Switch from rings and modules to analysis

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SUMMARY

The discussion centers on transitioning from abstract algebra to mathematical analysis, with a focus on recommended texts for self-study. Peter is considering "Principles of Mathematical Analysis" by Walter Rudin but receives advice that while it is a good supplement, it is not ideal for self-study. Instead, members recommend "Real Analysis" by Bartle for its clarity and inclusion of Henstock-Kurzweil integration, as well as the online resource MathCS.org for additional support. Peter also inquires about "Real Mathematical Analysis" by Charles Pugh and seeks online solutions for textbook problems.

PREREQUISITES
  • Understanding of abstract algebra concepts
  • Familiarity with basic calculus
  • Knowledge of Lebesgue integration
  • Ability to navigate online educational resources
NEXT STEPS
  • Purchase "Real Analysis" by Bartle for foundational understanding
  • Explore the online text "MathCS.org - Real Analysis" for supplementary learning
  • Investigate "Real Mathematical Analysis" by Charles Pugh for advanced topics
  • Search for online solutions and problem sets related to Pugh's book
USEFUL FOR

Students transitioning from abstract algebra to analysis, self-learners in mathematical analysis, and educators seeking supplemental resources for teaching analysis concepts.

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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
 
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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
 
Euge said:
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)
 
Last edited:

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