Algebra: Structures and Algorithms
Algebra: Strukturen und Algorithmen
6 CPirregularlyEN
Prerequisites
Recommended, as written
Knowledge of the content of the modules • 11101: Lineare Algebra und analytische Geometrie I or • 11112: Mathematik IT-1 (Diskrete Mathematik), and • 11113: Mathematik IT-2 (Lineare Algebra)
Contents
• Commutative rings and ideals • Affine varieties • Groebner basis and the Hilbert basis theorem • Elimination of variables with Groebner bases and resultsants • Hilbert's Nullstellensatz • Selected applications (e.g. global optimization, solution of kinematic problems, automated theory proving)
Learning outcomes
After successfully completing the module, students are able to work with basic algebraic concepts and know basic algebraic facts and constructions. They are able to use this knowledge to solve algebraic problems, with our without the assistance of computer-algebra systems. Students understand the basic algebraic algorithmic machinery of computational algebra.
Assessment
Final module examination: • Written examination, 90 min. OR • Oral examination, 30 - 45 min. (with small number of participants) In the first lecture it will introduced, if the examination will organized in written or oral form.
Literature (3)
- D. Cox, J. Little, and D. O’Shea: Ideals, Varieties, and Algorithms–An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer Publishing Company, 2010
- D. Cox, J. Little, and D. O’Shea: Using Algebraic Geometry, Springer Publishing Company, 2005
- S. Lang: Algebra, Springer Publishing Company, 2002
Remarks
• Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“ • Studiengang Mathematics M.Sc.: Wahlpflichtmodul im Komplex „Analysis / Algebra / Combinatorics“ • Studiengang Mathematical Data Science M.Sc.: Wahlpflichtmodul im Komplex „Advanced Mathematical Methods in Data Science“ • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Advanded Methods“ • Study programme Informatik B.Sc.: Compulsory elective module in „Praktische Mathematik" or in field of application „Mathematics" • Study programme Informatik M.Sc.: Compulsory elective module in „Mathematik" or in field of application „Mathematik" • Study programme Cyber Security M.Sc.: Compulsory elective module in complex „Computer Science“
Source: BTU's module description · retrieved 29 Sep 2026Original