Complex Analysis
by Lars V. Ahlfors |
Counterexamples in Analysis
by Bernard R. Gelbaum |
Mathematical Analysis
by Tom M. Apostol |
Visual Complex Analysis
by Tristan Needham |
Principles of Mathematical Analysis
by Walter Rudin |
Calculus On Manifolds
by Michael Spivak |
Mathematics
by Keith Devlin | 
Anno's Math Games
by Mitsumasa Anno | 
The Adventures of Penrose the Mathematical Cat
by Theoni Pappas | 
A Course of Pure Mathematics
by G. H. Hardy | 
Meta Math!
by Gregory Chaitin | 
Mathematics and the Search for Knowledge
by Morris Kline | 
Stalking the Riemann Hypothesis
by Dan Rockmore | 
Wonders of Numbers
by Clifford A. Pickover | 
Dr. Euler's Fabulous Formula
by Paul J. Nahin | 
A Short History of Nearly Everything
by Bill Bryson | 
Being Mortal
by Atul Gawande | 
What If?
by Randall Munroe | 
Godel, Escher, Bach
by Douglas R. Hofstadter | 
The Immortal Life of Henrietta Lacks
by Rebecca Skloot |
This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.This text is part of the Walter Rudin Student Series in Advanced Mathematics.