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Has anyone read this book? It has really good reviews but I'm not sure if it's suppose to be for people who already know the material but want an intuitive understanding, or for people expecting to learn something completely new. I tried to read through number theory and I was completely lost. So I'm wondering if either I'm not trying hard enough or I'm lacking basic foundation.

Kat
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  • Yes, I have read that book. It is a very nice book of course; but my personal opinion is thus: Courant, being an applications-oriented mathematician, is not the best person to make an introduction to number theory. For that, you may try Hardy and Wright's book on number theory or A. Weil's "Number Theory: An approch to history from Hammurapi to Legendre", depending on your tastes in number theory. –  Nov 01 '13 at 09:00
  • @Doldrums: I’d not recommend Hardy & Wright as an introduction; for that Dudley or LeVeque would be much better choices, and I’ve heard good things about Silverman as well. – Brian M. Scott Nov 01 '13 at 10:28
  • @Doldrums So does this mean that I should read his book to understand ideas that I already know a little, or learn ideas that are completely knew? – Kat Nov 02 '13 at 01:05
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    You already know those ideas a little because the subject is number theory; everyone interested in mathematics knows a little about numbers. However it is at the same time completely new. Courant is not a professional number theorist. But Weil and Hardy are. More precisely, Weil approaches number theory from more algebraically nnd also from the historic side and Hardy approaches number theory from the analytic and elementary methods. You will get somewhat different perspectives; but either will show you how a professional number theorist thinks. –  Nov 03 '13 at 02:19
  • (Contd.) It however needs to be said that these books are aimed at a person who intends to spend some nontrivial amount time on number theory. If number theory is only one part of a general interest or broader mathematical interest, then other books may be more suitable. –  Nov 03 '13 at 02:20

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I read it years ago and loved it.

I recently read it again and still liked it a lot.

Go ahead and read it.

Be sure to do the exercises. If there are any you can't do, ask here for help, but be sure to show what you have tried.

Also, it is by Courant and Robbins. The price (less than $20US) is quite reasonable.

marty cohen
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  • I do plan to read it eventually. On the topics that I do know, I understand completely what they are saying. On the ones that I do not know, I'm completely lost. I'm wondering if I need background to understand some of the material like topology, non-euclidean geometry, etc. – Kat Nov 02 '13 at 01:07