Which area of Economics involves heavy mathematics and also appears to be directly helping the people? The thing is that I am writing a scholarship essay and one of the questions asks me to list my career goals and suggests as to how would the college where I am applying for the scholarship to would help me achieve these career goals. So my career goal is that I want to pursue research in Economics and publish papers. But I want to connect with the fact that I am very much interested in Mathematics and also participate in a lot of community service projects. I, therefore, want to write about an area of Economics something like Econometrics or Quantitative Finance which bears a strong relation to above-mentioned themes because then I will be able to elaborate on how the college offers a strong program in these areas and that this would, in turn, would help me succeed in my career. 

PS. (1) I don't want to hint that I intend to make lots of money. So may be Quant is out. 

PS. (2) A list of courses can be viewed on this link (http://www.lse.ac.uk/resources/calendar/programmeRegulations/undergraduate/BScEconomics.htm).
Some ideas based on the course list:


Environmental economics is doing work to try to understand and mitigate the effects of climate change. Key concepts in this debate, such as common action problems and externalities will feature in EC325 Public Economics.
Game theory is used as a basis for auction theory, which plays a major role in the design of important auctions. Auctions are used, for example, to sell licenses to companies wishing to use the radio spectrum. You can read more about spectrum auctions here.
The market design/matching markets idea is a good one with some real practical applications. For a basic intro, take a look at section 20.5 of this free book. In particular, there is a neat video by Alvin Roth, who won the Nobel prize for work in this area.
Development economics studies the process by which countries do (or don't) escape from poverty and can help us to understand what sorts of policy interventions are likely to be helpful.
Industrial economics (also known as industrial organisation) helps us to understand how competition in markets works (and when it doesn't work). The insights from this field underpin the work of organisations such as the Competition and Markets Authority (the UK's competition regulator) in ensuring that markets deliver good outcomes for consumers. You can read more about competition policy here.