1. Read the text and translate it into Ukrainian Algebra

Algebra is the branch of mathematics which studies the rules of operations and relations, and the constructions and concepts arising from them, including terms, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Elementary algebra, often part of the curriculum in secondary education, introduces the concept of variables representing numbers. Algebra is much broader than elementary algebra and studies what happens when different rules of operations are used and when operations are devised for things other than numbers. Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields, studied in the area of mathematics called abstract algebra. Algebra may be divided roughly into the following categories:

- Elementary algebra records the properties of operations on the real number system using symbols to denote constants and variables. It also studies the rules governing mathematical expressions and equations involving certain symbols. This is usually taught at school under the title algebra (or intermediate algebra and college algebra in subsequent years).

- Abstract algebra, sometimes also called modern algebra, in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated.

-Linear algebra, in which the specific properties of vector spaces are studied (including matrices);

-Universal algebra, in which properties common to all algebraic structures are studied.

-Algebraic number theory, in which the properties of numbers are studied through algebraic systems.

- Algebraic geometry applies abstract algebra to the problems of geometry.

- Algebraic combinatorics, in which abstract algebraic methods are used to study combinatorial questions.

2. Find the English equivalents to the words and word combinations given below. Be ready for dictation: 1) правила, 2) операції, 3) зв’язки, 4) вивчати, 5) конструкції, 6) рівняння, 7) алгебричні структури, 8) аналіз, 9) теорія чисел, 10) чиста математика, 11) постійні величини, 12) змінні величини, 13) додавання, 14) множення, 15) поля, 16) групи, 17) символи, 18) абстрактна алгебра, 18) лінійна алгебра, 19) вектор, 20) алгебрична комбінаторика.

3. Make 7 sentences using the above listed words and word combinations.

4. Say what is meant

1. It is usually taught at secondary school.

2. It studies the properties of vector.

3. It studies the properties common to all algebraic structures.

4. It applies abstract algebra to the problems of geometry.

5. It consists of geometry, analysis, topology, combinatorics, number theory and algebra.

Література:

1. Барановська Т.В. Граматика англійської мови. Збірник вправ: Навч. посібник. Видання друге, виправлене та доповненею – Мова англ., укр. – Київ: ТОВ “ВП Логос-М», 2007. – 384с.

2. Л.В. Мисик, А.Л. Арцишевська, Л.Р. Кузнєцова, Л.Л. Поплавська. Англійська мова. Комунікативний аспект. / За ред. доц. Мисик Л.В. – Підручник. – К.: Атіка, 2000. – 368с.

3. Гужва Т. М. Англійська мова: Розмовні теми: Навч. посіб. Для студентів фак. Інозем. Філології, університетів, ліцеїв, гімназій та коледжів. – Харків: Фоліо, 2005. – 414с.

Практичне заняття № 3

Тема: Послуги працівників готелю.

1. Read, translate and try to retell the text