In the USA, there is a certain “snobbery” among math teachers, who think that “Problem Solvers” type books are “cheating,” at learning math and physics. You’re supposed to just have the problem, and the final answer, and come up with all the intermediate steps yourself, or you’re a dummy go major in English.
My math/physics tutor advocates this. It’s a mistake, and it keeps a lot of good people out of STEM.
Generating the intermediate steps between question and answer requires a familiarity with the subject matter that people simply do not have. They can acquire it, however, by practicing and memorizing thousands of problems.
The REA Problem Solvers books, and the Schaum’s Outlines, are a blessing to the auto-didact because they show step by step how a problem is done. If you understand each step, then you got it. You’re going to be able to learn that subject. If you cannot follow Schaum’s or a Problem Solver’s book, get a tutor or do something less advanced and build up to it.
I have spoken to both Russians and Chinese engineers about how they learned math, and they said by putting in thousands of hours of problems. They weren’t instant geniuses, like American math teachers seem to expect.
With the Problems Solvers books, you start off slow on a topic, but by the end of the chapter you are slamming the problems out. And when you finish it, what do you do? You do it again. And if you don’t just slam it out, then you do it a third time.
Повторение мать учения
Repetition is the mother of learning.
It’s interesting to note that Charles Dickens lampooned memorization in education in his book “Hard Times,” and this cliched memorization-phobia has persisted in Anglo-American education ever since.
I learned Russian language by memorization 30 years ago. I still speak Russian to this day.
I am learning math and physics by brute force memorization, and it’s working. I don’t need a teacher or a tutor.
We are importing our engineers from the lands where memorization is used in education.
I can teach you, to teach yourself. You can add value to yourself, from the comfort of your home, with nothing but books and notebooks and a smart phone and youtube.
Here’s a lecture about Jewish math students being excluded from Moscow State University in the 60’s and 70’s, so they started their own math group outside of MGU.
What he is describing that Jewish math students did for themselves in the USSR, we can do for ourselves, in our own way. He notes that to do pure mathematics, all you need is a pencil and paper, you don’t need expensive equipment. In other words, we can add massive value to ourselves, without funding or institutional support. We do it by self teaching and memorization.