## what the project meant

The NREUP Summer Research Program at Florida International University sponsored by the Mathematical Association of America (MAA) has been one of the most enlightening experiences of my academic career. I have performed research in various disciplines and this has been my first experience in mathematics. The research was intense, however it showed me a side of mathematics that I have never been aware of. A beautiful side that is only observed through careful logic and reasoning.

This type of research experience motivates lives and encourages the pursuit of further education ....
This research experience has improved my critical thinking skills and will further prepare me for graduate school by enhancing my research background and giving my fellow classmates and me the opportunity to present our work at a presitigious national conference. I enjoyed the experience and I am very grateful to the MAA for providing this magnificent opportunity to minority students like me. This type of research experience motivates lives and encourages the pursuit of further education leading to a doctoral degree in a field one enjoys; such as mathematics.

Mathematics is, to many, another language. I came into this project eager to learn and experience the elegance of math and patience needed to become a researcher.

Before entering the program I knew it would be tough because the subjects were difficult and had to be covered in only 6 weeks, ranging from differential geometry to category theory. Though subjects were abstract and complex, they amazed me. To see how everything I learned throughout my undergraduate career used in this research project was an incredible feeling. I would recommend any undergraduate to participate in similar research programs.

I came into this project eager to learn and experience the elegance of math and patience needed to become a researcher...
As one in a group of four students participating in this program and I can definitely say that I enjoyed it tremendously. I was happy to acquire all the knowledge needed to start the research in just four weeks. The lectures where held each day for eight hours with short breaks for lunch. As a group, we were tested every Friday on what we learned throughout the week.
Once the researched started I learned right away that this was going to take a great amount of patience and thought. More often than not, I found myself staring at a problem not knowing whether it had a solution or not. Asking questions which may or may not have had answers was common place. Though researching through books and books, trying to get ideas and inspiration consumed most of our free time, it was all worth it for the rush when we made breakthoughs. At the end of the day, I was satisfied with what I had discovered or what I could use the following day.

My involvement in this research has made me re-evaluate what I want to do in mathematics and physics. So much so, that now I am only a mathematics major. The project has lead me to specify which branch of mathematics, Algebraic Geometry.

Beyond the lectures, I learned to work together, learn from my peers, and even how to look at problems differently. I was also able to become well acquainted with the professors involved in this program - learning not only academics from them, but philosophy in mathematics.

I consider myself very fortunate to have the experience I had both in developing and presenting this body of work.

I went into this research, unbeknownst to me, blind to the spectrum of the mathematical world. It is an empowering idea to know that I went into a world filled with fog, and to have come out, victorious; enlightened to a world I had very little knowledge of. As a result, this research has influence me to pursue mathematics in addition to physics which will further both my understanding of the world around me and the logic that drives it. I suggest that future participants familiarize themselves with basic logic and methods of mathematical proof, if the participants do not have a background in upper division mathematics.

I went into this research, unbeknownst to me, blind to the spectrum of the mathematical world...

Insights I gained during this research project will be useful for a number of reasons. To begin with, learning to write scientific papers using $$\LaTeX$$ will greatly benefit the presentation of my work as a graduate student. There were several aspects of linear algebra, lie algebra and graph theory I studied which will help me in future courses. I whole-heartedly agree that participation in this research has given me a great amount of knowledge and opportunities that I would otherwise have not had.

Before entering the program I expected that I would encounter very difficult math topics and it would be nearly impossible to comprehend anything in the short amount of time. Especially since we were told that we lacked knowledge of some advanced linear algebra. To my surprise the material was quite straight forward. As a physics major, the linear algebra and lie algebra that I learned here has certainly helped me with my understanding of quantum mechanics.
This program has showed me that original research is accessible to undergraduates if you can learn the fundamentals of what you are looking into. Before the program I thought that original research was done only by geniuses and that it would be nearly impossible for someone like me. Because of this program I will definitely pursue participating in more research programs, whether they are math or physics related.
Before the program I thought that original research was done only by geniuses and that it would be nearly impossible for someone like me.
Besides all of the linear algebra, lie algebra, and graph theory I learned, I also believe that I have improved on my critical thinking skills. Because while I am doing homework or taking a test or quiz, I noticed that now I understand the question that is being asked a lot quicker and come up with the answer faster. I believe this is because of all the pressure we had on learning and understanding the advanced material in a short amount of time.
What I like most about the program was the process of being tested shortly after learning the new material. We would spend the whole day on presenting theorems and proofs and answering questions that challenged us. During the process this was my least favorite time, but in retrospect I quickly realized that this was the time I tested my own understanding and proved to the rest that I did understand the material.
I would recommend this program or any sort of research program to undergraduate students, because it really shows that the world of research is not an impossibility.