Preparing for the Real Analysis Comp

  • This Comp primarily covers material from the following course:
    • MATH 561A

    However, it also covers some material from the following course(s):

    • MATH 361B
    • MATH 561B
  • Here are some sample Comps in this field:


  • Formal syllabus. Includes topics and reference materials.


  • Informal advice from faculty:

    There are several different standard books for real analysis (see the Syllabus for references), and they develop key topics in different orders. For example, some prove the Monotone Convergence Theorem from scratch and then derive Fatou's Lemma as a consequence, and some do it the other way around.

    If you are asked to prove one of these seminal facts on the exam, you may do it either way, but you should define clearly the terms you will use and give careful statements of theorems you plan to use without proof. To be safe, you may want to use the development followed in your version of MATH 561A. The most recent teacher of 561A is always one of the graders for Real Analysis, so (s)he will be familiar with the development you learned and will know if you are following it correctly.


  • The following faculty members are knowledgable about this field and are willing to answer questions from students preparing for the Comp:
    • Dr. Joseph Bennish
    • Dr. Florence Newberger

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