Good undergraduate texts in analysis for self studying

Question

I know this question was asked many times but I have some specific questions. I know the usual recommendations but I am afraid of going for Rudin because I've read many reviews that said it wasn't good for self studying. I remember in one review I read the guy said " As you go through the book you get excited about some cool theorems and results only to find that Rudin gives a proof that only does the job and leaves out much of the intuition for you to either find on your own or look for elsewhere".

I don't like this type of texts because when the proof is too directed it becomes unsatisfactory. By directed I mean that the result is already established and we're just trying to make it formal by looking for arguments that just verify the fact without , for example , mentioning how one would first consider these arguments and how they would come up while trying to prove the result.

That said , There are other suggestions such as Barry Simon's comprehensive course in analysis. This is a new text which isn't reviewed a lot. The description says it may be suitable for a graduate level course but others say it gives a good introduction to the prerequisites but I'm not sure.

Any other suggestions ?

Edit : thanks for your answers

Answer 1

I would purchase a copy of Understanding Analysis by Abbott. There are a lot of pictures and the exercises are aimed at undergraduate students.

Answer 2

Try "Introduction to Real Analysis" by Donald R. Sherbert & Robert G. Bartle

The book is extremely great and an absolute beginner can read and understand it with immense pleasure, It starts with basic sets function and ends up to Riemann integrals and some glimpse of Topology. No doubt it will help you to make you strong in this field.

Answer 3

I like "Understanding Analysis" by Abbott, as suggested by @Axion004. Alternatively, you could look at Tao's "Analysis I" and "Analysis II." The series starts from the ground (natural numbers, set theory, real numbers) and, by the end of the last book, works up to the Lebesgue integral. The books feature clear examples and explanations. and many of the simple propositions are left as exercises, which you might like for additional practice.