Algebraic Number Theory (MATH 519)

2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Mohammad Sadek mmsadek@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Discussion based learning
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Programs\Type Required Core Elective Area Elective
Computer Science and Engineering - With Bachelor's Degree *
Computer Science and Engineering - With Master's Degree *
Computer Science and Engineering - With Thesis *
Cyber Security - With Bachelor's Degree *
Cyber Security - With Master's Degree *
Cyber Security - With Thesis *
Data Science - With Thesis *
Electronics Engineering and Computer Science - With Bachelor's Degree *
Electronics Engineering and Computer Science - With Master's Degree *
Electronics Engineering and Computer Science - With Thesis *
Electronics Engineering - With Bachelor's Degree *
Electronics Engineering - With Master's Degree *
Electronics Engineering - With Thesis *
Energy Technologies and Management-With Thesis *
Industrial Engineering - With Bachelor's Degree *
Industrial Engineering - With Master's Degree *
Industrial Engineering - With Thesis *
Leaders for Industry Biological Sciences and Bioengineering - Non Thesis *
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Leaders for Industry Electronics Engineering and Computer Science - Non Thesis *
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Manufacturing Engineering - Non Thesis *
Manufacturing Engineering - With Bachelor's Degree *
Manufacturing Engineering - With Master's Degree *
Manufacturing Engineering - With Thesis *
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) *
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) *
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) *
Mathematics - With Bachelor's Degree *
Mathematics - With Master's Degree *
Mathematics - With Thesis *
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Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) *
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) *
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) *
Physics - Non Thesis *
Physics - With Bachelor's Degree *
Physics - With Master's Degree *
Physics - With Thesis *

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 OUTCOMES

  • 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

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 35
Midterm 50
Group Project 15

RECOMENDED or REQUIRED READINGS

Readings

Marcus, Number Fields, Springer