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I'm currently taking Real Analysis, and realizing I have no understanding for the basic concepts and logic of proofs in math.

What resources explain the introductory concepts to know before studying Real Analysis? Extremely basic concepts like full explanations for what each symbol means; the properties of the triangle inequality; the logic behind why epsilon is used for proving limits; how to interpret concise math proofs in a full sentence format.

I have almost no knowledge about formal abstract proofs. I need to start at the beginning to pass Real Analysis, but I don't know where to start. My professor keeps telling me I should know this stuff already, then ignores my emails.

Bobby B
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  • There should be syllabus of Real Analysis at your University and there should be mentioned preconditions or pre-requirements. – zkutch Dec 09 '20 at 03:38
  • The course syllabus requires Calc I,II,II and Lin. Algebra I and II; all of which I've passed well and successfully. But those courses focused very little on the depth of abstract proof that is seen in a 3rd year Real Analysis course. I have never once been taught the logical methodology of an epsilon-delta proof; like the literal full explanation for how and why it works. Hence, I'm looking for some sort of "introduction to math proofs" resource. Something that would properly explain how and why we construct math proofs the way we do. – Bobby B Dec 09 '20 at 03:45
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    Daniel Velleman's "How to Prove It" is a popular recommendation for this sort of thing. I don't think it has anything on $\delta-\epsilon$ formalism though. – Glare Dec 09 '20 at 03:50
  • You can try reread calculus using Michael Spivak - "Calculus" or Rudin W. - "Principles of mathematical analysis" as they concentrated on proofs. Or your prof, maybe, ruins silence if you ask advice about some good book from his/her point of view. – zkutch Dec 09 '20 at 03:50
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    A useful resource may be Lara Alcock's "How to Think about Analysis" can be a useful resource. The content is basic, but it very thoroughly goes through the symbols and basic methods used in Real Analysis. – F McA Dec 09 '20 at 04:11
  • See https://math.stackexchange.com/a/592229/72031 and https://math.stackexchange.com/a/1105486/72031 – Paramanand Singh Dec 09 '20 at 07:55

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