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401-3111-72L 7 Credits BSC , MSC D-MATH
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Number Theory I

Lecturers & Examiners: Prof. Dr. Sarah Zerbes
VVZ CR n/a

Last Updated: 2026-06-01 11:31:23

Abstract

This course will give an introduction to various aspects of number theory, both algebraic and analytic.

Objective

The course will present some representative results in important directions of number theory. Students who attend the lecture will acquire a solid background in all aspects of modern number theory, both towards algebraic and analytic directions. They will also learn how to use software such as Pari/GP for experiments in number theory.

Content

The course will present some representative results in the following directions, each of which belongs to an important area of number theory: (1) congruences, including the law of Quadratic Reciprocity (2) diophantine approximation (Dirichlet's Theorem, continued fractions) (3) sums of two and four squares (4) elementary algebraic number theory (5) examples of Diophantine equations (6) the Prime Number Theorem (7) Dirichlet characters and primes in arithmetic progressions (8) Arithmetic functions and their statistical properties The lecture will emphasize the connections between the topics and their links to current research. Moreover, computer experiments using Pari/GP and other software will be part of the lecture.

Resources

Lecture Notes

The lecturer's notes will be scanned and available.

Literature

J-P. Serre, "A course in arithmetic" Ireland and Rosen, "A classical introduction to modern number theory" Hardy and Wright, "An introduction to the theory of numbers"

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 150 minutes
Aids
None

Course Components

Type Title Time & Place Hours
lecture with exercise Number Theory I
  • Wed 10:15-12:00 (HG E 1.1)
  • Fri 10:15-12:00 (HG E 1.1)
4 h weekly

Offered In