Great times we live in to study a wide range of subjects for free. This time I will not talk about Khan Academy, but lem.ma instead. Meet Pavel Grinfeld, a mathematics professor who kindly uploaded 24.4GB of linear algebra videos on YouTube which you can straight out call private high class lectures if you watch them on lem.ma. His website organizes the videos within different chapters, alongside problems and their solutions. What really made an impression on me is the thoroughness of his explanations and the variety of problem examples. You know, those examples that make you say: “Oh that’s a neat result, I wonder if it’s a coincidence?” So many educators just say the things they have to say and that’s it. Pavel on the other hand truly provides insight and infects you with the beauty of it all. Just watch the beginning of his first video in the determinants chapter.
To me these kind of educators are worth all the gold in the world. No matter how difficult a subject might be, no matter how daunting it might look, they stay on the ground with you and radiate their knowledge from many angles. Clearly this guy is enthusiastic about teaching and math. I can remember all my teachers who were similar, and Pavel will be one of them.
Now why did I mention him specifically? Well his sense of humor is one reason for sure, but there is another. In one of his videos he mentioned to do the mental arithmetic in your head to develop your mental RAM. Mostly I came across articles saying working memory can’t be improved, so it would be cool to know that it is quite possible indeed. I asked him if he had some sources backing up that claim. He answered that he didn’t have any sources, but speaks out his own experience. Good enough for me. Now go forth and multiply, mentally of course.
PS The music in the video is by Art Tatum, playing Caravan.