Basic number theory definition of divides
Even in cases where a serious mathematician such as van der Waerden has attempted to write a history of mathematics as inspired by the progress made by non-Europeans, the works of these non-Europeans are described in relation to and within the framework of modern European mathematics, or the Greek mathematics of the antiquity, in the sense that, what of the works of non-Europeans that has not been superseded and swallowed by some mathematical work developed by a European mathematician is often not considered worthy of review. There is, unfortunately, a shortage of modern, easily accessible texts putting in the correct historical perspective the progress of mathematics through the millennia. Mathematics has been practiced on every continent, by all sorts of people, for thousands of years, and there are distinguished mathematicians of every imaginable background today doing fantastic mathematics-and this should be emphasized in our teaching. To many of our students mathematics is a European invention, and will continue to be practiced by Europeans and people of European descent. Those of us who work as educators in North America are acutely aware of the fact that a good portion of our students are not of European descent. Getting the history right is not just a matter of intellectual curiosity. However-and this is far from an acceptable excuse-because of my lack of expertise as well my own Eurocentric education I am not able to do justice to the subject.
In this book I have made a conscious effort to highlight contributions by non-Europeans to number theory. In reality the history of mathematics is far more complicated and far more multicultural than a simple straight line connecting Athens of the antiquity to the North America and Europe of 21st century. This Eurocentricity does not stop at the history, and in fact it permeates every aspect of the practice of mathematics. The history of mathematics as told through these and other similar texts runs like this: The Greeks invented mathematics then as Europe was falling into the Dark Ages, Muslims ran to the rescue Muslims carefully guarded mathematics for a few centuries with the arrival of the Renaissance, the Muslims handed mathematics back to the Europeans who gracefully accepted the gift, and who have ever since been championing the progress of mathematics. As impressive as these books are, like many other books on the history of science, they are unfortunately very Eurocentric.
A more current reference for the history of mathematics is. Most of the material in this chapter has been reviewed in the first volume, especially Ch. If it does, then it will be the GCD of A and B.The standard reference for the history of classical number theory is Dickson’s History of the theory of numbers in three volumes. We can traverse over all the numbers from min(A, B) to 1 and check if the current number divides both A and B or not. Greatest Common Divisor (GCD) of two or more numbers is the largest positive number that divides all the numbers which are being taken into consideration.įor example: GCD of 6, 10 is 2 since 2 is the largest positive number that divides both 6 and 10. We have two numbers 5 and 2, then 5%2 is 1 as when 5 is divided by 2, it leaves 1 as remainder. Modulo operation gives the remainder after division, when one number is divided by another. For instance, solving large systems of equations and approximating solutions to differential equations. All of the problems requires more or less math tough. Problems in competitive programming require insight, so just knowing some topics is not enough at all. If you know number theory, that increases your ammo heavily in solving a lot of tougher problems, and helps you in getting a strong hold on a lot of other problems, too. Problems in competitive programming which involve Mathematics are are usually about number theory, or geometry.