Algorithm
The concept of an algorithm is now one of the most fundamental notions, both in mathematics and engineering.
An algorithm is 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.
The word “algorithm” originated in the Middle East.
It comes from the Latin version of the last name of the Persian scholar, whose textbook on arithmetic, written in 825 A.D., gave birth to algebra as an independent branch of mathematics.
An algorithm has 5 properties: discreteness, intelligibility, determinacy, mass character, effectiveness.
Discreteness means that the process under description is to be separated into certain instructions.
Intelligibility means that an algorithm should take into account, what orders an executor can understand and carry out and what orders he cannot.
Determinacy means that each instruction must have one single meaning.
Mass character means that a given algorithm may be used for solving a certain class of problems.
Effectiveness 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.
Algorithm- алгоритм
Computer since- програмування(комп’ютерна наука)
Textbook on arithmetic- підручник з арифметики
Algebra- алгебра
Author- автор
Executor- виконавець
A sequence of operation- послідовність операцій
5 properties- п’ять властивостей
Discreteness- дискретність
Intelligibility- зрозумілість
Determinacy- визначеність(однозначність)
Mass character- масовість
Effectiveness- ефективність
Some facts on the development of the number system
1) Counting represents a very important milestone in the progress of civilization.
2) For counters man used sticks, pebbles, his fingers and toes.
3) Historical record give evidence of the astronomical and arithmetical achievements of the early Babylonians, Sumerians, and Chinese.
4) Only about 300 years ago a great mathematician and philosopher, Rene Descartes (1596-1650), represented number pairs by points.
5) Newton was one of the inventors of the calculus which is now studied by college students who are seriously interested in mathematics or physical science.
6) Lobachevsky created one of the greatest masterpieces of mathematics – non-Euclidean geometry.
7) Our number system uses only the symbols 0,1,2,…,9.
8) Thus any integer can be expressed with these symbols in various combinations.
9) The base of our system is ten.
10) The invention of zero and our number system is one of the greatest achievements of the human race, without which the progress of science, industry, and commerce could be impossible.
Number system-Система числення
Progress of civilization-Розвиток людства
Important achievements-Важливі досягнення
Historical records-Історичні записи
Далеке минуле
Попередники
Математика
Фізика
Шедевр
Ціле число