Josh Hallam

School Experience

I love school and I love learning new things. When I got out of the Army, I went to school only because I didn't know what to do. I started school as un undeclared major, but a counselor really thought engineering was for me. So, I declared my major in aerospace engineering. I really enjoyed the coursework. The stereotype of an infantryman is some mindless grunt, so I was really surprised how much I enjoyed science. Physics just opened my eyes to the world in a way nothing else had. But, the math. I loved the calculus series. Seeing how all the factoring rules from Algebra 2 came together, finally seeing why we had learned so much stuff that seemed useless, was fascinating to me. Towards the end of Calculus 3 (multi-variable calculus), I was really getting bummed out that my math journey was over. This was my last class in the math department and I only had one more math class left, Engineering Math, through the Engineering Department. I decided to change majors. My next class was differential equations.

Again, I loved it. Seeing the why of all the calculus. Solving real problems with the tools I had been learning most of my life. It was amazing. I tried to take every differential equations class my school offered, including graduate courses, but there were more than I could take. As I studied differential equations, I learned to love chaos theory, which was a pleasant surprise since Ian Malcom was my favorite character in the book Jurassic Park, which was my favorite book as a kid. Two other sub-branches of differential equations that I grew to love were bifurcation theory and perturbation theory. Bifurcation theory is where you find the parameters of a system that cause the behavior of the system to change, like from alternating between some stable points to having no stable points so the solution diverges. In perturbation theory, you find an approximate solution to a problem by solving a similar problem exactly, and adding a small perturbation (less than one, usually denoted by the Greek letter epsilon, ε) that gets expanded as a power series so that the perturbation is raised to higher and higher powers and becomes less significant.

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