Text. 1. My future profession

When a person leaves high school, he understands that the time to choose his future profession has come. It is not an easy task to make the right choice of future profession and a job at once. Leaving school is the beginning of the independent life, the start of a more serious examination of a man’s abilities and character. As a rule, it is difficult for many school leavers to give a definite and right answer straight away.

As for me (as far as I am concerned), I am a “would be” mathematician - a great piece of luck! This year 1 have managed to cope with and passed entrance competitive exams successfully and now 1 am a “freshman” (a first- year student) of Moscow Lomonosov University Mathematics and Mechanics Department - world-famous for its high reputation and image. It aims to give the students the top level education and to enable them to carry on scientific research. After completing a course of five years our Department graduates can continue their studies and research and defend their thesis (dissertation) to get a scientific degree in both pure and applied fields of modern maths.

I have always been interested in maths. In high school my favourite subject was Algebra. I am very fond of solving algebraic equations, but it was elementary school algebra. This is not the case with university algebra. To begin with, Algebra is a multifield subject. Modern abstract algebra deals with not only equations and simple problems but with algebraic structures}such as “groups", “fields”, “rings”, etc. and comprises new divisions of algebra, e.g., linear algebra, Lie groups, Boolean algebra, homological algebra, vector algebra, matrix algebra and many more. Now I am a first-term (semester) student and study the fundamentals of the calculus.

I haven’t made up my mind yet to choose a field of maths to specialize in.

I am going to make my final decision when I am the fifth year student busy writing my research diploma project and consulting my scientific supervisor. It is equally too early to choose one of the hundreds of jobs to which I might be better suited upon graduation. It is for the future to decide whether it would be school, institute, government or business employment.

Vocabulary

to be fond of =	to like
to deal with	иметь дело с
equation	уравнение
to comprise	включать, охватывать
division	раздел
calculus	счет
make up one’s mind =	to decide
ignorance	невежество, незнание
demands	требования
to compel	заставлять
to suit	подходить
burning desire	жгучее желание
essence	суть, сущность
influence	влияние
employment	занятие

1. Give a summary of the text and discuss it with your friends.

2. Write five or six questions dealing with the information given in the text.

3. Answer the following questions:

1) Why did you make up your mind to become a mathematician?

2) What divisions of algebra do you know?

3) What made you enter the mathematical department?

4) What does a good teacher teach his students?

5) What job would you like to get upon graduation?

Text. 2. Mathematics

Read the text and be ready to discuss it.

What mathematicians study can be summed as relating to four major fields. They look at quantities - how much or how many. There is also the study of structure - how things are arranged together and the relationship between the parts. Then there is the study of space, where mathematicians are interested in the shape of things. Finally, there is change and how things move, over time or through space.

Quantity is mostly concerned with numbers. Mathematicians are interested in both natural numbers and integers. Natural numbers are those which are greater than zero, while integers may be zero itself or more or less than zero. There are four ways these may combine together; these are called operations. In arithmetic, we know the operations as addition (+), subtraction (-), division (:) and multiplication (x). For a fuller, more philosophical understanding of number and the operations that can be applied to them, mathematicians look to Number Theory.

The study of the structure of things is said to have begun with the Greek mathematician, Pythagoras, who lived from 582 to 507 BC. Every mathematician has to learn his most famous theorem. A theorem is a proof of mathematical truth. Pythagoras showed us that in a right- angled triangle, the square of the side of the hypotenuse is equal to the sum of the squares of the other two sides. The hypotenuse is the longest side of such a triangle and that length, multiplied by itself is the same as the length of one side multiplied by itself and added to the other side multiplied by itself. Mathematicians find it easier to write this as: a- +b2=сЗ, (a squared plus b squared equals с squared) where с is the hypotenuse. It is Pythagoras' Theorem which gives us algebra, a branch of mathematics that originated in Arab world. Another Greek mathematician laid the foundations for our understanding of space. More than 200 years after Pythagoras, Euclid used a small set of axioms to prove more theorems. This, we know today as geometry. He saw the world in three dimensions - height, width and length. Developments in other sciences, most notably in physics, have led mathematicians to add to Euclid's work. Since Einstein, mathematicians have added a fourth dimension, time, to Euclid's three. By combining space with number we have developed the trigonometry used in making maps both on paper and in satellite navigation systems.

From algebra and geometry comes calculus. This is the most important tool that mathematicians have to describe change, for example, if you calculate the speed of a moving car or analyse the way the population of a city changes over time. The most significant area of calculus is function, which is concerned with the relationship between argument and result. Indeed, the field of functional analysis has its most important application in quantum mechanics, which gives us the basis for our.study of physics and chemistry today.

There is more to maths than this. For example, pure maths involves a more creative approach to the science. An important field of study is statistics which uses Probability Theory, the mathematical study of chance, to predict results and analyse information. Many statisticians would say that they are not mathematicians, but analysts. However, without maths, statisticians would all agree, there would be no statistics at all.

Vocabulary

to sum up	резюмировать, суммировать
to relate	приводить в связь, быть связанным
to arrange	располагать, классифицировать
shape	форма
quantity	количество
to be concerned with	заниматься чем-либо
integer	целое число
to apply	заниматься ч-л., использовать
to prove	доказывать
proof	доказательство
angle	угол
originate	происходить, появляться
height	высота
notably	особенно, исключительно
to involve	включать в себя