My question comes from first few paragraphs of preface of "Analysis on Manifolds" by James R. Munkres, as excerpted below:

A year-long course in real analysis is an essential part of the preparation of any potential mathematician. For the first half of such a course, there is substantial agreement as to what the syllabus should be. Standard topics include: sequence and series, the topology of metric spaces, and the derivative and the Riemannian integral for functions of a single variable. There are a number of excellent texts for such a course, including books by Apostol [A], Rudin [Ru], Goldberg [Go], and Royden [Ro], among others.

There is no such universal agreement as to what the syllabus of the second half of such a course should be. Part of the problem is that there are simply too many topics that belong in such a course for one to be able to treat them all within the confines of a single semester, at more than a superficial level.

At M.I.T., we have dealt with the problem by offering two independent second-term courses in analysis. One of these deals with the derivative and the Riemannian integral for functions of several variables, followed by a treatment of differential forms and a proof of Stokes' theorem for manifolds in euclidean space. The present book has resulted from my years of teaching this course. The other deals with the Lebesgue integral in euclidean space and its applications to Fourier analysis.

As says by the third paragraph, the text "Analysis on Manifolds" by James R. Munkres is the text for one of the two independent second-term courses in analysis at MIT. But the text for the other second-term course having different syllabus ("Lebesgue integral in euclidean space and its applications to Fourier analysis") in parallel with "Analysis on Manifolds" is not mentioned. If you happen to know (or enrolled in), can you please tell me what textbook is used for this "other second-term course in analysis at MIT"? It would be more than appreciated if you can also let me know its course number and the link to a course website of "the other second-term course in analysis at MIT." Thanks a lot.

  • $\begingroup$ I’m voting to close this question because it is off topic. I am not sure where it would belong/ $\endgroup$
    – Amy B
    Nov 27, 2022 at 9:10
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    $\begingroup$ Have you tried asking the mathematics department at MIT? That might get you further than hoping to strike it lucky here. Good luck! $\endgroup$
    – J W
    Nov 27, 2022 at 13:08
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    $\begingroup$ I'm wondering if this question is actually outdated. Geometry of smooth manifolds remains a central part of mathematics, but analysis with non-smooth real-(vector)-valued functions, especially the more technical aspects, seems to be a much less popular topic than it was 40 years ago (especially when you get farther away from functional analysis). In particular, I'm not sure who on their faculty now would teach such a course, though I'm very far from analysis and might not be able to tell. $\endgroup$ Nov 27, 2022 at 17:35
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    $\begingroup$ MIT still has a two term model for analysis, where the first class 18.100 is roughly as described. There are now three alternatives for the second class: 18.101 "Analysis and Manifolds", 18.102 "Introduction to Functional Analysis" and 18.103 "Fourier Analysis: Theory and Applications". You can read brief course descriptions here student.mit.edu/catalog/m18a.html . $\endgroup$ Nov 28, 2022 at 4:51
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    $\begingroup$ @AlexanderWoo you wrote that analysis with non-smooth functions seems less popular now compared to years ago. The non-smooth functions in the OP are from Lebesgue integration. That is still a fundamental part of analysis (Fourier analysis, probability, etc) and anyone in analysis should be qualified to teach measure theory and integration. $\endgroup$
    – KCd
    Dec 4, 2022 at 13:48


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