Algorithm

The term "algorithm" has come into usage quite recently. Its appearance in our life is due to the rapid rise of computer science which has the study of algorithm as its focal point.

The word "algorithm" originated in the Middle East. It comes from the Latin version of the last name of the Persian scholar Abu Jafar Mohammed ibn Musa al-Khowaresmi (Algorithmi), whose textbook on arithmetic, written in 825 A. D., gave birth to algebra as an independent branch of mathematics. In the 12th century this textbook was translated into Latin and it had a great influence for many centuries on the development of computing procedures. The name of the textbook’s author became associated with computation in general and used as a term "algorithm".

The concept of an algorithm is now one of the most fundamental notions, both in mathematics and engineering. An algorithm is defined as an exact and intelligible order for a certain executor to carry out a sequence of operations, aiming at getting certain results or solving a given problem.

An algorithm has 5 properties of its own. The first of them is called discreteness. This property means that the process under description is to be separated into certain steps (instructions).

The second property of an algorithm may be called its intelligibility. It means that an algorithm should take into account, what orders an executor can understand and carry out and what orders he or it cannot.

The next distinguishing feature of an algorithm is that all vagueness must be eliminated – each instruction must have one single meaning. This property of an algorithm is called the property of determinacy.

Another property of an algorithm is its mass character, which means that a given algorithm may be used for solving a certain class of problems.

The last property of an algorithm is its effectiveness. It means that the exact carrying out of all orders of the algorithm should lead to termination of the process after a finite number of steps.

TEXT 4

Read the text and say why Math is one of the most important subjects at school.

Mathematical component of the curriculum

Educators consider mathematics as one of the best media for the development of thinking skills. The often-heard opinion that a person who is good in mathematics could be a good chess player does not refer to computational ability but rather to reasoning ability. In the process of teaching mathematics, the teacher must be able to seize opportunities for developing the skills of reasoning, for developing in the children habits of organized thinking.

Mathematics should not be regarded as an isolated body of knowledge. The teacher should be able to see mathematics in the environment and in other disciplines. This is pedagogically important, since the teacher must use or provide experiences or situations that are the starting points for children to discover and develop the inherent mathematics. In technical language, we say that a physical situation is used to introduce and develop a "mathematical model" of the reality of the situation. On the other hand, the teacher who can readily see mathematics in the environment may be able to point to those different situations to which similar mathematical descriptions apply.

National drives and politics impact curricular programmes in mathematics. The teacher should become aware of national goals and policies and should then seek to bring about a closer relation between what is taught in the classroom and what is learned and done outside of it in terms of these national efforts, at least within the child’s surroundings or community. Examples might include development of the countryside, better nutrition improved health and sanitation, and population education. Economics oriented activities may be simulated in the classroom.

Special teaching plans are needed to help a child understand "volume", not only as something upon the button of a radio set, which is within the child’s experience, but also as a mathematical concept of the quantity of space occupied. Again, the younger children usually think of multiplication as repeated addition. They, therefore, may find it confusing to conceptualize 3/4 x 1/4, where repeated addition does not apply. The sensitive teacher who anticipates this difficulty would plan her teaching strategy to broaden the idea of multiplication before confusion arises. A similar situation arises when children are drilled in subtraction to use the following language:

10 take away 1 is 9. 10 take away 2 is 8. 10 take away 3 is 7.

The drill emphasizes the "take away" idea of subtraction to the exclusion of comparison (i.e., how much more, or how much less), which also invokes subtraction.

TEXT 5

Read the text and be ready to tell about the most important milestones in the history of the number system.