Universität Wien FIND

Due to the COVID-19 pandemic, changes to courses and exams may be necessary at short notice (e.g. cancellation of on-site teaching and conversion to online exams). Register for courses/exams via u:space, find out about the current status on u:find and on the moodle learning platform. NOTE: Courses where at least one unit is on-site are currently marked "on-site" in u:find.

Further information about on-site teaching and access tests can be found at https://studieren.univie.ac.at/en/info.

250031 VO Computational Commutative Algebra (2020W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Tuesday 06.10. 14:00 - 14:45 Digital
Wednesday 07.10. 14:00 - 15:30 Digital
Tuesday 13.10. 14:00 - 14:45 Digital
Wednesday 14.10. 14:00 - 15:30 Digital
Tuesday 20.10. 14:00 - 14:45 Digital
Wednesday 21.10. 14:00 - 15:30 Digital
Tuesday 27.10. 14:00 - 14:45 Digital
Wednesday 28.10. 14:00 - 15:30 Digital
Tuesday 03.11. 14:00 - 14:45 Digital
Wednesday 04.11. 14:00 - 15:30 Digital
Tuesday 10.11. 14:00 - 14:45 Digital
Wednesday 11.11. 14:00 - 15:30 Digital
Tuesday 17.11. 14:00 - 14:45 Digital
Wednesday 18.11. 14:00 - 15:30 Digital
Tuesday 24.11. 14:00 - 14:45 Digital
Wednesday 25.11. 14:00 - 15:30 Digital
Tuesday 01.12. 14:00 - 14:45 Digital
Wednesday 02.12. 14:00 - 15:30 Digital
Wednesday 09.12. 14:00 - 15:30 Digital
Tuesday 15.12. 14:00 - 14:45 Digital
Wednesday 16.12. 14:00 - 15:30 Digital
Tuesday 12.01. 14:00 - 14:45 Digital
Wednesday 13.01. 14:00 - 15:30 Digital
Tuesday 19.01. 14:00 - 14:45 Digital
Wednesday 20.01. 14:00 - 15:30 Digital
Tuesday 26.01. 14:00 - 14:45 Digital
Wednesday 27.01. 14:00 - 15:30 Digital

Information

Aims, contents and method of the course

The aim of this lecture is to study commutative rings, their ideals and modules over commutative rings. This can serve as a basis for algebraic geometry, invariant theory, algebraic number theory and other subjects. We will cover the basic notions, and introduce, among other things, localizations, Noetherian rings, affine algebraic sets, Groebner bases, modules, integral extensions, Dedekind rings and discrete valuation rings. Moreover we will consider the computational aspects of the theory and compute several examples. Here the computation of Groebner bases and its applications is one of the main goals.

Assessment and permitted materials

There will be a written examination after the end of the lecture. There are no tools allowed.

Minimum requirements and assessment criteria

50 percent of the total points required to pass.

Examination topics

Exam material contains all topics covered in the lecture including examples and computations.

Reading list

[AM] M.F. Atiyah, I.G. Macdonald: Introduction to commutative Algebra, 1969.
[COX] D. Cox, J. L. Donal O’Shea: Geometry, Algebra, and Algorithms.
[EIS] D. Eisenbud, Commutative Algebra, 1995.
[SAZ] P. Samuel, O. Zariski: Commutative Algebra, 1975.
[SHA] R. Y. Sharp: Steps in commutative algebra, 2000.

Association in the course directory

MALV, MAMV

Last modified: Mo 09.11.2020 11:29