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January 15th, 2012, 06:38 PM   #1
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Is baby rudin a good first exposure to analysis?

hello. i am a freshman, and i will be taking an analysis (honors) course next quarter, and the textbook used will most likely be baby rudin. That will be my first exposure to the subject, although i did take an honors multivar calculus sequence last quarter that attempted to be more rigorous and formal than your typical calculus class. right now i'm taking an honors linear algebra (lower div) class which so far is below the level we treated calculus.

i've heard that rudin's book is hard and i feel like i might be unprepared for it. can i read something in advance so that i won't be struggling to keep up when the time comes?
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January 16th, 2012, 08:25 PM   #2
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Re: Is baby rudin a good first exposure to analysis?

The natural lead up to an analysis class is an advanced calculus course. More or less, an advanced calculus class goes back over many of the ideas and results from calculus building everything up formally, proving everything (or most things, at any rate), focusing on limits of sequences, series and continuity to prove everything you know about calculus. If you have had this kind of course, then you are about as prepared as you can reasonably be for an analysis. In fact, there will be a lot of overlap between an advanced calc class and an introduction to real analysis. The multivariate class you've had may be enough of a middle ground to work fine. In the end, if you satisfy the prerequisites for the class, you should be as prepared as most students for the material and the pace is ultimately driven by the instructor, so hopefully will not be too unreasonable.

In that vein, if you would like some references which embelish on the motivations for various ideas that will come up, or if you would just like a supplement to the way Rudin expresses concepts, then my advice would be to look into either of the standard advanced calculus books: Apostle's Calculus (the first volume should suffice) or Spivak's Calculus.

But if this is the first truly proof intensive math class you will have taken, there is no getting around that this will probably be a challenging course. An enormous part of this stage of a mathematical education is to spend the proper time to understand what is going on, which will be a lot of time. But if you spend that time, you will feel like you've accomplished something significant and you will learn a great deal.
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November 10th, 2014, 11:11 AM   #3
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the differences between principle of math analysis and math analysis can be seen clearly in Baby Rudin and Apostle's Calculus. One emphasize the path of theory development, the other emphazise the analysis problem solving, calculation$

Well, here is a link to Notes and Solutions to Principles of Mathematical Analysis
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