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 An unpublished paper dated 22 January 1684 contains very satisfactory notation and results.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.

Jeremy Wong (29) 4J

GreenWave Project - Individual Reflections 1

In the course of this project so far, there have been many things that i've learnt. Firstly, the problems and difficulties we had in finding a research problem that was viable, do-able, and would result in a project solution that was manageable. Most of our preliminary ideas were rejected due to the lack of coherence to these important aspects of reality. Realism in a project must be ideal, because, ultimately, it is the product that matters, and not the proposal. Our first proposal, about rain trees and the amount of rain cover they gave, was not accepted as it was seen to be extremely easy, and not worth 6 months of our time to do. This forced us to hunt for a much more interesting, in-depth research topic. Hence we arrived at our second idea, to design a clogging-resistant drain design to prevent drains from being clogged up by rubbish. This project, although in-depth and interesting, was not realistic as resources were going to be hard to manage, and the product was extremely difficut to create.

And so finally, we arrived at our present, and most viable proposal. A computer game to prevent more air pollution from ruining our Singapore. Not only is this project realistic, and in-depth and interesting, it also conveniently played up to our abilities, like mine, which is computer programming. Moreover, although seen as non-innovative and "old", this project is actually the first of its kind in Singapore as far as we know. And Google Searches have indeed yielded nothing to prove us wrong. Therefore, we took it up. It is now our responsibility to educate the children in Singapore about air pollution.

During the course of these few weeks, I have learnt to cope with much stress. Teamwork plays an important part in our project, and with Han Lin, Ling Han, and Alex, I hope to be able to influence them to participate much more actively in this and many other projects that might come. So far, our proposal has been the one key document keeping us busy.

By doing the proposal, in which i did the Research Methodology, Rationale for Project, and the Gantt Chart, I have a very clear mind of what we all have to do, what time frame we have, and what other things we can do, about the project. Research Methodology and Rationale for Project were nothing more than proses in which we could explain our Project in detail. The Gantt Chart, however, was exceptionally interesting to me as it was the first time i had effectively drawn one. Using graphical freeware found on the net, this Gantt Chart, was simple yet effective. Divided into blocks of weeks, using the freeware, I could create a feel of what was to come, for all of us. It might not be exactly adhered to, in the future, but, with this Gantt Chart, the feel of the project and its requirements is definitely more solid now, giving us the insight to "plan ahead".

There is nothing more i would want to say now about this project, other than that it does create in me a concern for the environment, especially in Singapore, after all the initial, preliminary research we have done for air pollution. I hope that through this project, I would be able to attain some sort of greater empathy for Singapore's air environment, and, ultimately, contribute to making it cleaner for everyone.

Rationale for Project

One reason for choosing this project is that air pollution in singapore is growing into a serious problem. We do want to find out what is causing it, specifically, which industry sector, etc., and how best to counter it, so as to prevent dire consequences of our air pollution from endangering our lives in the future.

Another reason we chose this topic is the high awareness behind the cause of air pollution, and amount of air pollution, but the lack of proper, systematic information on how to counter it. The government, for example, has not implemented many useful laws to counter the pollution as of yet. Like, buying "green" vehicles is still considered as a voluntary option, and therefore does not aid in countering air pollution in Singapore.

We also find that sources on air pollution do not give specific air pollution details about Singapore, mainly giving basic and broad information about pollution and global warming all over the world. Specific information on Singapore, being scarce, should thus be boosted and better popularized by both our research and end product.


Research Methodology

Firstly, we intend to achieve a conclusion on game type and game concept based on statistical data analysis acquired from samples of our target audience. This includes surveys, interviews and basic observations of our target audience playing games. We intend to spend at least 1 month on this aspect as it will inadvertently affect much of our game's effectiveness in educating and humouring them. 1 month or more should be enough for us to achieve an unbiased, extremely reliable conclusion.

Secondly, we would have to acquire our in-game information. Basically statistics and data about air pollution specifically in Singapore, this information can be acquired from a large variety of sources. Common sources like the WWW, and libraries, would be enhanced with unusual, original sources of information. For example, we will go to car manufacturers to acquire precise data on car emissions and fuel consumption etc. Or even go to factory plants to observe and enquire about emissions. All this information, of course, would be included in our game.

Thirdly, based on our limited "school-based" skills and resources, we intend to creatively enhance effects of our game, including research on how to create fun game concepts so that our target audience would understand and appreciate our game.

Lastly, to back-up our research data and to ensure there are no major complaints about our project or its end product, we intend to track every segment of our research and game development on a website, or web log, such that we could refer to it ourselves. This also allows other people to conveniently comment on our research, and enable us to discover faults within our project that we might otherwise be blind to. For example, if people had any complaints about our game being too "role-playing"-like, they could comment on this website, and thereby influence us to change the game concept. Also, if people found faults with the information on air-pollution we put up on the website, they could correct us by commenting, and thereby prevent much errors in our end-product. This website could even be a "secondary" end-product, giving other students an example, or basic guide, to do their own research project about air pollution in Singapore.

6/2 RE periods

Picked 5 Essential Oils (Anti-bacterial)

1. Lavendar
2. Eucalyptus
3. Bergamot
4. Lemongrass
5. Peppermint
(and more - researched)

Comprehensive Research on

1. Steam Distillation ( probably not needed )
2. Sources for essential oils (shops etc.)

Initial Plans

1. Acquire variables ( essential oils & antibiotics)
2. Compare antibacterial strengths
3. Repeated Experiments - To prove that bacteria does not mutate to defend against essential oils but does so against antibiotics.