250060 VO Algebraic number theory (2018W)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Thursday
31.01.2019
13:15 - 15:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday
11.02.2019
Tuesday
19.02.2019
Tuesday
05.03.2019
Thursday
07.03.2019
Tuesday
19.03.2019
Friday
17.05.2019
Thursday
12.09.2019
Friday
15.11.2019
Monday
25.11.2019
Friday
06.03.2020
Lecturers
Classes (iCal) - next class is marked with N
Wednesday
03.10.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
05.10.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
10.10.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
12.10.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
17.10.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
19.10.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
24.10.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
31.10.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
07.11.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
09.11.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
14.11.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
16.11.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
21.11.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
23.11.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
28.11.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
30.11.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
05.12.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
07.12.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
12.12.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
14.12.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday
17.12.
11:30 - 13:30
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
09.01.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
11.01.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
16.01.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
18.01.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
23.01.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Friday
25.01.
13:15 - 14:45
Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
30.01.
16:45 - 18:15
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Assessment and permitted materials
Written or oral exam
Minimum requirements and assessment criteria
To pass the written or oral exam
Examination topics
Content of the lecture
Reading list
Neukirch "Algebraische Zahlentheorie"Koch "Algebraische Zahlentheorie"Lang "Algebraic number theory"I. Stewart, D. Tall, Algebraic Number Theory and Fermat's Last TheoremD.A. Marcus, Number FieldsW. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers
Association in the course directory
MALZ
Last modified: Mo 07.09.2020 15:40
attempt to generalize the quadratic reciprocity law to higher
power residues. While the quadratic reciprocity law can be formulated entirely in Q, i.e. it
can be formulated using only rational
numbers the formulation of higher reciprocity laws involves n-th roots of unity, i.e. it
necessarily takes place in a finite extension of Q. This creates the need to consider
finite (i.e. algebraic) extensions of Q - the so called
algebraic number fields - in analogy with Q. The goal of algebraic number theory thus is
to extend the essential properties of
the field Q to finite extensions of Q. Briefly, this means- to find an analogoue in number fields of the ring of integers Z in Q; in particular this analogoue is a ring and it should have some kind of factorization into primes property.
The study of these rings is a fundament of algebraic number theory.- to find an analogoue of the embedding of Q into R (and also into p-adic fields Q_p); this makes possible to relate algebraic numbers to geometry and analysis.If time permits we can occasionally touch on aspects of the modern formulation of
algebraic number theory which evolved in connection
with the geometric interpretation of algebraic numbers.Prerequisites for the course ``Algebraic number theory'' are Algebra 1 and Algebra 2.