What is algebra?
Algebra is the branch of mathematics that studies the combination of elements such as numbers, letters, and signs to create different elementary arithmetic operations. Algebra differs from arithmetic because it uses letters as abstractions to represent unknown variables or quantities. It also lets you write formulas (algebraic formulas) that express a rule or principle and which make it easier to solve equations.
The term comes from the treatise “The Compendious Book on Calculation by Completion and Balancing” by Muhammad ibn Musa al-Jwarizmi, a Persian mathematician who developed symbolic operations to solve equations systematically.
What is algebraic language?
In the study of algebra, there are different terms for expressing the language of operations. Among them are:
- Algebraic term: this is the simple expression of a combination of letters and numbers, with no addition or subtraction. It is composed of: a sign, which can be positive or negative; a coefficient, which is the number that accompanies the variable; the variable, which is the unknown; and the exponent, which represents the power to which the variable is raised.
- Algebraic expression: this consists of a set of numbers and variables that can be combined with different arithmetic operations. It can be composed of a single algebraic term (monomial) or up to more than three terms (polynomial).
- Algebraic equations: this is the association of two algebraic expressions by an equal sign. They can be first-degree, when the variable is raised to the power of 1, or second-degree, when the variable is raised to power 2, also called a quadratic equation.
What are the origins of algebra?
The first indications of algebraic operations are found in Babylonian mathematics, which used pre-calculated tables to formulate and solve equations. These models were always positive, as they solved only real problems.
Greek mathematicians, on the other hand, developed geometric algebra. Diophantus of Alexandria is considered the father of algebra. His book, Arithmetica, is among the highest-level ancient arithmetic books, though only the first six of thirteen books have survived to today.
The first time zero and the possibility of negative numbers were considered was in the book Brahmasphutasiddhanta, by the Indian mathematician and astronomer Brahmagupta. Later, algebra was developed to more complex levels by the Arabs. The Persians are particularly noteworthy: Al-Juarismi, whose transliterated name gave birth to the word algorithm, and Omar Jayam, the creator of the concept of a function.
What is linear algebra, and how is it used?
Linear algebra is the branch of mathematics that focuses on vectors, matrices, systems of linear equations, and dual space. It is used in most sciences: from civil engineering, enabling modeling and computing all sorts of structures to determine materials, shapes, and strengths of the constructions; to computing, by making image processing, web searches, and image processing for video games and films possible; and even code manipulation to optimize Machine Learning algorithms.