The mathematical influence of G. Hardy over mathematical education was and remains strong, as can be seen by reading this masterpiece. There are few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in , this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

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Celebrating years in print with Cambridge, this edition includes a Foreword by T. Koerner, describing the huge influence the book has had on the teaching and development of mathematics worldwide.

Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to. Read more Read less.

## A Course of Pure Mathematics by G. H. Hardy

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Can you make it clear? Hey, are you a graduate student? In the formula described in eg.

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Can you help me? Your description of the series via diagonals and rectangles is correct, but you mistyped in the series itself.

Anyway, when laid out in a grid like you suggested, it looks like this, so indeed, your description works. I kept thinking that the diagonal was merely an imaginary line of sorts i.

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All I can say is that I hope you quickly return to this labor and do keep up on this work. Robert To get what he means in the next to last paragraph, consider a square in the grid I drew above, say the 4X4 square containing only the terms shown below. The reason we are dividing this result by two is because we only want to count the fractions on the upper left half of the diagram, which is.

I realized that my third number grid did NOT typeset out right. I meant for the diagonal to remain there as empty spaces where the fractions were.

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## ISBN 13: 9780521052030

Maybe I need to learn how to use that MathJax thing. Or if you can correct it yourself, that would be great. Sorry about that. Thanks for this! I have a simpler solution for the last question — here we group the terms to simplify things for us:.

## A Course of Pure Mathematics by G.H. Hardy

Consequently, their sum remains the same. Some thoughts on your proof of uniqueness of decimal representation. Trying to prove the same thing through uniqueness of integers …. Hence, this case cannot exist.