Real Mathematical Analysis

Rigorous and proof-based book for all those who feel that calculus failed to give answers to their mathematical curiosity. The only negative points are that some ( just a few ) theorems are offered as excersices to be proven by the reader, another negative point is that the theoretical matter lacks solved examples ( of course this is a feature of good calculus books that are required prior to reading this one ) and the third negative point is that the abundant sets of excersises offered are left without answers in the appendix.

The pages come off the spine the moment I opened it. It looks that the defective book has been bound somehow and sent to me. Does not create a goodwill . The saler is taking the customer for a ride. Very unpleasant experience

Book came in perfectly. Nice pages, no problems with any printing, no clear defects on the hard cover. Great self-study book for the more mathematical mature.

This book is a pleasure to read, and contains some of the best sections of topology related materials. While there are some excellent and standard exercises spanning over several pages... some of them appear out of the blue in difficulty that would often be solved using methods of functional analysis. If you have a professor that can guide you through exercises and pick out those appropriate then the book is excellent - but if not you could be stuck down a rabbit hole on some of them never to return.

When I try to describe what this book accomplishes, I keep coming back to the idea that mathematics is not only a collection of theorems but a journey of understanding. Charles Chapman Pugh captures this with extraordinary talent. I have read many real analysis textbooks over the years—as anyone who loves mathematics eventually does—but this one surprised me completely. I opened it expecting a solid reference; instead, I found one of the most engaging, humorous, and pedagogically sharp mathematical books I have ever encountered. Pugh anticipates every hesitation the reader might have and addresses it with uncanny precision. Teaching mathematics is fundamentally different from proving theorems or producing research. It requires guiding someone through unfamiliar territory, where each new abstraction threatens to outpace intuition. Pugh understands this distinction deeply. His explanations unfold with perfect timing: definitions are motivated, theorems appear exactly when the reader is ready for them, and even the famous “weird counterexamples”—so often feeling artificial or disconnected from genuine mathematical life—become meaningful. By the time they appear, the reader truly feels why they must exist. The exercises, abundant and beautifully graded in difficulty, form a genuine path of practice. They teach mathematics as it must be learned: through problems that gradually reshape one’s way of thinking. More than once I found myself comparing my own past attempts at teaching with a kind of embarrassment, simply because the pedagogical quality here is so striking. Pugh sets out to “lift the reader off the ground,” and the book consistently makes good on that promise. If you already know the subject, this book will refresh your understanding with joy; if you are encountering real analysis for the first time, it may very well define what good mathematical writing can be. I cannot imagine anyone regretting the time spent with it.