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Undergraduate analysis learning recommendations

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This page provides subject-specific learning recommendations for the subject undergraduate analysis. See all our learning recommendations pages |

This page lists learning recommendations for undergraduate courses and sequences in real analysis. The undergraduate real analysis syllabus is not so much about analysis as it is about introducing students to general mathematical ideas (ranging from algebraic ideas such as vector spaces to topological ideas such as open sets and compactness to analytic ideas such as measure).

Learning recommendations

  • Introduction to Analysis (Dover Books on Mathematics)by Maxwell Rosenlicht(Amazon link) is a cheap and reasonably good book on the subject, ideal for people who want to learn the material quickly and effectively but do not need to go into great depth.
  • Real Mathematical Analysis (Undergraduate Texts in Mathematics) by Charles Pugh (Amazon link) is a more expensive book that goes into greater depth and might be better suited for people who intend to go on to higher mathematics.
  • Principles of Mathematical Analysis by Walter Rudin (Amazon link), colloquially called baby Rudin to contrast with Rudin's analysis textbook for graduate students, is one of the standard recommendations for analysis. In our view, the book is not sufficiently different or better compared to our other choices to justify the cost differential. If, however, you already own the book or can get it at a low price, it would be worth using.