Two years have passed since I graduated with a B.Sc in mechanical engineering from the University College of Bergen, which is, by many, not regarded as an institution that provides high quality education. Even though I have fared rather well working as a mechanical designer in the oil industry, I feel that my current knowledge of mathematics and physics is not up to par compared to graduates from more prestigious universities.
Throughout my education prior to College, I had a slightly above average interest in mathematics. I am by no means a natural talent, nor did I work excessively hard, but I do think I had an appreciation for the subject not shared by all my class mates.
On the other hand, I did not appreciate the way mathematics was taught. It was portrayed as this mystical collection of formulas created by super humans long since dead. No mention of the millions of men and women involved, or the intricate history of the subject.
As most others, I did what was expected of me. I memorized formulas, solved equations, drew diagrams and forgot most of it.
It was time for my first Calculus class and I expected a rough ride. Having grown up listening to my uncle’s tales of how mathematics was taught back when he was a student, I was worried that my stay at college would be a short-lived one. My uncle got his degree in Bosnia and Herzegovina back in the 60’s, which had a similar educational system to that of the Soviet Union.
Soon I realized that this was no different from before. The professor taught us techniques instead of focusing on understanding the subject. Unfortunately, I once more did what was expected of me. I worked hard on solving problems, and eventually got straight A’s in all my math-subjects. Even the most simple of proofs were by the professors considered too advanced and when I asked why we were not being taught this, they told me to look elsewhere for answers. Three years passed and the worst part is that I thought I understood the mathematics I had been taught.
After I received my degree I found a job and started working full-time. There was a lot to be learned in the first few months, but eventually a lot of it turns in to routine-work. I was again seeking challenges, and what better place to find some than in the world of mathematics. After some searching I arrived at the MIT open course ware site, and began watching Gilbert Strang’s lectures on Linear Algebra (LA). I did not expect to get too much out of the lectures, as I had already taken LA. I could not have been more wrong. After the first 10 lectures the amount of familiar material started to run thin, and it’s not because I had forgotten it, it was simply because I had never learned it! From this moment on I started getting up 5am each morning to do mathematics for two hours before going to work. In about six months I had devoured most of the topics covered in the MIT course, and had a lot of fun in the process. Even if MIT covered much more than my College did, their style of teaching was still pretty much aimed at the engineers, not mathematicians. The online course gave me a better understanding of Linear Algebra, but was not particularly rigorous.
In the lack of private tutors in my area, I came in contact with a professor of mathematics via Skype. He suggested a book called Finite-Dimensional Vector Spaces by Paul R. Halmos. Armed with digital drawing tablets and headsets, we began meeting once a week where we would talk about theory, and the problems I had tried to solve. This professor was nothing like any I had before, and neither was the book. It was all about proofs and details. It took quite some time to get somewhat comfortable with this new way of thinking about mathematics and I must admit that I still find pure mathematics to be a bit scary. Almost six months passed and I gave my local university a call. It is called the University of Bergen and has a decent math department (or so I hear). They told me that I had taken enough mathematics and could apply for a M.Sc in Applied Mathematics, but that Pure Math differed a bit too much from what I had done earlier. I will know if I get accepted or not in a couple of weeks.
Now, the real reason I am creating this blog is something I read on Terrence Tao’s blog, What’s new. He has a career advice section where he amongst other things writes how important expository writing is in learning mathematics. I had never really written much about math, most of my time was spent solving problems. What I would like this blog to become is a collection of expository articles on subjects I find interesting, challenging or both. My first course at the University (if I get accepted) will most likely be Numerical Linear Algebra, and my articles should reflect that. As a consequence of these articles, I hope to get a deeper understanding of the mathematics I learn, and also improve my English.