In this post, I want to highlight the stages that occur in research as it progresses along. Let me outline the stages of research for you (in chronological order):
- Find a problem to work on. Make sure it is a somewhat important problem and you can solve it in time. Consult your supervisor whether a topic is a suitable problem for both you and your supervisor.
- Start doing literature review on the topic you have chosen. Make sure you read the important papers in the field. You know it is important when you see a paper have a high citation on Google Scholar. At this stage, you not trying to solve the problem yet. You want to know what are people doing and how might you be able to use previous finding to aid you in your research.
- Once you have a good idea, formulate your problem in a scientific way. You want communicate clearly what you are trying to solve (or show) and how do you want to do it.
- Solve your problem (or show your hypothesis is true). In this stage, you would use the papers relevant to your research and start applying or extending it to your research. There is no quick formula for success here. If you fail, continue to read other papers, until you find the key to solve your problem.
- Write up your solution. This may mean writing it into your thesis or even in a paper. Sometimes, you will find a small problem and may need to revisit the process of solving your bigger problem.
Typically, you will find a solution from a paper. But, how you find that paper maybe another story. One good way to get inspiration is to talk to your friends and colleagues about your problem. Sometimes a different view is just what you need.
Finally, I would like to introduce 2 useful software for research. In order to help researcher with their researches, two companies have created two math-related software respectively - MATLAB and Maple. MATLAB is a widely used numerical computation software in the scientific community. If you want to do number crunching or data analysis/visualization, then MATLAB is for you. On the hand, Maple is a symbolic computation tool. This means that if you want to solve equation to obtain mathematical expressions, then Maple is what you need.
To summarize, I have: (i) presented the process of research, (ii) highlighted the importance of the ability of finding relevant information to your problem, and (iii) introduced 2 useful software. If you would like to read on more on "how to do research", I am including a few sites related to this topic:
- How to do research in MIT AI Lab
- Terence Tao on Research
I hope you find this post useful!