4. Перепишите предложения и переведите их, обращая внимание на модальные глаголы и их эквиваленты.

1. We can store many instructions or many items in a computer.

2. A resume should list your work experience.

3. All candidates must have research strengths in one of mathematical fields.

4. When he was a child he was allowed to do exactly as he liked.

5. You are to define this term in a more precise and formal way.

6. They have to give a reason and possible justification for this restriction.

5. Перепишите предложения. Подчеркните Participle I и Participle II, определите их функцию в предложении. Переведите предложения.

1. The law just referred to was discovered by Newton.

2. Considered from this point of view the question will be of great interest.

3. Each branch of mathematics is built on the basis of the same logical pattern: first basic objects, relations and operations are introduced, and then axioms are formulated.

4. When being ready to solve a problem, you can get the computer to sort through its stored facts and use only the proper ones.

5. The phenomena accompanying this reaction are well understood.

6. Прочитайте текст, перепишите и письменно переведите 1, 2, 3 и 5 абзацы.

algebra

Algebra is actually an extension of arithmetic. It uses the same operations, the same laws of order and grouping and the symbols as arithmetic. In fact, algebra is often known as generalized arithmetic. Algebra differs from arithmetic in its use of letters to stand for numbers, its wide use of equations and inequalities in problem solving, and the inclusion of negative and imaginary numbers in its operation.

The word algebra comes from Arabic word “al-jebr”, which was a word in a title of a book by the Arab mathematician al-Khowarizmi in the ninth century. This word referred to certain topics dealing with equations.

Algebra introduces some additional symbols not used in arithmetic. The symbol ≠ means ‘is not equal to ‘’. One may write¹: 6≠4. Multiplication is indicated by a dot or by parentheses around the factors and no sign between the set of parentheses.

Algebra usually begins with a study of the properties of the natural numbers, followed by the properties of the integers, the rational numbers, and the irrational numbers. The natural numbers are the numbers used in counting. They are represented by the symbols 1, 2, 3 ... (the three dots indicate an unending succession of numbers). If a + sign is put in front of each natural number, the set of symbols is known as the positive integers. If +2 may be compared with a reading on a thermometer of two degrees above zero, then -2 would be considered² as two degrees below zero. If each of the positive integers had its + sign, the set of symbols so created would be called the negative integers. The positive integers, the negative integers and zero form the set of integers.

A rational number is one which can be expressed as the quotient of an integer and a nonzero integer. The proper and improper fractions of arithmetic are rational numbers. Any periodic decimal is also a rational number. An irrational number cannot be written as the ratio of an integer to a nonzero integer, nor as periodic decimals. The set of rational numbers together with the set of the irrational numbers comprise the real numbers. This is why rational numbers are often defined as numbers which can be expressed as decimals. Properties that hold true³ for the integers and the rationales in general hold true for the real numbers.

The algebraic expression is composed of symbols which are combined by one or more of the operations of algebra. An algebraic expression represents a number. A term is composed of a single symbol, or symbols, combined by any of the operations of algebra except addition or subtraction.

Notes:

¹ – можно записать

² – рассматривалось бы

³ – считаются истинными