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So far I've studied a lot of courses like Algebraic topology, Homological Algebra, Differential Geometry and Manifolds but I've never studied Number theory and I am going to be enrolled to a master programme that includes in its curriculum the courses Algebraic Number theory and Arithmetic Geometry. I would like recommendations of number theory books (ideally with solved exercises) that build solid background for these two courses.

Thank you very much in advance!

T. Wildwolf
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  • So I'm less familiar with books that have solved exercises, but Ireland and Rosen's book A Classical Introduction to Modern Number Theory is a nice look at the flavors of modern number theory. For arithmetic geometry a good knowledge of schemes is always helpful. – Geoff May 04 '21 at 16:32
  • I've noticed reading comments on this cite that this book is not an ideal option for someone without any knowledge on number theory and it's actually quite difficult in reading and learning. Is there another more elementary approach? I mean, of course I should delve into some concepts but I'm starting from scratch – T. Wildwolf May 04 '21 at 16:38
  • For a standard algebraic number theory course I'd rather try to get a solid commutative algebra background. – Yagger May 04 '21 at 16:44
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    If there is an "Algebraic number theory" class in the curriculum, I don't really see any reason why you would need to build background, usually those classes only have requirements in general algebra (mostly basic Galois theory and commutative algebra). – Captain Lama May 04 '21 at 16:49
  • So, there is no need in learning elementary number theory, right? @CaptainLama – T. Wildwolf May 04 '21 at 16:50
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    No, you need elementary number theory. – D_S May 04 '21 at 17:26
  • What elementary theory exactly do I need? @D_S Are the 4 chapters of Ireland, Kenneth; Rosen, Michael. A classical introduction to modern number theory enough for covering basic elementary theory? Because now I am confused since according to Captain Lama there is no reason to build such a background – T. Wildwolf May 04 '21 at 18:57
  • Do you want to pass a class or do you actually want a comprehensive understanding? There are many things you will have thrown at you in ANT that you will have no intuition for if you don't put in the work to learn the basic context out of which ANT was developed. – D_S May 04 '21 at 19:10
  • It's like learning real analysis and not knowing calculus. – D_S May 04 '21 at 19:14

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