MA 313: Algebraic Number Theory

Credits: 3:0

Pre-requisites :

  1. Linear algebra (MA 219 or equivalent)
  2. Basic algebra : Groups, rings, modules (MA 212 or equivalent), and algebraic field extensions

Algebraic preliminaries: Algebraic field extensions: Normal, separable and Galois extensions. Euclidean rings, principal ideal domains and factorial rings. Quadratic number fields. Cyclotomic number fields. Algebraic integers: Integral extensions: Algebraic number fields and algebraic integers. Norms and traces. Resultants and discriminants. Integral bases. Class numbers:Lattices and Minkowski theory. Finiteness of class number. Dirichlet’s unit theorem. Ramification Theory: Discriminants. Applications to cryptography.

Suggested books and references:

  1. Artin, E., Galois Theory, University of Notre Dame Press, 1944.
  2. Borevich, Z. and Shafarevich, I., Number Theory, Academic Press, New York, 1966.
  3. Cassels, J.W. and Frohlich, A., Algebraic Number Theory, Academic Press, New York, 1948.
  4. Hasse, H., Zahlentheorie, Akademie Verlag, Berlin, 1949.
  5. Hecke, E., Vorlesungen uber die Theorie der algebraischen Zahlen, Chelsea, New York, 1948.
  6. Samuel, P., Algebraic Theory of Numbers, Hermann, 1970.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 Sep 2019