A significant event that impacted his contributions was his visit to Paris, during which he furthered mathematics under Christiaan Huygens. He made some discoveries about the summing series, which also spurred him to focus increasingly on mathematic problems, beginning first with a calculating machine, and then, calculus.

Leibniz developed the basic features of his version of calculus in Paris, during the 1670s. on 21 November 1675 he wrote a manuscript using the f(x) dx notation for the first time. In the same manuscript the product rule for differentiation is given. By autumn 1676 Leibniz discovered the familiar d(xn) = nxn-1dx for both integral and fractional n.

Obviously. one of Leibniz's greatest contributions to mathematics was his development of calculus, mainly differentiatial calculus and integral calculus.
Another major mathematical work by Leibniz was his work on determinants which arose from his developing methods to solve systems of linear equations. Although he never published this work in his lifetime, he developed many different approaches to the topic with many different notations being tried out to find the one which was most useful. An unpublished paper dated 22 January 1684 contains very satisfactory notation and results.

Aims and Objectives of Project

There are several aims to our project. Firstly, the state of air pollution in singapore is getting serious, and our group wants to do something about it. Our country's education plays a big role in our country's future, and if we start polluting less of the atmosphere, we must also educate our children so that they would not continue to pollute the atmosphere in the future.

Secondly, there are a lot of games and applications on air pollution, but there is nothing of the sort based specifically on Singapore itself, locally. Our game will serve as the first of its kind to solve local air pollution, kept in track with our country's industrial developments and local geography.

Thirdly, we aim to find out more about air pollution in Singapore, so as to be able to critic our local air pollution problems, and solve them subjectively. For example, older, leaded petrol or diesel cars, which produce considerably more air pollution are now banned due to our small city size and congested roads and airs, which would cause smog and smoke to stay in Singapore. This is the kind of solution we would like to implement, or at least, introduce, to the public. Solutions to clean our air up, unique to Singapore.