Course Archives Theoretical Statistics and Mathematics Unit

Course: Algebraic Number Theory Instructor: Ramdin Mawia Room: G23 Level: Postgraduate Time: Currently 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. Evaluation: Midterm Exam 30 marks Assignment 20 marks Final Exam 50 marks Total 100 marks Top of the page Past Exams

Midterm 05.pdf 07.pdf 09.pdf 11.pdf 13.pdf 15.pdf 17.pdf 19.pdf 25.pdf Semestral 05.pdf 09.pdf 11.pdf 13.pdf 15.pdf 17.pdf 19.pdf Supplementary and Back Paper 11.pdf 15.pdf 17.pdf Top of the page

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