Algebraic Number Theory

Algebraic number theory is concerned with number fields, finite extensions of $\bb Q$, whose elements are the algebraic numbers. It uses the methods of algebra to study notions from number theory, such as primes and factorisation.

These notes follow the graduate course MA5202 Number Theory, offered in AY2018/19 Semester 2 by Prof Chin Chee Whye. The main text for this course is D. A. Marcus, Number Fields, 2nd ed. (2018).

• A Refresher in Galois Theory
• A Refresher in Commutative Rings
• Algebraic Number Theory (I): First Examples
• Algebraic Number Theory (II): Number Fields
• Algebraic Number Theory (III): Algebraic Integers
• Algebraic Number Theory (IV): Number Rings
• Algebraic Number Theory (V): Cyclotomic Fields
• Algebraic Number Theory (VI): Dedekind Domains

(In progress, last updated 25 Apr 2019)