Algebraic Number Theory (MATH 519)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Mohammad Sadek mmsadek@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
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CONTENT

Contents: The aim of the course is to give an introduction to the basic concepts of algebraic number theory. Following topics will be covered: algebraic number fields, rings of integers in number fields, integral bases, discriminants, unique factorization of ideals and Dedekind domains, ideal class group and class number, structure of the group of units (Dirichlet┬┤s theorem), ramification of prime ideals in extensions of number fields.

OBJECTIVE

The aim of the course is to give an introduction to the basic concepts of algebraic number theory.

LEARNING OUTCOME

Upon completion of the cours "Alegraic Number Theory", students are supposed to:

- discuss by examples the role of algebraic numbers for the solution of "elementary" number theoretic problems
- recall the basic notions of algebraic number theory, e.g. integer elements, rings of integers, unique factorization, units, etc.
- discuss the concepts of ramification, splitting, ... in extensions of number fields

RECOMENDED or REQUIRED READINGS

Readings

Marcus, Number Fields, Springer