Reflection: Where I'm going and where I've been

I'm now winding down the time that I've spent at Grand Valley. It's hard to believe that it's been four and a half years already, but here I am about to graduate. Over the last few months I've been working a part time internship at an IT company, and as soon as I've graduated I'll be starting work there full time. While I may not be asked to prove the limit of a converging sequence, I do think that the skills I've learned over my years at Grand Valley in my mathematics classes will prove useful. 

Calculus

Since I changed my major a significant number of times during my academic career (uh... 5 times...), my mathematics curriculum didn't exactly look like that of a traditional mathematics student. I started with Calculus 1, 2, and 3. At the time of Calc 1 and 2, it simply felt like a lot of memorization of rules of derivatives, integrals, and trig functions. I mainly stuck with mathematics through this time period because it was something familiar to me that I had been doing ever since I was a kid. On the other hand, Calc 3 was a breath of fresh air. My thinking clicked with my professor's explanations, and I felt like I was using my intuition of 3 dimensions in tandem with my understanding of previous classes to do something new. Ultimately, though, looking back, I'm not sure the most important lesson that I learned from Calculus classes even had to do with mathematics. Calculus really taught me a different way to approach a problem - just like we break down a curve with using the Riemann sum method, if you have a big, messy problem that you aren't really sure what to do with, sometimes it's best to try to break it down into many small pieces and look at how they interact with each other. 

Discrete Structures

At the time, I was a computer science major (later I changed to a computer science minor), and therefore I had to take Discrete Structures 1 and 2. To be honest, I don't remember too much about what I learned in this class as far as actual mathematics, but there were two very important lessons that I learned from Discrete Structures 2 specifically, simply because of the grading structure that it had. The class was set up to be a flipped classroom approach. I had taken classes like this before and had a very poor experience, but this one was done extremely well - the professor had done all of his own videos explaining the topics that we were studying in a very clear and concise structure, outside links were provided in case you didn't clearly understand the explanation the videos gave, and well thought out preview questions were done in a poll method at the beginning of each class so that the professor knew what material needed to be revisited. Throughout the semester, we were offered the opportunity to take each section's test multiple times and receive feedback on each attempt. Rather than cramming for a mid term and a final, and having the majority of my grade hinge on my ability to perform in one exam, I was given clear cut goals, and had the opportunity to pursue them and get thoughtful feedback on them throughout the semester. The first lesson that I learned is not all flipped classrooms feel like a professor handing you a syllabus and saying "Good luck"! The second was that I'm much more apt to progress in leaps and bounds when I'm given more control of my own learning (but still with the proper guidance in the background). 

Proofs, Modern Algebra, and Advanced Calculus

As I mentioned, I progressed through my mathematics curriculum in a very abnormal way, and as such wasn't exposed to proofs until my last three semesters of college. My initial reaction was "Wow... this is a pain in the neck". From what I hear, this reaction isn't exactly uncommon. The more  that I learned about proofs and the history of mathematics, however, the more I began to appreciate the history of the proofs that I was doing, and the ingenuity of thinking that was required of the first person that wrote them. While proof based mathematics has a completely different feel to it than computational mathematics, it was a whole new style of problems for me to tackle which tapped well into my background with logic that I had from my Computer Science experience. The biggest lesson that I learned during my proof based studies was that a strong understanding of fundamentals drive your ability to thrive in a field. Just like you can't write a proof without understanding the necessary definitions and theorems, you can't provide a professional service (well, I guess you can try...) without understanding, inside and out, the basics of the service that you are providing. 

One of my favorite questions to ask my mathematics teachers and professors was "When am I ever going to use this". Now that I'm coming to the close of my undergraduate career, I'd like to remind myself of something so that going forward, I never get so caught up in the specifics of what I'm learning at the time. It isn't always about the immediate lesson. Sometimes it's having the experience of approaching and struggling with a new type of problem, a new work setting, or a new set of expectations that will actually pay off at the end of the day.