Three Steps to Take Off in Graduate Study
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I have had the best supervisors in my graduate study. They train me with mathematical problems and allow me to think independently.
I summarize the three steps from my own experiences, by which I have the greatest motivation and energy being a researcher.
First, we should be familar with one technical approach. For example, you can learn how to calcualte a bound for a machine learning problem. Also, online algorithms are very popular now. I like solving complicated mathematical problems but also providing managerial insights. So my approaches are mainly focused on dynamic programming, optimal stopping theory, mechanism design. This step is necessary for me to bulid the confidence to be a researcher.
Second, we may need to know how to dig research gaps in existing works. This may help to survive in a field. When reading papers, compare them and find out why it was raised and published in a top journal.
Third, talk at a high level. By this, I mean, we may either be familar with the actual opeations in industry, or we regularly read articles in other fields. I always think that an expert in one field is also familar with the frontier issues in other fields.