Read and translate the text

Unit 1

TEXT 1A  

Mathematics as a science

1. Learn the following active words and word combinations.

to acquire – приобретать

acceptable – приемлемый

definition – определение

quantity –количество

shape – форма

valuable – ценный

obvious – очевидный

to apply –применять

application – применение, приложение

addition – сложение

subtraction – вычитание

multiplication– умножение

division – деление

to solve – решать

branch –отрасль

Give the Russian equivalents for the following words and expressions from the text.

pure mathematics, applied mathematics, proportion, multifield subject, origin, quantity, space, engineering, everyday life, angles, architecture.

Find the answers to these questions by quickly reading the text.

1. What does Mathematics study?

2. What are the branches of Mathematics?

Read and translate the text.

“Mathematics” is a Greek word, and by origin it means “something that must be learnt or understood”, perhaps “acquired knowledge” or “knowledge acquirable by learning”. It is impossible to give a concise and readily acceptable definition of maths as it is a multifield subject. Mathematics is the abstract science of number, quantity, and space, studied in its own right (pure mathematics), or as applied to other disciplines such as physics, engineering, etc. (applied mathematics).

There are several different branches of mathematics, and they are valuable both in science and everyday life. The first actual contact which most people have with maths is through arithmetic. That two and two make four is usually taken for granted as a simple math proportion. Arithmetic, therefore, is a good subject to begin with in order to discover the most obvious characteristic of math as a science. The first noticeable fact about arithmetic is that it applies to everything: to apples, to sounds, to angles, to the ideas of the mind, etc. The nature of the things is perfectly indifferent and irrelevant; of all things whatever, it is true that two and two makes four. Arithmetic consists of addition, subtraction, multiplication, and division of numbers; it helps you work out the change when you buy something.

Geometry takes its name from two Greek words meaning “Earth” and “to measure”. Geometry is the study of shape and angle; it is useful in carpentry, architecture, and many other fields. Architects use geometry to construct buildings. Engineers need geometry to build safe roads and bridges. Because of its immediate practical applications, geometry was one of the first branches of mathematics. The principles of geometry were first discovered and written down by Ancient Greek scholars, but we still use them today. 

Algebra is a kind of mathematical language in which people solve problems using symbols in place of varying or unknown numbers.

Find in the text English equivalents for the following Russian words and word combinations.

умножение, деление, сложение, вычитание, прикладная математика, чистая математика, углы, означать, приобретать, определение, форма, абстрактная наука, происхождение.

 

TEXT 1В  

Bits and bytes

Learn the following active words and word combinations.

binary – двоичный

character – знак, символ

calculation – вычисление

electronic circuits – электросхемы

digital – цифровой

current – ток, поток

represent – представлять

keyboard – клавиатура

arrangement – организация

storage – хранилище

capacity – ёмкость

Give the Russian equivalents for the following words and expressions from the text.

to do calculations, binary code, detect the difference, two states, on or off, to pass through, binary digit, information interchange, avoid, complex.

Find the answers to these questions by quickly reading the text.

1. What is a binary code?

2. What are the units of memory?

 

Read and translate the text.

 

Computers do all calculations using a code made of just two numbers – 0 and 1. This system is called binary code. The electronic circuits in a digital computer detect the difference between two states: ON (the current passes through) or OFF (the current doesn’t pass through) and represent these states as 1 or 0. Each 1 or 0 is called a binary digit, or bit.

We group bits into eight-digit codes that typically represent characters (letters, numbers and symbols). Eight bits together are called a byte. Thus, each character on a keyboard has its own arrangement of 8 bits. For example, 01000001 for the letter A, 01000010 for B, and 01000011 for C.

Computers use a standard code for the binary representation of characters. This is the American Standard Code for Information Interchange, or ASCII – pronounced /aski/. In order to avoid complex calculations of bytes, we use bigger units such as kilobytes, megabytes and gigabytes. We use these units to describe the RAM memory, the storage capacity of disks and the site of a program or document.

 

 

Unit of memory	abbreviation	exact memory account
binary digit	bit, b	1 or 0
byte	B	8 bits
kilobyte	KB	1,024 bytes
megabyte	MB	1,024 KB, or 1,043,576 bytes
gigabyte	GB	1,024 MB, or 1,073,741,824 bytes
terabyte	TB	1,024 GB, or 1,099,511,627,776 bytes

 

Find in the text English equivalents for the following Russian words and word combinations.

двоичный, электросхема, ёмкость, символ, буква, цифра, электрический ток, хранилище, клавиатура, представлять, два состояния, выполнять вычисления.

Unit 2

TEXT 2A 

Real-Number System

Learn the following active words and word combinations.

integer – целое число

notation – oбозначение

at least – по крайней мере

assume – предполагать

refer – относиться

constitute – составлять

certain – определенный

convenience – удобство

field – поле

order – порядок

completeness – полнота

concept – понятие

quotient – частное

set- множество

Give the Russian equivalents for the following words and expressions from the text.

to study, to relate, to begin, to use, to define, to construct, to describe, to denote, to mean, to say, to exist, to fall, to call, to satisfy.

 

Find the answers to these questions by quickly reading the text.

1. What are real numbers?

2. What does mathematical analysis study?

 

Read and translate the text.

     Mathematical analysis studies concepts related in some way to real numbers, so we begin our study of analysis with the real number system.

     Several methods are used to introduce real numbers. One method starts with the positive integers 1, 2, 3…… as undefined concepts and uses them to build a larger system, the positive rational numbers (quotients of positive integers), their negatives, and zero. The rational numbers, in turn, are then used to construct the irrational numbers, numbers like  and p which are not rational. The rational and irrational numbers together constitute the real number system.

     For convenience, we use some elementary set notation and terminology. Let S denote a set (a collection of objects). The notation x S means that the object x is in the set, and we write x  S to indicate that x is not in S.

     A set S is said to be a subset of T, and we write S T, if every object in S is also in T. A set is called nonempty if it contains at least one object.

     We assume there exists a nonempty set R of objects, called real numbers, which satisfy ten axioms. The axioms fall in a natural way into three groups which we refer as the field axioms, order axioms, completeness axiom (also called the upper-bound axiom or the axiom of continuity).