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I've been looking up resources for learning to do math proofs. I come across resources that are advanced and covering techniques like 'prove by contradictions' etc. However, what I need is to first understand each and every arithmetic components in every single line of proof.

For example, sometimes I will struggle why certain terms are grouped together and why certain transformation is legit. Why pushing something (operators, e.g. summation, derivative signs etc.) inside the blanket works sometimes and fail for another. These kind of things can be find here and there in math textbooks, but the techniques are so dispersed and not organized!

So my question is, what are the resources best for someone who find it hard even to read proof line by line? I'm imagining there is something that is summative and group all techniques together for beginner to get a good grasp of all those essential/fundamental arithmetic operations needed for understanding every single line of proof.

Thanks in advance!

Wong
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  • I do not understand what you are exactly trying to find. From what I understood you are not really searching a text on proof-writing, but more of basic algebra? When you want to learn how to proof something, I find "Book of Proof" by Richard Hammack very good. You find this online (with permission of the author). A good text for basic algebra I do not know, or can not recommand something. When you want to get into mathematics as a science, you will either pick that stuff up just-in-time, or you will not need it as much anyways. – Cornman Dec 14 '21 at 03:59
  • There is no magic resource that will take you from basic mathematics to more rigorous mathematics. You take courses, you study and you practice. You will encounter many ideas that are new and difficult to comprehend at first. Stick with it. It's like exercise. You will get stronger. – John Douma Dec 14 '21 at 04:12

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