Fairleigh Dickinson University (Part 1 - Professor Dolbin)
(8:10 - 12:05)
Today
was the first day of my new internship with Professor Dolbin. I began studying
from a textbook for undergraduates recommended by the professor, called “Abstract
Algebra: an introduction” by Thomas W. Hungerford. I began studying the concept
of field extensions, which are essentially fields that act as vector spaces
over other fields. (It sounded just as complicated to me when I first saw it.)
Throughout the day, the professor talked with me about the concepts, provided
additional exercise problems for me to solve or prove, and clarified certain
notions. At first, I had a difficult time grasping the higher-level concepts,
but with some guidance I managed to understand an entire chapter of the
textbook. I have already learned so much more about abstract algebra under his
guidance, and I hope to continue this learning process so that I will be
well-equipped to handle even more difficult problems in abstract algebra later
on. I’m really thankful for Professor Dolbin, as he devotes a significant
amount of time to help me learn.
(Part 2 - Professor Farag)
(1:00 - 3:00)
In class, we tackled another interesting and difficult problem in the field of group theory. We further discussed the "First Homomorphism Theorem," which relates groups that are deceptively different. Also, in the middle of class the students and the professor suddenly entered a gigantic, almost-philosophical debate about whether things are "well-defined"; the problem arose when a student suggested a function that might not always map a value of "x" to the same value of "y." However, after this heated discussion, we settled down and had a good, long laugh about it, and the rest of the day passed by normally. I finished the notes for the past week in time, although I have yet to write the solution set for the newest homework assignment. Surprisingly, I learned that these problem sets might not be as difficult as I had originally assumed!
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