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I totally agree that many mathematicians omit steps and make it really hard to follow what they are doing. As with most advanced subjects, what comes off as "o
by atrettel 3y ago
I totally agree that many mathematicians omit steps and make it really hard to follow what they are doing. As with most advanced subjects, what comes off as "obvious" to experts isn't always obvious to others (sometimes called the curse of expertise).
For more advanced subjects in mathematics, I like to find books with lots of problems that I can work on. That is difficult, especially at the graduate level, but when I find a good book with good problems, I can usually learn the material quite well. Many books only have the answers but some have full step-by-step explanations. I always first do a problem without looking at the answer or explanation, so that I learn by making mistakes (a good way to learn). This then gives me a much more hands-on feel of the material from start to finish.
It would be helpful if you could say what subjects you are interested in learning more about. Then somebody could recommend resources, etc.