Учебно-методическое пособие для студентов I-II курсов заочного отделения неязыковых факультетов

Adult and Continuing Education

The concept of continuing (or lifelong) education is of great importance to Americans. In 1991, 57 million Americans 17 years and older furthered their education through participation in part-time instruction, taking courses in universities, colleges, professional associations, government organisations or even churches and synagogues. Most participants in continuing or adult education have a practical goal: they want to update and upgrade their job skills. As a result of economic changes and the rapid advance of the "information age," the necessity to acquire new occupational skills has increased. Adult education thus fills a need of many Americans who want to improve their chances in a changing job market. This is one explanation for the continuing growth of adult education classes over the past several years. Of course, not all people who take courses in adult education do this for job-related purposes. Many simply want to broaden their knowledge or learn something they would enjoy doing such as printmaking, dancing, or photography.

Continuing education courses are provided mainly by community or junior colleges and mostly take place in the evenings. The types of courses adults enrol in range from hobby and recreational activities to highly specialised technical skills. Courses in business, health care and health sciences, engineering, and education are most popular. Most of these courses are taken by employees because the employer provided major support for educational programs, either by paying part of the fees, giving time off, or providing other incentives. While some 50 percent of all people in adult education are enrolled in programs sponsored by educational institutions, about 15 percent were sponsored directly by business and industry. Over 80 percent of all companies today conduct their own training programs. Many large corporations offer complete degree programs, and some even support their own technical and business colleges and universities.

In the 1980s about 5 million students took industry-sponsored university programs and roughly twice that number were involved in corporate education of some kind. A great many universities and colleges, public and private, also admit part-time students to their programs. Many offer evening courses so those who work can attend, and most institutions have summer semesters, as well. This way many American are able to earn a university degree, bit by bit, and year by year. State universities have long "taken education to the people" by setting up extension campuses in small towns, or largely rural areas. Therefore, someone at home in Stevens Point, Wisconsin, for example, will be able to take courses taught by professors from the University of Wisconsin’s main campus in Madison.

THE FACULTY OF MATHEMATICS

The Whole Numbers

Generally when numbers are written the numerals are grouped by threes so that it becomes easy for the eye to distinguish them. Thus five million six hundred seventy-five thousand four hundred ninety two is written as 5 675 492. The groups of threes are often separated from one another by commas, that is: 5,675,492.

Numbers, when written, are often described by the number of numerals they contain, the number of places. Thus 72 is a two place number and 4895 is a four place number. Four place numbers, especially dates, are often written without commas or spaces, as 1905, 1943.

Addition of Whole Numbers

The addition of two or more numbers is an arithmetic operation by means of which a new number is obtained. This new number contains as many units as are contained in all added numbers taken together. The numbers that are added are known as the addends. The number resulting from addition of two or more numbers is known as the sum. The sign for addition is + (plus).

Addition is best performed when the numbers are written in columns so that units, tens, hundreds, and so forth are written vertically. For example, the sum of 1,562 and 1,891 is obtained, as follows:
1,562

+1,891

3,453
Addition is performed from right to left. We can easily observe that addition of 8 to 35 gives the same result when 35 is added to 8. In either of the operations of addition the sum is 43. So the sum of two or more numbers does not change when the order, in which the numbers are added, is changed.

Subtraction of Whole Numbers

Subtraction is an arithmetic operation by means of which one of the addends is obtained, when the sum and another addend are given. The result is known as the difference of the two given numbers. The number from which another number is to be subtracted is known as the minuend. The number that is subtracted is known as the subtrahend. Subtraction is an operation opposite to addition. The sign is - (minus).

Subtraction of many-place numbers is performed as follows:
986

-354

632
We begin subtraction from the right and we subtract the numbers in the same column. Thus: 6 – 4 = 2; 8 – 5 = 3, etc.

Multiplication of Whole Numbers
Multiplication is an arithmetic operation by means of which one number is repeated as an addend until it occurs as many times as it is indicated by another number. There are two numbers involved in multiplication. The result of the operation of multiplication is known as the product. The number which is repeated is known as the multiplicand. The number by which the multiplicand is multiplied is known as the multiplier. The sign is “x“or “”.

Division of Whole Numbers

The operation by means of which a factor is obtained when the product and the other factor are given is called division. The arithmetic operation is performed on the number, which we take as the given product. In division this number is called the dividend. The given factor is known as the number by which the dividend or the product is to be divided. This number is called the divisor. The result of the division of the dividend by the divisor is called the quotient. The sign of division is “:” or “/“ in England.

Fractions
A fraction is a part of a unit, such as ½; ¼; etc. A fraction has a numerator and a denominator. For example in the fraction ¾ - 3 is the numerator, and 4 is the denominator. In the fraction the numerator is divided by the denominator. The fraction 2/7; indicates that 2 is being divided by 7.
A mixed number is an integer together with a fraction, such as 2 3/5; 7 3/8 etc. An integer is the integral part and a fraction is the fractional part. An improper fraction is one in which the numerator is greater than the denominator, such as 19/6; 23/4 etc.
To change a mixed number to an improper fraction you must:

a) multiply the denominator of the fraction by the integer;

b) add the numerator to this product;

c) place the sum over the denominator of the fraction.

For example let’s change 3 4/7 to a fraction.

The solution is: 7 x 3 = 21; 21 + 4 = 25; 3 4/7 = 25/7 .

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