I can do most of the problem in Goldsten/Poole

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I am studying classical mechanics by myself (math major). Should I go back to books like Halliday/Resnick also? Or if I can do most of the problems in Goldstein, then is this not required? I have never taken a physics course in university (just wanted to study classical mechanics).

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It depends on what your aim is. Goldstein says, flat out, if you don't have the conceptual understanding you won't get it from that book. At that point it is assumed you have had Classical Mechanics as a freshman, senior/junior, and now as a graduate student. So, if you want to know how to DO mechanics then keep chugging away... If you're after a deeper understanding of the underlying meaning then hit the undergrad texts, then Goldstein. I would recommend Taylor, he does a good job. Have fun!