Midterm Reflection:

It’s been another month and I have made a lot of progress. Above, I attached some samples of work that really shows the progress that I have made. In terms of content, I have progressed into much more theoretical territory. The current chapter that I am on is about subspaces and dimensions of linear transformation: in other words, thinking about representing the solution sets of matrices. I feel like this theory does make sense, although as I have gone along I will say that one thing I learned is that it’s not possible to get every single one of your questions answered, and still keep up with content. That is difficult to accept, and a little uncomfortable, but I think it is part of the independent study experience. One thing that I found very helpful more towards the middle of this last month or so was looking at the last few lessons and compiling a written list of terms and proofs that summarized everything. I think that this will be something that I continue to do periodically because it allows me to to synthesize more than the videos do. 

One thing that I am noticing more and more is that for the very theoretical concepts, I understand them, and the examples, and can often get onto the right track with the problem sets, but it is difficult to go that extra step of thinking outside of the box and using creative proofs. This is something that I obviously want to improve at, but I don’t know if there is any way other than continuing on and getting more and more familiar with thinking that way. 

Some things that have been really enjoyable are really diving into theory, and how to apply the basics of what I have learned in the first chapter to the second and third chapters. It’s really picked up to the point that now I am learning about the subspaces of a dimension: a topic that is more conceptual and requires imagining the spaces that vectors and matrices inhabit. This has been very enjoyable so far. 

My posts have also improved because I found a better way to film and also started adding a general update post that is less focused on math and more on the general learning experience. While this is more work, it is also really helpful in terms of appealing to my audience more. I know that not everyone wants to learn theoretical math! 

In terms of my goals for the last bit of the year, I want to get more strategic about the questions that I ask Dr. Prudhom so that I can maximize how much I get out of our meetings, and I want to clarify what the final “assessment” is. That is one thing that I am a little bit confused about, because in the beginning I thought that I heard something about a presentation to some sort of board about the project. If that is true I would love to have a little bit more information so that I can start preparing, and figure out how I would like to communicate my experience.