B. Match the words to make phrases

5 6 7 8 9 10 11

1 applied A of mathematics

2 branch B developments

3 mathematical C variety

4 final D mathematics

5 second E terms

6 knowledgeable F model

7 real G solution

8 major H stage

9 mathematical I life

10 wide J mathematician

Reading

Applied mathematics

Most of the major developments in mathematics were the result of trying to solve a particular problem. When faced with a problem, people would ask themselves 'How can we do this?¹'What's the best way of doing that?¹ Thus, mathematics arose. Today, we have many different branches of mathematics, all of which can be used to answer questions like the ones above.

When mathematics is used to solve problems in other related areas of life, it is known as applied mathematics. Mathematics is applied, that is, used, to provide us with answers and solutions. It is used in numerous ways. A few examples are numerical analysis, engineering and programming. In these and other areas, applied mathematics takes problems from real life, and gives us successful and creative tools for solving them. Often, the first step when using applied mathematics is to create a mathematical model. This is a description of the problem in mathematical terms. This model is then studied to obtain exact or approximate solutions. If the solution is exact, the model is applied to the problem; if it is approximate, the model is refined until it is exact. Then, the conclusions are interpreted and explained in comprehensible terms. Often the model is changed to be more realistic or to include more features of the problem. Thus, the modelling process may involve many adjustments. The second stage is the final solution to the problems mathematically formulated in the first stage. Mathematics is used or applied to other fields to solve problems in these fields.

It is often not clear which mathematical tools will be useful in the study of a new problem, for example, algebra or differential calculus. For this reason, applied mathematicians need to be well trained in a range of mathematical areas so they will have a wide variety of mathematical tools available to them. They must not only be skilled mathematicians but must also be knowledgeable in the specific area to which mathematics is being applied. For example, in dealing with business and industry, a knowledge of economics is necessary. In this way, a good applied mathematician can then create and interpret appropriate models. A good applied mathematician must therefore be knowledgeable in both mathematics and the field of application in order to successfully deal with a problem.

When it comes to creating models, the mathematician will make choices about which factors to include and which to exclude. The goal is to produce a model that is realistic enough to reflect the main aspects of the problem being studied, but simple enough to be treated mathematically.

Sometimes the mathematician has to either simplify this model so it can be analysed, or devise new mathematical methods that will allow the model to be analysed. The modelling process may involve a sequence of models of increasing complexity. Problems sometimes lead to new mathematical methods, and existing mathematical methods often lead to a new understanding of the problems.

Mathematics in its most useful, practical form becomes a tool with which we can improve our world. That is exactly what applied mathematics is and what it does.

Pronunciation guide

Adjustments

Approximate

Numerous

B Comprehension

Read the text. Then put the events (A-F) below in the correct order, from first to last, to show the procedure for using applied mathematics.

EVENT 1.................. A The revised model is applied.

EVENT 2.................. B The model is adjusted.

EVENT 3.................. C A mathematical model is created.

EVENT 4.................. D A problem arises.

EVENT 5.................. E A solution is found.

EVENT 6.................. F Approximate solutions are obtained.