MHB Switch from rings and modules to analysis

[Math Amateur]

I am temporarily switching my studies from abstract algebra to mathematical analysis.

I am thinking of reading the following book:

Principles of Mathematical Analysis by Walter Rudin.

What books to MHB members advise me to use in order to gain a full understanding of undergraduate level analysis ... eventually building to a full understanding at beginning graduate level.

Another bit of assistance i would like from MHB members is help with locating online solutions to textbook problems ...

Any help will be much appreciated ... ...

Peter

 

[Euge]

There are several books in mathematical analysis that are suitable for self-study, but in my opinion, Rudin's text is not one of them. However, Rudin's book would be great as a supplement.

I recommend Bartle's real analysis book. It's simple to follow, and it has contains something very important which few analysis books have -- Henstock-Kurzweil integration. This kind of integration is more general than Lebesgue integration, but simpler in many respects.

I also think it will be beneficial to you if you follow this online real analysis text:

MathCS.org - Real Analysis: Real Analysis

 

[Math Amateur]

There are several books in mathematical analysis that are suitable for self-study, but in my opinion, Rudin's text is not one of them. However, Rudin's book would be great as a supplement.

I recommend Bartle's real analysis book. It's simple to follow, and it has contains something very important which few analysis books have -- Henstock-Kurzweil integration. This kind of integration is more general than Lebesgue integration, but simpler in many respects.

I also think it will be beneficial to you if you follow this online real analysis text:

MathCS.org - Real Analysis: Real Analysis

Thanks Euge,

I do not have Bartle's book but, given that you have recommended it, I am considering purchasing the text on Amazon ...

Thanks also for the guidance regarding the online text ...

I do have a copy of Charles Pugh's book: Real Mathematical Analysis ... do you have an opinion regarding this book ...

Further, does anyone have any knowledge regarding online solutions for Pugh's book ...

Thanks again, Euge ...

Peter***EDIT***

Does anyone else have recommendations for analysis texts (and possibly online solutions)