My goal in the future is to earn a Ph.D. in Mathematics, specialized in combinatorics and/or algebra and do more research in these areas. However, my ultimate goal is to use the logic of algebra and combinatorics, combine with the understanding of neuroscience to explore one of the most complex systems existed for million years - the brain. Even though at St. Olaf College, I have been involved in both Mathematics and Neuroscience research, my experience in integrating the two areas is still limited. Therefore, I want to have more research experience in the field of algebraic geometry and combinatorics so that I have more understanding of the structure of algebra. Besides one mathematics project I did in the past, most of my experience in mathematics …show more content…
in Mathematics, specialized in combinatorics and/or algebra and do more research in these areas. However, my ultimate goal is to use the logic of algebra and combinatorics, combine with the understanding of neuroscience to explore one of the most complex systems existed for million years - the brain. Even though at St. Olaf College, I have been involved in both mathematics and neuroscience research, my experience in integrating the two areas is still limited. Therefore, I want to have more research experience in the field of algebraic geometry and combinatorics for more understanding of the structure of algebra. Besides one mathematics project I did in the past, most of my experience in mathematics come from textbooks and classes. I want to have an opportunity to think outside the box, to use tools that I have never used before and approached problems that are not designed to find the solution from the textbooks. Joining MSRP program also means that I will have the opportunity to work with more people in the field of mathematics. I realize that for a particular math problem, different researchers have various ways to approach and solve it. Working in a research environment with many different mathematicians can help me to increase my creativity in approaching a problem. Moreover, MSRP program will intensively expand my knowledge in algebra and give me a new and fresh perspective on what I need to do to in the future if I want to go …show more content…
I want to use the incredible logic of mathematics in algebra to explore the neural systems, specifically neural algebra. I want to explore more about the structure of mathematics, to draw a connection between different mathematical objects and to explain the bizarre questions not only in mathematics but also in other natural science areas, especially neuroscience. I am amazed at the idea of representation theories in abstract algebra that I can reduce problems in abstract algebra to problems in linear algebra by using linear transformation. What if there are more structures in mathematics that can actually help me to answer questions in neuroscience that other subareas in neuroscience struggle to answer. I want to be the person to find more of these relationships. Moreover, a better understanding of mathematical objects is extremely crucial in computational modeling and neuroengineering. I hope that I can collaborate with people in these areas to develop better systems of neural mapping and to have more insight into the area of system neuroscience. Finally, I want to show people that the applications of mathematics are not limited in the world of numbers but also in other natural science