Books like Principles of Mathematical Analysis by Walter Rudin

Real and Complex Analysis by Walter Rudin is a rigorous, advanced textbook suitable for a one‑ or two‑semester course in mathematical analysis, used by mathematics, science, computer science, and electrical engineering majors at the junior, senior, or graduate level.

A comprehensive bridge from elementary calculus to advanced real and complex function theory, this textbook introduces the abstract reasoning characteristic of modern mathematical analysis.

Written for undergraduate courses, this new edition includes coverage of current topics of research and contains more exercises and examples. New topics covered include: Kakutani's fixed point theorem; Lomonosov's invariant subspace theorem; and an ergodic theorem

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 rigorous yet accessible reference for students, mathematicians, scientists, and engineers, covering calculus and global analysis with clear exposition and extensive examples.

As the title implies, this is an introductory text on mathematical analysis. It focuses on the logical basis of particular math topics which nowadays (as of 2012) are typically featured in a pre-calculus text. The 1967 teacher's edition is accessible to anyone who understands basic algebra. It is designed to prepare students to approach math in a methodical and rigorous manner from an elementary level. Some of the topics are outdated--it includes log and other tables. Although it is an elementary text, the approach used by the authors was meant to introduce logical rigor into high-school mathematics. The lessons are concerned with structure; some of the methods are quite out of favor now that electronic calculators are ubiquitous. This is the sort of math that a student ought to be able to appreciate without a calculator, i.e., it is more concerned with logical structure and proof (at least by the authors' standards) than with memorization of axioms without proof, backed by blind faith in calculators. At the time the text was first written there were no handheld calculators, so elegant algorithms were in demand. The text was designed to teach students how to construct algorithms based on mathematical reasoning. The one exception would be the inclusion of various log, trig, and other tables in the back that were probably computer generated, the algorithms for which were slightly beyond the scope of the text.

A Beginners choice for learning Real Analysis.

A clear, sequential introduction to mathematical analysis covering continuity, differentiability and integration with numerous diagrams, margin notes, graded examples, and complete solutions for self-study or university courses.

Ben shu zhu yao fen san bu fen:di yi bu fen wei shi bian han shu lun, Di er bu fen wei chou xiang kong jian, Di san bu fen wei yi ban ce du yu ji fen lun.

A classic compilation of challenging analysis problems and theorems drawn from leading mathematicians between 1850 and 1925.