Maths

# Algebra.

Algebra is a branch of mathematics that substitutes letters for numbers, and an algebraic equation represents a scale where what is done on one side of the scale is also done to the other side of the scale and the numbers act as constants. Algebra can include real numbers, complex numbers, matrices, vectors, and many more forms of mathematic representation.

The field of algebra can be further broken into basic concepts known as elementary algebra or the more abstract study of numbers and equations known as abstract algebra, where the former is used in most mathematics, science, economics, medicine, and engineering while the latter is mostly used only in advanced mathematics.

An example to illustrate this: We can notice that in order for the sentence to be true x + 5 = 9, we must substitute x with the number 4, because 5 + 4 = 9, but in some other equations it is possible to substitute the symbol for a number or more, for example On that, in order to validate the algebraic statement x + y = 10, we might set x equals 5, y equals 5, or x equals 6, and y equals 4.

The Golden Age of Islam, a period from the mid-seventh century to the mid-13th century, saw the spread of Greek and Indian mathematics to the Muslim world. In A.D. 820, Al-Khwārizmī, a faculty member of the House of Wisdom of Baghdad, published “Al-jabr wa’l muqabalah,” or “The Compendious Book on Calculation by Completion and Balancing.” It is from “al-jabr” that we derive our word “algebra.” Al-Khwārizmī also developed quick methods for multiplying and dividing numbers, which are known as algorithms — a corruption of his name. He also suggested that a little circle should be used in calculations if no number appeared in the tens place — thus inventing the zero.

Who is Al-Khwarizmi, the founder of algebra?

• The founder of algebra is Muhammad ibn Musa al-Khwarizmi, who lived in Baghdad from 780 to 854 CE, and was one of the first to write about algebra using words and not letters.

Al-Khwarizmi is the founder of algebra science, and the numbering system adopted in the East and West to this day. Al-Khwarizmi’s greatness is evident in that he founded a new science that did not exist before, as he is the founder of algebra and the father of computers, because algorithms are the basis of programming science now.

The difference between al-Khwarizmi (founder of algebra) and Diophantus (father of algebra).

• The Greek mathematician Diophantus was known historically by the title “father of algebra”, but in recent times many discussions have emerged about whether or not al-Khwarizmi, the founder of algebra, deserves this title instead of Diophantus.

• Supporters of Diophantus point to the fact that the science of algebra invented by Al-Khwarizmi was written in a rhetorical style, while supporters of Al-Khwarizmi point to the fact that he introduced the methodology of “simplification” and “balance”, a methodology originally expressed by the word “algebra”, and he also gave an explanation Details on solving quadratic equations, supported by engineering proofs.

•Al-Khwarizmi, founder of algebra, studied the equation for its own sake. In general, he not only found the equation in the context of solving the problem, but used it to define a class of infinite problems.

• Therefore, people have agreed that the name of the founder of algebra is “Al-Khwarizmi”, and the father of algebra is “Diophantus”.

Terms used in algebra:

_ Exponentiation, a number placed above a number or variable on the left side to indicate the number of times it is used as a factor.

_ The grouping signs, the two parentheses (), the parentheses {}, and the square brackets [], are also used in algebra to restrict algebraic formulas.

_ A number squared or quadratic, a variable multiplied by itself, i.e. used as a factor twice.

_ Binomial, an expression in algebra that consists of two terms between the symbol (+) or the symbol (-).

_ The constant, a number or variable whose domain is a set of one element.

_ Roots of the equation, the numbers that make the equation a correct report when substituting the variables in the equation.

_ Limit, part of a mathematical formula that relates to other terms using addition or subtraction.

_ Formula, a number or variable or numbers and variables related to each other by operations such as addition, subtraction, multiplication, division.

_ Factors, two or more formulas, multiplied by each other.

_ The absolute value of a number is the magnitude of the number, whether it is positive or negative.

_ A polynomial is a term made up of two or more terms.

_ Equation, a mathematical sentence expressing two equal formulas.

_ The parameter is what a variable or number is multiplied by, usually written before the variable.

_ A variable, an algebraic symbol, is usually a symbol and can be substituted for it with one or more numbers.

References :

Deb Russell (10-5-2018), “Algebra: Using Mathematical Symbols”، www.thoughtco.com

Robert Coolman (26-3-2015), “What Is Algebra?”، www.livescience.com

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