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Number Theory I
Last Updated: 2026-02-05 16:02:14
Abstract
This course will give an introduction to the theory of number fields, which are fundamental objects in algebraic number theory.
Objective
In this course, we will cover the following topics: - review of field extensions, algebraic numbers - rings of integers, discriminants, integral bases - examples: cyclotomic fields - non-unique factorisation of algebraic integers, unique factorisation into prime ideals - fractional ideals, class groups - lattices and Minkowski's lemma, finiteness of the class group - computations of the class number - group of units of a number field - Dedekind zeta functions, class number formula
Resources
Literature
I. Stewart and D. Tall, Algebraic Number Theory and Fermat's Last Theorem (Third Edition, Peters, 2002) Neukirch, Algebraic Number Theory, Springer
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Number Theory I |
|
4 h weekly |
Offered In
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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