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Number Theory I
Last Updated: 2026-06-03 00:07:54
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" E. Kowalski, "Number theory I", lectures notes from HS 2024 (which will be updated)
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 | No time listed | 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 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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