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math algebraComprehensive Analysis
Mathematics (colloquially, maths, or math in North American English) is the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".[2] Lynn Steen[3] and Keith Devlin[4] maintain that mathematics is the science of pattern, that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.[5] Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life. Refinements of the basic ideas are visible in mathematical texts originating in ancient Egypt, Mesopotamia, ancient India, ancient China, and ancient Greece. Rigorous arguments first appear in Euclid's Elements. The development continued in fitful bursts until the Renaissance period of the 16th century, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.[6] Today, mathematics is used throughout the world in many fields, including science, engineering, medicine, economics, and the social sciences. Applied mathematics, the application of mathematics to such fields, inspires and makes use of new..." 2) "Algebra" -- As to math algebraalgebraPronunciation: 'al-j&-br& Function: noun Etymology: Medieval Latin, from Arabic al-jabr, literally, the reduction 1 : a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic 2 : any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities (as complex numbers, matrices, sets, vectors, groups, rings, or fields) manipulated in symbolic form under operations often analogous to those of arithmetic -- compare BOOLEAN ALGEBRA - algebraist /-"brA-ist/ noun Pronunciation Symbols Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī titled (in Arabic كتاب الجبر والمقابلة )Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations. Together with geometry, analysis, and number theory, algebra is one of the several main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots. Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.
Algebra may be divided roughly into the following categories:
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