Principles of Mathematical Analysis

Here are some notes from my reading of Walter Rudin’s (deservedly) celebrated book “Principles of Mathematical Analysis” 1

From reviews and discussions from various online mathematics communities, a common theme I found among opinions of the book was that the proofs tend to be “dense” or “too slick”. Personally, I am a fan of this style of proofs. Perhaps this is why I find so much satisfaction in writing slick but often impenetrable one-liners with higher-order functions and list compressions when I program. The problem is, while it may be fun to write, it does not make for a light and enjoyable read. But maybe that’s the point.

In these notes, I give my own interpretation of the proofs. My aim is to expand and decompress the proofs, and to lighten the typography and make it a bit more readable.


  1. Rudin, W. (1964). Principles of Mathematical Analysis (Vol. 3). New York: McGraw-Hill. ^