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Becareful that you don't just remember STEPS ON HOW to do it, but WHY THE METHOD WORKS. Once things become common sense and then you practise-practise-practise it's hard to forget. Don't be scared to get it wrong if it helps you understand why it works. Not sure what level maths you are doing but try googling virtualb15 and wootube. NSW syllabus but the ...


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A funny thing about Munkres' Topology book is that he writes "backwards": the first sentence of a paragraph is usually a claim which is then justified by the later sentences of the paragraph. This makes it very easy to see an outline of the proof. I used to like this style of writing a lot and emulated it for some time before realizing it wasn't perfect ...


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In learning there are two goals, one is obtaining knowledge and the other is obtaining skill. Having knowledge without skill means you can talk about it, but when it comes time to act, you lack the tools to produce results. Having skill without knowledge means you can generally produce results, but your limited understanding of the world has you relying on ...


2

Self study can be a nightmare. When you attend a university course, you don't worry about how much time the course takes: the instructor must worry about it. When you study on your own, it is rather difficult to organize your time. As a pure mathematician I must say that proofs are often (often, not always) more important than statements. The proof of the ...


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It all boils down to what you want to do with the knowledge you gain. Do you want to prove (some/all) theorems? Or do you just want to apply those theorems to solve problems? If you want to solve theorems, perhaps you should read a book about proving theorems, if you haven't done so already. With it, you can learn several techniques and patterns that ...


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I am self-studying Calculus from Apostol's book. At first, I did what exactly you do, then I realized that I was losing too much time. I changed my approach to the subject and just started paying attention to main theorems. Of course, you should be able to understand theorems which are required to prove a main theorem but you do not have to spend too much ...


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I'd suggest that you don't try to proof all the theorems in the book on your own and instead concentrate on the exercises and maybe on proving the corollarys yourself. Especially in the late chapters of a book the proofs will become more and more complicated and you will waste more and more time only finding a specific kind of idea. When reading a book I ...


3

I have studied calculus, real analysis, linear algebra on my own following various books. Currently I am studying multivariable calculus. At first, in Calculus, I tried to prove all theorems myself and tried to do all exercises at the end of the chapter. I was too slow, I couldn't make any progress. Because the definitions and concepts like ...


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In my experience, it is better to be able to apply the theorems than to prove them (unless you need proofs for an exam). I would personally weight towards spending time on the exercises. Read through the proofs, certainly, to get a feel for which methods are used to prove things in this area, but the main theorems are "main" for a reason: their applications ...


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Although this is an opinionated question, I prefer to actually have both. In an ideal situation I would use the thinner book more as a study guide, or if it has easier/more straightforward examples I would do them first and only then look at the thicker book. The thicker book probably increases your understanding of the subject more than the other one, since ...


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The much-upvoted MIT materials are really good. I have actually looked at some of them instead of just reading about them. But I'm betting that a "lazy type person" will not learn calculus this way, especially if you fall into a habit of watching rather than doing. An alternative approach might be to google 'Calculus Caltech' and look at their course, not ...


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It is a metaphor. The meaning is that if someone claims to have solved a long-outstanding problem, then it is both instructive and time-saving to (initially) ignore parts of their proof that are "standard" (i.e., use mathematical tools that are known and understood) and look for the key new insight. Obviously this does not always require reading the entire ...


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I am somewhat involved with the national olympiad in Mexico. Here is the official website. In Mexico they do a national Olympiad where each state sends six students. The cut-offs are the same percentages as in the imo. The gold medallists are invited to several training camps (each a couple of weeks long). During these training camps participants write ...


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Though it's not obvious by the community's title, Physics Forums has an entire subforum dedicated to various branches of pure mathematics including Linear and Abstract Algebra, Calculus, Differential Geometry, Topology and Analysis, Logic & Set Theory, "General Math" and others. Each branch is headed with the warning: [MUST READ] This forum is not ...


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I don't think this is the place to ask that kind of question. But since you asked, if you're having difficulty with this book and you're having trouble finding motivation to read it, why don't you just leave it for a bit, and come back to it after you're done with your other books? Or perhaps it is a too complex book for your level? I don't really know...



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