I'm a CS major and self studying sheldon ross's first course in probability book, before that I have taken a calculus based probability course, not a strong one, which ended with superficially covering content in ross's 6th and 7th chapter. We proved gamma(1/2) = pi, solved integrals for calculating moment generating functions of some common ditributions, joint pdfs, jacobian determinant etc.
The problem is, although doing a calculus based probability course and being comfortable with linear algebra and calculus I spend a lot of time understanding example problems in this book. My intention was studying some real analysis and measure theory and continue with stochastic calculus and I was hoping that at least at the end of summer I would get my feet wet in stochastic calculus. With this speed it seems that I would only be able to complete the ross's book at the end of summer if I attempt fair amount of exercises for each chapter.
As an example, I was reading sum of independent random variables and the author explains it by convolution and I lost lots of time (hours) just understanding the convolution integral and its applications to the problem but this is only a single example in the book and there are many examples of this kind.
I love to learn math and doing this as an hobby, but I have started to think that I am a bit stupid for learning math. What do you suggest me for studying math books efficiently ? And for professional math major students, do you spend a lot of time on text or do you grasp it very quickly ? Can you give some strategies for learning faster ?
As a note I'm a foreign student and do not have abundance of qualified instructors or tutors who would help me with points I do not understand.
Best Answer
The only way by which you can, learn Math more faster and efficiently, is to devote more time to it.
Note down the important results/theorems and try reproducing the proofs on your own.
Ask yourself dumb questions. Prof. Terence Tao, has a written a very nice article.
Solve all the exercises. By solving problems, one masters the subject and acquires problem solving skills.