You know, I'm glad that you're able to easily manipulate symbols, but when I look at them, my eyes glaze over. It took years for me to learn linear algebra because not a single teacher ever told me "a matrix is also mapping from one space to another one", until Massi Pontil of UCL.
At that point, all the linear algebra I couldn't figure out for the life of me all those years finally made sense. And it was the same for most of my classmates. After that, whenever I saw xY, I thought "the vector x is being moved into a new space", and all the equations made sense to me.
You could explain what an SVM is with equations to me all day, but it's only when you say "you're trying to get the plane to separate your data by a margin as wide as possible" do I actually get it, and then all the math becomes easy.
Different people have different ways of manipulating the abstract symbols, and for me it's to equate them to something I already have experience in. Then I can get the solutions intuitively, rather than pore over pages and pages of equations.
In the end, I quit academia precisely because I couldn't manipulate symbols, and thus my way of learning wasn't compatible with everyone's way of teaching. Maybe I can come up with something better if someone explains things to me in terms I can understand.
An excellent example of how math poorly taught is hard to understand. Nearly all math is poorly taught, therefore nearly all math students drop out in frustration. Only a handful of students can overcome poor instruction.
seems to me that different people can grok stuff in different ways. teaching is about trying to find a way to explain something so the learner can grok it, and in your case a lot of teachers failed before one finally succeeded.
I think anyone is capable of grokking anything, just the time taken to do so is variable. people that give up on "learning" something (academia in your case) just don't want to spend that time.
p.s. I also gave up on academia for the same reasons :)
* Math is full of symbology with implied meaning. For example, theta is often used for 'angle'. How many other symbols have implied meaning like that? Granted, it forms dense, concise, precise papers. Which brings me to my second point.
* If you don't know the symbology, it's difficult to read it. I believe that people suffer reading comprehension problems if they don't know how to verbalize a symbol like 'θ'.
* Lastly, the symbols make it very difficult to google for concepts.
At that point, all the linear algebra I couldn't figure out for the life of me all those years finally made sense. And it was the same for most of my classmates. After that, whenever I saw xY, I thought "the vector x is being moved into a new space", and all the equations made sense to me.
You could explain what an SVM is with equations to me all day, but it's only when you say "you're trying to get the plane to separate your data by a margin as wide as possible" do I actually get it, and then all the math becomes easy.
Different people have different ways of manipulating the abstract symbols, and for me it's to equate them to something I already have experience in. Then I can get the solutions intuitively, rather than pore over pages and pages of equations.
In the end, I quit academia precisely because I couldn't manipulate symbols, and thus my way of learning wasn't compatible with everyone's way of teaching. Maybe I can come up with something better if someone explains things to me in terms I can understand.