the only God. After the death of Muhammad Muslims didn’t have any prophet, however, they had the four rightly guided caliphs. After several years the muslim’s capital was changed from Mecca to Damascus and then from Damascus to Mecca.

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The Islam is a religion that help a lot in the evolution of science, it help in the advances of all type of sciences. However, muslim contributions in the sciences were most recognizable in medicine, mathematics, and astronomy. In the medicine area, a Persian scholar named al-Razi was the greatest physician of the Muslim world. He wrote an encyclopedia called the Comprehensive Book and he believed patients would recover more quickly if they breathed cleaner air. In the scientific area, muslims translated and studied Greek texts. They solve problems by conducting experiments in laboratory settings. Finally, in the mathematical area, scholars believed that mathematics was the basis of all knowledge. Al-Khwarizmi wrote a textbook in the 800s explaining “the art of bringing together unknowns to match a known quantity.” He called this technique al-jabr — today called algebra. Many of the advances in mathematics were related to the study of astronomy. Muslims had many studies and advances, however this essay will be concentrated in algebra. Specifically, in what process did muslims follow to discover algebra, and what were the subtopics they did research on?

Algebra is the term given to a branch of mathematics which applies numbers, letters, and symbols in order to make reference to multiple arithmetic operations. The discipline known as elemental Algebra serve the purpose of solving arithmetic operations, such as addition, multiplication etc. What differences algebra from arithmetic is the use of symbols which in many cases are letters (a,b,c,d.etc) in replacement of numbers. This symbols replacing a number or a numerical value are known as variables. The use of variables allowed to create general laws and to make reference to unknown values, which makes possible the appearance of equations. Algebra counts with different laws which allowed to known the different properties of arithmetic operations. For example, addition is commutative, a + b = b + this means which no matter the order it will always be the same value in contrast with subtraction which is associated and have an inverse operation. Some of this properties are shared in a single operation, such as in the case of multiplication. Multiplication has both associative and commutative properties. Understand algebra basic concepts means to construct a better base of any more advanced and complex mathematics. The bases of algebra consist of two elements. The first one is the arithmetic basic operations which we all know. The second one is the variables. For example in the operation “X + 3” we are adding to the number 3 a numerical value which we still do not know. If we were told that X + 3 = 10, then I could solve this new equation to know the numerical value of X. In an equation, you want to separate your variables from your numbers. In order to do that we will need to move number 3 to where number 10 is. If we move a number, then the number will pass to the other side of the equation but with the inverse operation. X + 3 = 10 X = 10 – 3. So at the end, in this case, we know X is 7, X = 10 – 3 X = 3. To check your answer you can always replace the variable for the value of itself and start operating.

Algebra began in ancient Egypt and Babylon. Anyone has been given complete credit for the subject of algebra, however, Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi and Diophantus are considered as the “Fathers of Algebra”. Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi developed techniques to reduce and balance algebraic equations. He also introduced algorithms, this is the mathematical operations or rules. Diophantus wrote 13 books designated to “Arithmetic”, it contains algebraic problems with its solutions. Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi was the principle Islamic contributor in mathematics, especially in algebra. In his first part of his book called “the art of bringing together unknowns to match a known quantity” he showed the procedure for solving six different types of equations. This are called: squares equal roots, squares equal numbers, roots equal numbers, squares and roots equal numbers, squares and numbers equal roots, and roots and numbers equal squares. In the second part of the book he justified all his procedures by geometric explanations. Since that time he started justification all his process with geometry. Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi was inspired and based in the Greeks to do and develop all of this methods. When Al Khwarizmi died in approximately 850, algebra continued evolving. The renaissance was a crucial time for algebra and mathematics in general. Leonardo Pisano and Fibonacci are some examples of mathematicians that were very important in the evolution of algebra in the renaissance. After the renaissance algebra has still been used and evolve.

Algebra has six major topics. Symbols and expressions are the most basic aspect of Algebra. Let a letter “x” stand for a number the same way the pronoun “he” stands for a man. Linear equations are equations which have one or two variables. Quadratic equations are types of problem which deals with a variable multiplied by itself. This is known as squaring. The word “Quadratic” cames from “Quadratum” which is a Latin word that means square. Functions are like a machine that has an input and output. The output is related to the input. f(x) is the classic way of writing a function, but there are plenty of other ways. For example,x2is squaring an squaring is a function. f(x) = x2 shows us that function ‘f’ takes ‘x’ and squares it. Algebra of polynomials, “A polynomial is a mathematical expression that is constructed from one or more variables and constants, using only the operations of addition, subtraction, and multiplication.”. x2- 5x- 3, is a polynomial of only one variable, in this case, the variable is “x”. If the terms were not separated by a subtraction symbol, then it will be a monomial like this x2 5x 3. Polynomials at a more advanced level become an abstract study of the structure of Algebra. All of this subtopics of algebra have a certain purpose and all of them use variables instead of numbers to make the equations generally apply.

We use algebra in our daily lives sometimes without notice it, in fact, we need it. Algebra is one of the most important branches of mathematics. Pythagoras, a Greek philosopher, had the idea that “all things are numbers”. He thought numbers ruled our ideas and it’s formes. All the universe follow certain rules and mathematical proportions, for that reason, if we understand the numerical and mathematical relationship of things, we will reach the structure of all things. Math, especially algebra is a basic model of philosophical ideology. Apart from philosophical thoughts as mentioned before, algebra helps you in daily life situation. For example, we purchase ten apples at a store. We need to buy bags in order to store this apple bought. Each bag can hold up to 3 apples. We use a simple algebraic formula to solve this. The number of apples ( represented by the variable “x” ) divided into the number of bags (represented by the variable “y” ) xy. Ten divided into three is equal to 3.333… So I know I need 4 bags in order to store the 10 apples I bought. For all of this reason mention, algebra is immensely important in our lives. Every person should know at least the basics of algebra since it is universally useful in our lives and in our society.

Finally, after reading all our work we can say that we were able to answer our question. We could give a brief explanation about the rise of Islam and their main scientific discoveries. Then we could explain what algebra is and its meaning. We also wrote about how Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi discovered algebra and why this was very important because it showed us what mathematicians in the Muslim society were thinking at the time. Then, we explain the most important subtopics of algebra, in algebra, there are many subtopics but we mention the most common ones which are Symbols and expressions, Linear equations, Quadratic Equations, Functions and Algebra of polynomials. These main subtopics give birth to many of other subtopics in Algebra and in mathematics as a whole. Finally, we explain how algebra affects the world, society, and us nowadays, which shows us the importance of Algebra in our lives. Sometimes, we think algebra or mathematics are not important in our lives if we are going to be artists, or musicians or maybe historians but the truth is that algebra can be applied and is present in daily common lifes situations. We could say that we accomplish our goal that was answering our research question in a detailed way, investigating a lot, and using critical thinking. Also, we could say that we did it in a very organized, complex, and complete way at the same time. We were able to answer when, where, why, who, and what in our research question.

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