Comprehension
I. Answer the following questions:
1) What does the word algebra mean?
2) What is the object of algebra?
3) What subareas of algebra can you name?
4) What does abstract algebra study?
5) When did algebra appear as a branch of mathematics? What divisions of math existed before that?
II. Translate the following phrases into English:
Выполнять арифметические операции; нечисловой математический объект; теория колец; полиномиальное уравнение; алгебраическое расширение; алгебраическое выражение; первоначально (изначально); неизвестное; неизвестная величина; квадратное уравнение; арифметические вычисления; многочлен; появление алгебры; исчисление бесконечно малых величин.
III. Look at the last passage of the text enumerating subareas of algebra. Use them to complete the following definitions:
_______________ is a branch of algebra in which the specific properties of linear equations, vector spaces and matrices are studied.
_______________ is the study of commutative rings.
________________ is a branch of algebra in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.
_______________ is the study of algebraic structures that are fundamental to study topological spaces.
_______________ is a branch of algebra in which algebraic methods are used to study combinatorial questions.
_______________ is the implementation of algebraic methods as algorithms and computer programs.
_______________ is a part of algebra that is usually taught in elementary courses of mathematics.
_______________ is a branch of geometry, in its primitive form specifying curves and surfaces by solutions of polynomial equations.
_______________ is a branch of algebra in which algebraic methods are used to study combinatorial questions.
_______________ is a branch of algebra in which the properties of numbers are studied from an algebraic point of view.
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