NOC:Algebraic Number Theory

Lecture 1 - Overview and Motivation

Lecture 2 - Algebraic Numbers

Lecture 3 - The ring of integers

Lecture 4 - Lattices

Lecture 5 - Properties of ring of integers

Lecture 6 - Discriminant

Lecture 7 - Dedekind Domains (DD)

Lecture 8 - Algebraic properties of DD

Lecture 9 - Unique Factorization of Ideals - 1

Lecture 10 - Unique Factorization of Ideals - 2

Lecture 11 - Ring of Integers is a DD

Lecture 12 - Ideal Class Group

Lecture 13 - Integral Ideal in an ideal class

Lecture 14 - Finiteness of ideal class group

Lecture 15 - Geometry of numbers - 1

Lecture 16 - Geometry of numbers - 2

Lecture 17 - Dirichlet's Unit Theorem - 1

Lecture 18 - Dirichlet's Unit Theorem - 2

Lecture 19 - Relative extension - 1

Lecture 20 - Relative extension - 2

Lecture 21 - Decomposition Group

Lecture 22 - Inertia Group

Lecture 23 - The Artin map

Lecture 24 - Valuations

Lecture 25 - Archimedean valuations

Lecture 26 - Non-archimedean valuations

Lecture 27 - p-adic numbers

Lecture 28 - p-adic completion of a Number field

Lecture 29 - Product formula

Lecture 30 - Hensel's lemma

Lecture 31 - Finite extensions of local fields

Lecture 32 - Factorisation of conorm of a prime ideal in a finite extension - I

Lecture 33 - Factorisation of conorm of a prime ideal in a finite extension - II

Lecture 34 - Different - I

Lecture 35 - Different - II

Lecture 36 - Different - III

Lecture 37 - Ramification and different ideal

Lecture 38 - Quadratic Fields

Lecture 39 - Binary quadratic forms - I

Lecture 40 - Binary quadratic forms - II

Lecture 41 - Reduced binary quadratic forms

Lecture 42 - Class group of imaginary quadratic fields and binary quadratic forms - 1

Lecture 43 - Class group of imaginary quadratic fields and binary quadratic forms - 2

Lecture 44 - Computation of Class group of imaginary quadratic fields using binary quadratic forms

Lecture 45 - Order two elements in Class group of imaginary quadratic fields

Lecture 46 - Pure cubic fields - 1

Lecture 47 - Pure cubic fields - 2

Lecture 48 - Pell's equation - 1

Lecture 49 - Pell's equation - 2

Lecture 50 - Biquadratic fields - 1

Lecture 51 - Biquadratic fields - 2

Lecture 52 - Cyclotomic fields - 1

Lecture 53 - Cyclotomic fields - 2

Lecture 54 - Compuation of class groups - 1

Lecture 55 - Compuation of class groups - 2

Lecture 56 - Compuation of class groups - 3

Lecture 57 - Compuation of class groups - 4