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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?

cheeseinthetrap
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    You can do whatever you want as long as you're willing to accept the consequences, which may or may not include not actually understanding the material. – Qiaochu Yuan May 12 '15 at 05:18
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    One could legitimately ask whether it is *beneficial*, but I can't imagine it possibly being *harmful*. –  May 12 '15 at 05:19
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    My opinion: Unless you are one-in-a-million, it is essential that you do a handful of exercises for each chapter to truly grok the material. However, I do think what you are doing is at least somewhat beneficial. It always astounds me how much easier university lectures are to follow when I've read beforehand, even though in reality I might not have that great a grasp on the material! – Kaj Hansen May 12 '15 at 05:21
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    You are doing good thing .Reading before actual lectures is always helpful .My cousin did this in one of his semester and he got 9.9 GPA .He said reading prior to lectures was beneficial – Taylor Ted May 12 '15 at 05:23
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    @Rahul: one way in which it might be harmful is that it might cause you to overestimate how well you understand the material, which isn't ideal. – Qiaochu Yuan May 12 '15 at 05:26
  • I don't think this is good to do. I always try my best not to read the proofs of the theorems before I attempt to prove them myself and actually get stuck. Proving results is a valuable skill which I think that would quite hinder it. –  May 12 '15 at 05:28

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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.

Danny
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