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As a physic undergraduate with some knowledge of calculus (Lebesgue integral, stochastic analysis, complex analysis) I'm interested in learning about number theory.

Anyone who has a good tip for me, with which book to start?

Thank you!

The Short One
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  • Would you mind being a little bit more specific about your knowledge of calculus? I have (almost) no idea what "analysis I to IV" covers. – Arnaud D. Nov 30 '17 at 18:42
  • @ArnaudD. I know about differential calculus, i know the lebesgue integral, a little of measurement theory. I had a course in stochastic and complex analysis as well. –  Nov 30 '17 at 18:43
  • You should edit this into the question, so that everyone can see it more easily. – Arnaud D. Nov 30 '17 at 19:01
  • Bordes "Arithmetic Tales" or Laroche "escapade arithmetique" – Maman Nov 30 '17 at 21:05

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I'd start with a sensible undergrad text. I like Ken Rosen's Elementary Number Theory because it has lots of exercises and introduces almost every topic in the field.

After that, there are two books: Ireland and Rosen's (different Rosen) A Classical Introduction to Modern Number Theory, which will introduce the algebraic side of number theory, and Apostol's , Introduction to Analytic Number Theory, for the analytic side.

Then maybe Silverman/Tate Rational Points on Elliptic Curves.

B. Goddard
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