Switch from rings and modules to analysis

In summary: Peter?In summary, Peter is temporarily switching his studies from abstract algebra to mathematical analysis and is considering reading Walter Rudin's "Principles of Mathematical Analysis." He is also seeking recommendations for other analysis books and online solutions for textbook problems from MHB members. Euge suggests Bartle's real analysis book and the online text "MathCS.org - Real Analysis: Real Analysis" as helpful resources. Peter also mentions having a copy of Charles Pugh's "Real Mathematical Analysis" and asks for opinions on the book and if there are any online solutions available.
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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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  • #2
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
 
  • #3
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:

Related to Switch from rings and modules to analysis

What is the difference between rings and modules and analysis?

Rings and modules are algebraic structures used to study abstract mathematical objects, while analysis is a branch of mathematics that deals with the study of continuous change and limits. In other words, rings and modules focus on discrete structures, whereas analysis focuses on continuous structures.

Why would someone want to switch from studying rings and modules to analysis?

While rings and modules are important tools in mathematics, analysis has a wider range of applications in various fields such as physics, engineering, and economics. It allows for the study of continuous phenomena, which are more prevalent in the real world.

Do the concepts and techniques used in rings and modules apply to analysis?

Yes, many concepts such as continuity, convergence, and topological properties used in analysis have their roots in the study of rings and modules. However, analysis also introduces new concepts such as differentiation and integration that are not found in rings and modules.

What are some practical applications of analysis?

Analysis has numerous practical applications in fields such as physics, engineering, economics, and computer science. For example, it is used to model and predict the behavior of systems in physics and engineering, and to analyze data in economics and computer science.

What are the main branches of analysis?

The main branches of analysis include real analysis, complex analysis, functional analysis, and harmonic analysis. Each branch focuses on different aspects of continuous functions and structures, and has its own set of techniques and applications.

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