In mathematics and computer programming , the order of operations or operator precedence is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses can be used to indicate an alternative order of operations or to simply reinforce the default order of operations. The order of operations, which is used throughout mathematics, science, technology and many computer programming languages , is expressed here:   .
Order of Operations
Mathematicians seek and use patterns   to formulate new conjectures ; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic , mathematics developed from counting , calculation , measurement , and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics , most notably in Euclid 's Elements.
SQL and Relational Theory, 2nd Edition by C.J. Date
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols today written as Latin and Greek letters represent quantities without fixed values, known as variables. Just as sentences describe relationships between specific words, in algebra, equations describe relationships between variables. Take the following example:.
Various derivations of the word "algebra," which is of Arabian origin, have been given by different writers. The first mention of the word is to be found in the title of a work by Mahommed ben Musa al-Khwarizmi Hovarezmi , who flourished about the beginning of the 9th century. The full title is ilm al-jebr wa'l-muqabala, which contains the ideas of restitution and comparison, or opposition and comparison, or resolution and equation, jebr being derived from the verb jabara, to reunite, and muqabala, from gabala, to make equal. The root jabara is also met with in the word algebrista, which means a "bone-setter," and is still in common use in Spain. The same derivation is given by Lucas Paciolus Luca Pacioli , who reproduces the phrase in the transliterated form alghebra e almucabala, and ascribes the invention of the art to the Arabians.