Once in a while you end up on a website you wish you would have found years ago. My most recent discovery is BetterExplained.com.
I’ve minored in mathematics in University of Jyväskylä but the explanations of complex numbers, pi and e among others on this site were way better than in my classes.
It’s unfortunate that most of the mathematics classes emphasize memorization of difficult formulas instead of explaining the concepts and showing examples of why they’ve been invented and why they are so useful. Some might argue that proving the formulas is the same as explaining them but I’ve found that I usually just end up memorizing the proofs instead of understanding them.
Of course I have to accept part of the blame. I could have used more of my own time to find explanations for these concepts but finding books that explain the concepts of university level mathematics in a simple manner without oversimplification is quite hard.
I think that the current situation is sustained because of two main reasons:
Firstly the professors of mathematics are usually mainly researchers and are forced to teach classes. Because they are so well versed in their subject, it’s very difficult to understand the perspective of novice students. This added with the lack of motivation leads to teachers who don’t even try to put themselves in the shoes of students and who just wish that they were back in their rooms continuing their research.
Second reason is academic arrogance. Unfortunately some of the academics show off their education by using difficult, long words and overly complex explanations. They think that all university students should be able to understand in the same way or else they are stupid. This is not true. Paraphrasing Einstein: “Everything should be made as simple as possible, but no simpler.” Solving difficult problems with science should be all that matters. Everything else is just ego tripping.
Unfortunately the situation in Finland is unlikely to change anytime soon. Because Finland is in the top places in international PISA rankings, there is no hurry to make things better.
This is already the best. Allegedly.