I'm preparing to start a year-long sequence of 400-level real analysis using Rudin's(adsbygoogle = window.adsbygoogle || []).push({}); Principles of Mathematical Analysis3E in my second undergrad year, and my advisor recommends I take the graduate-level sequence the following year throughReal Analysisby Stein and Shakarchi. Since both of them seem to cover the same field of mathematics I was wondering what general topics I might expect to see in the 500-level course that might not be covered (or covered in as much depth) in the undergraduate course?

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# 400-level versus 500-level Real Analysis

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