My final portfolio assignment (this semester; fourth revision, fourth time I’ve taught the course) for the mathematical modeling course is to
- Identify and include an excellent piece of mathematical writing you did this semester; alternatively select a piece of writing that posed a substantial challenge to you this semester. The writing sample should be between one and two pages long (not including figures).
- Select some Matlab code you feel represents one of your best efforts at
using Matlab in one of our modeling projects OR select one to three graphs that you feel represent your best efforts at demonstrating the behavior of a mathematical model.
- Letter to Dr.Jinx: Write a 1000-1500 word (2-3 page) letter to me
discussing what you learned in this course. You should include thoughts on
your writing sample and on the code or graph sample you are including in this
- Letter to a friend taking the course next semester: Suppose a friend
of yours is taking this course next semester. What advice would you give your
friend to insure his/her success with this course? What study habits, writing
habits, programming habits helped you the most? Make your advice as specific
as possible, and give examples from your experience this semester. Your letter
should be at least 400 words long (1 page).
I am giving myself a solid A in final portfolio assignments. I did it right this time. It helps that I managed the class well; I really concentrated on making a good learning environment (and trusting that if I did that, gave meaningful assignments, and sufficient assistance, that learning would occur).
I have loved reading the letters. I’ve teared up a few times. There many excerpts and quotes that I want to share. Note: these are excerpted and lightly edited (spelling, grammar) unless otherwise indicated. I am only taking excerpts that show deep learning in some aspect of the course.
- “I knew what I wanted from the course: to be able to use the programming skills I learned as a computer science major in a mathematical setting. To this end, I cannot say that I was disappointed. But when I reflect on what I learned this semester, programming is not one of the things that comes to mind. … The primary thing I believe I learned from this course is the process of mathematical modeling as a whole. … I was fascinated by the entire process … I learned that, at the heart of it, math modeling had very little to do with specific areas of mathematics or programming; it is about representing the real world with the tools you have.”
- ” … In every other math class I had taken, the answers were solid and concrete. … But in modeling, the process of arriving at the results was more important than the results themselves.”
- “In terms of the actual mathematical model involved, the first project was my favorite. I really liked how the concept of chaos applied to weather. … This project helped me understand why it is actually impossible to predict the weather. As we were working on this project, I wondered if chaos theory could be applied to small scale wind patterns that are extremely important for competitive sailing. I found all of the same sailing strategy articles I have already seen and studied. As a side note, I watched the original Jurassic Park in 3D when it was re-released and was very amused when Dr. Ian Malcolm constantly rambled about chaos theory. When I first watched the movie some years ago I had no idea what he was talking about.”
- “I am most proud of learning to use Matlab during your class. As a freshmen taking Calculus II, I struggled to finish the Matlab exercises and by the end of the class I hated Matlab. I had taken no programming classes before coming to Texas A&M, so I just did not have the programming mindset. After three and a half years of classes, I have done some programming and learned the basic elements of coding. Taking Linear Algebra also helped a lot. When you said that Matlab actually stood for `matrix’ laboratory instead of mathematics laboratory as I had assumed, I immediately understood better why I struggled so much as a freshmen. Through your class I came to enjoy using Matlab and appreciate its usefulness in many applications.”
- “With that said, I would like to talk about what I learned about writing during this semester. While I am an English major and consider myself to be a very good writer, this class did pose a challenge to me. I am so accustomed to
writing papers over literary works, such as Shakespeare, that I have developed a method for analyzing something and then determining what it is I want to say and how I should say it. However, mathematics is a long way from Shakespeare and I had to reformulate my analytic approach to my writing. I certainly took more time to understand what was going on in any given situation and took a much longer time in developing my thoughts before ever putting them down on paper. This class helped me develop this different approach and I feel that I am a much better writer than I was before. Discussing mathematics is not a very simple task and I feel that this class has better prepared me to do so in the future.”
- “In my ﬁnal project, it was gratifying to be able to take what I had learned so far and use it to understand an entirely new and much more complicated mathematical model than I had ever worked with before. I was excited to be able to read and understand a fairily dense scientiﬁc paper and make connections with many of the topics and models we had discussed throughout the earlier part of the semester. Wrestling with understanding the bifurcation diagram in the Kirschner and Panetta  paper was also a great learning experience. It forced me to more carefully scrutinize the authors’ explanations of the model and graphs they produced, which in turn really helped me with deciding what needed to go into my report. The understanding I gained through this process is reﬂected in the writing sample I chose to include in this portfolio.”
- “The final project is where everything got interesting. The idea of providing the prices of a set of stocks as input and getting back an optimal portfolio seemed really attractive compared to the rest of the projects. While programming the Efficient Portfolio Frontier on Matlab, I started getting frustrated by the constraints of only having five different companies and the need of typing each price if I wanted another one. I decided to automate the process and use Python since I am familiar with it. … Other than math modeling, this course taught me valuable lessons. One was that I don’t need to be an expert on a topic to do good work on a topic; you only need dedication and perseverance. I really enjoyed working on the EPF. I even worked on it for two extra-curricular events: a one-night Hackathon and I presented it on 3 Day Startup as a business idea. It was really interesting to hear people’s suggestions, there were even some that approached me saying that I should keep working on it.” (Note from Dr. Jinx: Holy crap! I am impressed.)
That is nowhere close to all of them, although it is some of the best of them.
Look at all the deep learning expressed here. I got to help with that. I love my job!