Real Analysis

Context: I read this book along side baby Rudin or Rudin’s Principles of mathematical analysis. For the express purpose of reading and understanding Munkres’s Topology.

This text provides a highly readable introduction to real analysis. The author here does not seem to be concerned with over bearing rigor or immense breadth, rather the friendly readability and heavy explanation of topics. The standard text on this topic in my circles seems to be baby Rudin, a rather rigorous book (phenomenal breadth, but dry). Here Cummings provides a gradual decent into the body of analysis, asking provoking questions and guiding interesting thoughts. A continuous event is a historical philosophical paradox met with a (somewhat) fundamental theorem of analysis answer. This method is not novel, in fact this is how my math professors taught however I had not seen it in a text before. The problem sections feel rewarding and gradually more difficult. Theorem explanation usually has two or three proofs to solidify understanding, this is helpful at times an redundant at others. I always appreciated the small jokes and lively writing style in contrast to baby Rudin.