Course Archives Theoretical Statistics and Mathematics Unit
Course: Algebraic Number Theory
Level: Postgraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus: Review of norm and trace, Number fields and their rings of integers, Prime decomposition in number rings, Kummer-Dedekind discriminant criterion for ramification, The Ideal Class Group, ray class group, their finiteness and Dirichlet's Unit theorem, Valuations and completions of number fields, Decomposition and inertia groups, Frobenius automorphism, Artin symbol, Dedekind zeta function and the Distribution of ideals in a number ring, Kronecker limit formula, Frobenius density theorem. Time permitting, introduction to class field theory.

Suggested Texts :
1. G.J. Janusz: Algebraic Number Fields (chapter 1-4), AMS (1996).
2. D.A. Marcus: Number Fields, Springer-Verlag (1977).
3. J.Neukirch: Algebraic Number Theory, Springer (1999).
4. I. Stewart and D. Tall: Algebraic Number Theory and Fermat's Last Theorem, A.K. Peters (2001).
5. J. Esmonde and M. Ram Murty: Problems in Algebraic Number Theory, Springer (Indian reprint 2006).
6. TIFR pamphlet on Algebraic Number Theory.

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Past Exams
Midterm
05.pdf 07.pdf 09.pdf 11.pdf 13.pdf 15.pdf 17.pdf
Semestral
05.pdf 09.pdf 11.pdf 13.pdf 15.pdf 17.pdf
Supplementary and Back Paper
11.pdf 15.pdf 17.pdf

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