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I am taking real analysis course in my graduate class of Maths. My classes will start in 3 months. I have studied real analysis but not very rigorously. Whenever I see theorem I have no idea on how to prove it or even how do I start it. I understand when I read them. But I cannot reproduce them in my own way when needed.

Basically I want to redo it again before my actual classes.

Can anyone suggest me book which contains pictorial and diagrams for proofs and also idea of proof is given with each proof. I feel like as I lack tools for proofs. This will help me a lot

Thanks

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  • $\begingroup$ Someone suggested to me that, when reading a real analysis book without illustrations, I should always have pencil and paper handy so I could draw pictures for it myself. $\endgroup$ Commented Apr 26, 2015 at 20:57
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    $\begingroup$ Look at Victor Bryant's Yet Another Introduction to Analysis. I've written about this book several times since 2000 -- google its title along with my name. $\endgroup$ Commented Apr 27, 2015 at 19:44
  • $\begingroup$ @DaveL.Renfro Thanks i have seen the book ..It is a good book .Can you suggest slightly advanced text $\endgroup$
    – Taylor Ted
    Commented Apr 28, 2015 at 15:22
  • $\begingroup$ A little more advanced, with lots of intuition (and I think pictures) is Bressoud's A Radical Approach to Real Analysis. Bressoud's book is less advanced than Pugh's book mentioned below (a book I like a lot, by the way) and a little more advanced than Abbott's book mentioned below (another book I like a lot). $\endgroup$ Commented Apr 28, 2015 at 20:58
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    $\begingroup$ Does this answer your question? Visual book of real analysis $\endgroup$
    – user53259
    Commented Jul 22, 2021 at 8:34

3 Answers 3

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I would suggest Understanding Analysis by Abbott . It's a pretty rigorous book but it was written with the beginner in mind. It may help you review.

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  • $\begingroup$ Abbott's book lacks many pictures though. $\endgroup$
    – user53259
    Commented Jul 20, 2021 at 7:44
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C.C.Pugh 's Real Mathematical Analysis is a very good book in this regard.It contains all the proofs with pictures.

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  • $\begingroup$ can't find it online ? $\endgroup$
    – Taylor Ted
    Commented Apr 28, 2015 at 15:57
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    $\begingroup$ Why? Google shows it $\endgroup$
    – Learnmore
    Commented Apr 29, 2015 at 3:24
  • $\begingroup$ Can you provide link $\endgroup$
    – Taylor Ted
    Commented Apr 29, 2015 at 14:29
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I finally found this GEM that has proof strategies, motivation for every proof with over 100 pictures:


Edit by non-OP:

The link overhead is broken. I divine this to have been intended:

Ajit Kumar and S. Kumaresan. A Basic Course in Real Analysis (2014).

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