I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis on Manifolds, and Chapter 5 on Herstein's Topics in Algebra. However, I've only been reading the material without actually doing the problems. I just read the annotations/comments, read through the steps for Theorems, Definitions, etc. I'm just reading ahead for now and I understand the "reading" part but I've skipped doing the problems because they seem too hard. Is it ill-advised to read any more if I can't do the problems? How can I fix this and is it harmful if I just read the books without doing the problems in a casual sense, treating as entertainment/pastime?
closed as primarily opinion-based by user99914, Najib Idrissi, user91500, apnorton, quid♦ May 12 '15 at 17:26
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Reading, in pretty much any form, will almost always benefit you. Chances are you won't have a solid grasp on the material if you don't complete the problems, but this sort of reading will allow you to become informed about the larger ideas at play in various areas of mathematics and will help inform your future learning. It sounds like you'll end up taking the classes associated with these books during your time at college, so you can do the problems then.