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I am looking for a good reference to self study algebraic number theory, as no undergraduate course is given at the university. I've web-searched a lot of online notes and courses, and I don't seem to understand what's happening. Could anyone who took/is taking/teaching a course in algebraic number theory say what are the prerequisites and the corequisites to tackle the subject in an efficient way? Further, could anyone suggest a good reference to learn the subject?

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    $\begingroup$ This question is not answerable. There are ANT courses with any number of different prerequisites. Moreover, it would be interesting why you want to study ANT. $\endgroup$ – quid May 31 '15 at 13:48
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    $\begingroup$ "Introductory Algebraic Number theory, Alaca" is elementary and very detailed. "Algebraic Theory of Numbers, Samuel" still elementary but more elegant. "Number Fields, Marcus" wonderful exercise oriented introduction. In any case, you need to pair this up with an abstract algebra textbook that covers basic rings and Galois theory, e.g. Fraleigh! $\endgroup$ – Weaam May 31 '15 at 13:49
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    $\begingroup$ I would recommend Pierre Samuel's little book: Algebraic Theory of Numbers. You can take a look at this scanned copy on this site $\endgroup$ – Bernard May 31 '15 at 13:57
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At the University of New South Wales (UNSW), which is considered to house the best school of mathematics in Australia, we have a third-year undergraduate course entitled Algebraic Techniques in Number Theory.

Having read the course outline, it appears that a background of linear algebra and discrete mathematics comes in handy.

Unfortunately, they don't recommend any textbooks as the course is self-contained, and claim that any textbook on number theory would be useful. However, it appears as though A Classical Introduction to Modern Number Theory by Ireland and Rosen is a popular choice.

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