Summary Post

What a great summer spent!! At the end of the research project, I am so thankful for this opportunity to conduct research with Dr. Carman on the mathematical analysis of the rank of unit group of Burnside ring, which is a topic in abstract algebra that I’ve always been very interested in. I am so lucky to have a mentor like Dr. Carman who is so responsible and helpful. He discussed many ideas with me and taught me about many mathematical concepts. I am very grateful that Charles Center provided me with this precious opportunity to learn and grow in my first research project. During the seven weeks, I learned to plan a research, to do literature review, and to solve the problems we encountered along the way. In this process, I not only gained a lot of knowledge about Burnside ring and abstract algebra but also learned to think more critically as a researcher. There were several challenging parts in this research and I leanred that doing research is not as simple as taking a course. For example, in week 3 I spent two days finishing the first version of the code in GAP. I was so happy when it could finally generate the correct output, but it could not run for larger group. My original plan was to improve based on the existing algorithm. However, I found that the origin of the inefficiency was caused by its mathetical basis, which means that it can only be improved by finding an entirely new way of approaching the problem. It was a little frustrating when I had to give up the old results and codes and start from the begining, but I learned to think as a researcher.

I keep thinking about how grateful I am for the experience I had during this summer. As entering into my junior year, I hope to continue my work this summer and my passion about research. This summer would not be complete without this research opportunity and the help from Dr. Carman and Charles Center.

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