Question

Make up an outline of the text. On its basis prepare the rendering of the text using the Algorithm. Algorithm of Text Rendering Треба зробити Алгоритм реферування тексту по таких пунктах. ТекстAlgebra 1 State the title and the author of the text (article). 2.State the main topic of the text (article). 3.Define the purpose, the subject and the object. 4. Make an outline of the text (it is often useful to express each paragraph in one sentence). 5. Join the sentences of the outline together using time and space indicators (фрази, що слугують індикаторами часу та місця) like: at the beginning, at first, then, in the second / third / following / next part of the article /text, later, finally etc. 6. Make a conclusion of the text: say what the author proves and express your own opinion of the text (article) you’ve read. If you like /dislike the text, give your motivation. 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. In its most general form algebra is the study of symbols and the rules for manipulating symbols and is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Near East, by such mathematician as Omar Khayyam (1048-1131). Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values. For example, in the letter is unknown, but the law of inverses can be used to discover its value: . In , the letters and are variables, and the letter is a constant. Algebra gives methods for solving equations and expressing formulas that are much easier (for those who know how to use them) than the older method of writing everything out in words. The word algebra is also used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", and the word is used, for example, in the phrases linear algebra and algebraic topology. A mathematician who does research in algebra is called an algebraist. Algebra as a branch of mathematics Algebra began with computations similar to those of arithmetic, with letters standing for numbers. This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation can be any numbers whatsoever (except that cannot be ), and the quadratic formula can be used to quickly and easily find the value of the unknown quantity . As it developed, algebra was extended to other non-numerical objects, such as vectors, matrices, and polynomials. Then the structural properties of these non-numerical objects were abstracted to define algebraic structures such as groups, rings, and fields. 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 19th century on, many new fields of mathematics appeared, most of which made use of both arithmetic and geometry, and almost all of which used algebra. Today, algebra has grown until it includes many branches of mathematics: -General algebraic systems, -Field theory and polynomials, -Commutative algebra, -Linear and multilinear algebra; matrix theory, -Associative rings and algebras, -Nonassociative rings and algebras, -Category theory; homological algebra, -K-theory and -Group theory. Algebra is also used extensively in Number theory and Algebraic geometry.

Answer 1

Title: Algebra Author: Unknown

Main topic: Algebra as a branch of mathematics

Purpose, subject, and object: The purpose of the text is to provide an overview of algebra as a branch of mathematics. The subject is the study of symbols and the rules for manipulating symbols, and the object is to explain the importance and applications of algebra in various fields.

Outline of the text: 1. Algebra is one of the broad parts of mathematics, along with number theory, geometry, and analysis. 2. Algebra encompasses everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. 3. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as applications in medicine and economics. 4. Abstract algebra is a major area in advanced mathematics, primarily studied by professional mathematicians. 5. The word "algebra" is also used in certain specialized ways, such as linear algebra and algebraic topology. 6. Algebra began with computations similar to those of arithmetic, allowing proofs of properties that are true regardless of the numbers involved.

Rendering of the text using the algorithm: The text titled "Algebra" provides an overview of algebra as a branch of mathematics. Algebra encompasses a broad range of mathematical concepts, including elementary equation solving, as well as the study of abstract mathematical structures. Elementary algebra is essential for various fields, while abstract algebra is primarily studied by professional mathematicians. The word "algebra" is also used in specialized ways, such as linear algebra and algebraic topology. Algebra began with computations similar to those of arithmetic, allowing proofs of properties that are true regardless of the numbers involved. Overall, the text emphasizes the importance and applications of algebra in mathematics and other fields. Personally, I find the text informative and valuable in understanding the significance of algebra in various areas of study and research.