Books like Real Mathematical Analysis by Charles Chapman Pugh

A comprehensive introduction to real analysis, suitable for advanced undergraduate mathematics students.

Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it.

A thorough introduction to real analysis, covering limits, series, differentiation, and integration on the real line and in Euclidean spaces.

A Beginners choice for learning Real Analysis.

An accessible bridge from calculus to real analysis, offering straightforward proofs, motivating explanations, and numerous examples – including new topics such as π’s irrationality, Baire category, and continuous nowhere‑differentiable functions.