Would you list what is a natural and effective progression to self-study topics in analysis in order to gain a broad knowledge of the enormous corpus of knowledge that modern analysis involves. As a first step, I think that one should opt for Spivak and Apostol 1 and 2. But how would you organize a complete curriculum in analysis (every branch: e.g. real, complex, etc) up to modern research material? It would be really useful if you listed both topics and reference books.
2026-03-28 02:04:54.1774663494
Natural progression in a curriculum for self-study of analysis
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You may want to consider the Princeton Lectures in Analysis, developed by Elias Stein. The series covers Fourier, complex, real, and functional analysis, and stresses the interrelations between these fields. Unlike some older texts, this series also includes extra material relevant to recent innovations in the field.