Course Archives Theoretical Statistics and Mathematics Unit
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Course: Algebraic Number Theory Level: Postgraduate Time: Currently not offered |
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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. Top of the page Past Exams | |||||||||||||||||||

Midterm
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[ Semester Schedule ][ SMU ] [Indian Statistical Institute] |