Course Archives Theoretical Statistics and Mathematics Unit | ||||||
Course: Algebraic Number Theory Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: (Note: A priori knowledge of Commutative Algebra is desirable.) Algebraic numbers and algebraic integers; Brief review of integral extensions; Norm, trace and discriminant; Existence of integral basis. Dedekind domains, ideal class group. Minkowsky theory, finiteness of class group. Dirichlet unit theorem. Factoring of prime ideals on extensions, fundamental identity; Quadratic number fields (computation of class numbers, prime decomposition, Pells equa tions). Hilberts ramification theory (decomposition and inertia groups); Cyclo tomic fields. Valuations, completions, local fields Suggested Texts : (a) G.J. Janusz: Algebraic Number Fields, (chapter 1-4), AMS (1996). (b) D.A. Marcus: Number Fields, Springer-Verlag (1977). (c) J. Neukirch: Algebraic Number Theory, Springer (1999). (d) P. Ribenboim: Classical Theory of Algebraic Numbers, Springer Science and Business Media (2001). (e) J. Esmonde and M. Ram Murty: Problems in Algebraic Number Theory, Springer (Indian reprint 2006). (f) TIFR pamphlet on Algebraic Number Theory. Top of the page Past Exams | ||||||
Midterm
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