Учебное пособие по английскому языку для студентов 2 курса факультета математики и информационных технологий Уфа риц башгу 2020
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- Бұл бет үшін навигация:
- Before you read Mark the following sentences as true or false
- Reading Read the text and check your answers. Algebra Algebra
UNIT 7. ALGEBRABefore you start Read the key words: algebraic extension – алгебраическое расширение witness – свидетельство, доказательство essentially – в сущности indeterminate – мат. неизвестная величина amount – равняться, быть равнозначным substitutе – заменять emergence – появление infinitesimal calculus – исчисление бесконечно малых величин roughly speaking – грубо говоря Before you read Mark the following sentences as true or false: 1) The word algebra came from the Arabic word meaning “non-numerical object”. 2) Before the 16th century, mathematics was divided into only two subfields, algebra and geometry. 3) Before the 19th century algebra and arithmetic meant the same and covered the same mathematical topics. 4) Algebra is intended to perform operations of arithmetic with non-numerical mathematical objects. 5) Nowadays, algebra appears to be a collection of branches sharing common methods. Reading Read the text and check your answers. Algebra Algebra (from Arabic al-jebr meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. Algebra arose from the idea that one can perform operations of arithmetic with non-numerical mathematical objects. These objects may have various basic properties, and, presently, algebra is divided into several subareas which include linear algebra, group theory, ring theory and combinatorics. Elementary algebra is the part of algebra that is usually taught in elementary courses of mathematics. Abstract algebra is a name usually given to the study of the algebraic structures (such as groups, rings, fields and algebras) themselves. The adjective "algebraic" usually means relation to algebra, as in "algebraic structure". For historical reasons, it may also mean relation with the roots of polynomial equations, like in algebraic number, algebraic extension or algebraic expression. This comes from the fact that, until the end of the 19th century, algebra was essentially the same area as the theory of equations. A witness of that is the fundamental theorem of algebra, which nowadays is not considered as belonging to algebra. Algebra can essentially be considered as doing computations similar to that of arithmetic with non-numerical mathematical objects. Initially, these objects represented either numbers that were not yet known (unknowns) or unspecified numbers (indeterminates or parameters), allowing one to state and prove properties that are true no matter which numbers are involved. For example, in the quadratic equation are indeterminates and is the unknown. Solving this equation amounts to computing with the variables to express the unknown in terms of the indeterminates. Then, substituting any numbers for the indeterminates, gives the solution of a particular equation after a simple arithmetic computation. As it developed, algebra was extended to other non-numerical objects, like vectors, matrices or polynomials. Then, the structural properties of these non-numerical objects were abstracted to define algebraic structures like groups, rings, fields and algebras. Before the 16th century, mathematics was divided into only two subfields, arithmetic and geometry. Even though some methods, which had been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from 16th or 17th century. From the second half of the 19th century on, many new fields of mathematics appeared, some of them included in algebra, either totally or partially. It follows that algebra, instead of being a true branch of mathematics, appears nowadays, to be a collection of branches sharing common methods. In fact, algebra is, roughly speaking, the union of elementary algebra, abstract algebra, linear algebra, commutative algebra, computer algebra, homological algebra, algebraic number theory, algebraic geometry, algebraic combinatorics. жүктеу/скачать 0.59 Mb. Достарыңызбен бөлісу:
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