A Course of Pure Mathematics Centenary edition (Cambridge Mathematical Library)

This is the most beautiful book that I have ever read. This is coming from someone who was average at math in school and hated it to the bone in university. If I had read this book while I was at university I would have definitely switched from engineering to math. I really cannot describe how this book makes me feel. Korner ends the foreword with the following: "May this book give as much pleasure to you as it has given to me". Hardy is a master of the subject as well as a master of prose. The only person that I think writes better than him is Russell. Open the book on a random page and chances are that you will see one equation and many paragraphs. The way Hardy describes the construction of the rational and irrational numbers is beyond description. Also, for the first time in my life I truly understand the true meaning behind the words 'limit' and 'convergence'. Previously, I could easily find whether a certain function converged or not by applying one of the many tests mechanically. Now, I actually understand how the function behaves just by looking at it and in many cases I know the answer without having to use any of the 'tools' which we memorize in school and university. The book is not easy, but it is very clear. There are many parts which I had to re-read over and over not because Hardy doesn't explain them right, but because the material is complicated. This book does not make analysis easy, because it is not (and many of the problems included prove that). What this book does is that it reveals the beauty of math while explaining the concepts clearly. This book will require effort on the part of the reader, but believe me, you will cherish every moment. I am at the end of the book and once I finish it I will go over it again. Why? Because I have never enjoyed another book more than this.

The fact is they never have and never will. This is the reason you should read old textbooks.What really makes this great is Hardy's connection with the reader. The entire book reads like a discussion between a professor and a student. He is not simply instructing, but he is offering his complete justifcation and analysis. He provides exactly what information you need in a very methodical order. And he does not waste time on trivial proofs for the obvious, and graphs are limited to only the essentials.He does not waste his time or the readers time and there is not one wasted page in this book. Ironically his concise instruction is by no means superfical. He spends 30 pages discussing what a function of real variables actually means. And his discussion goes beyond a set of rules presented on a few pages of a modern textbook. Honestly I think if you used his definition in today's courses you would get the question wrong. However, you would have a complete understanding from Hardy so you could probably argue it with your professor and get the credit back.This is by no means an easy read. It is very difficult, but the reader will be rewarded with a knowledge beyond modern courses.I read alot of old textbooks, and sometimes it is a waste, but more often it presents techniques long forgotten with the age of calculators.As another reviewer mentioned this makes modern textbooks with neat graphics and colors look like a complete joke. ( most probably are anyway ).I am only two chapters into this, so I cannot say how much of it is relevent with modern techniques, but I think it is a priceless resource.

There are many stunning insights in G.H. Hardy's work. The book is extremely well written and has a number of examples that are thought-provoking, and concrete. It has the best description of the Dedekind cut I've ever read. Real numbers aren't assumed but built from rationals. It is not "abstract" as for instance the Baby Rudin is. Instead of metric spaces and topology, it uses the epsilon-delta method of proof.This book is a classic. It is meant to be read and lovingly reread. One gets an insight into not only mathematics but a unique and brilliant mind. It is of value to the applied mathematician, because of its concrete cases, despite the title talking about "Pure Mathematics."In terms of development of advanced calculus, it is comparable to Spivack and to Apostol, though unlike Apostol no discussion of linear algebra. I'd say the book is more leisurely than these classics, and goes deeper into interesting limits and calculations.I'm not saying it is the only analysis book you will ever need, or the only reference you will ever need. You will still need something like Rudin's Principles of Mathematical Analysis for a reference work, and you will need a book to serve as a reference to linear algebra, differential forms, manifolds, and other tools of modern analysis. What this book will give you is a beauty so deep it will make you weep with joy.