# 13911 - Algebra: Structures and Algorithms Modulübersicht

 Module Number: 13911 Module Title: Algebra: Structures and Algorithms Algebra: Strukturen und Algorithmen Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology Responsible Staff Member: Prof. Dr. rer. nat. Averkov, Gennadiy Language of Teaching / Examination: English Duration: 1 semester Frequency of Offer: On special announcement Credits: 6 Learning Outcome: 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. Contents: Commutative rings and ideals Affine varietiesGroebner 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) Recommended Prerequisites: Knowledge of the content of the modules 11101: Lineare Algebra und analytische Geometrie I or 11112: Mathematik IT-1 (Diskrete Mathematik), and11113: Mathematik IT-2 (Lineare Algebra) Mandatory Prerequisites: None Forms of Teaching and Proportion: Lecture / 3 Hours per Week per Semester Exercise / 1 Hours per Week per Semester Self organised studies / 120 Hours Teaching Materials and Literature: D. Cox, J. Little, and D. O’Shea: Ideals, Varieties, and Algorithms–An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer Publishing Company, 2010D. Cox, J. Little, and D. O’Shea: Using Algebraic Geometry, Springer Publishing Company, 2005S. Lang: Algebra, Springer Publishing Company, 2002 Module Examination: Final Module Examination (MAP) Assessment Mode for Module Examination: Final module examination:Written examination, 90 min. OROral 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. Evaluation of Module Examination: Performance Verification – graded Limited Number of Participants: None Part of the Study Programme: Master (research-oriented) / Angewandte Mathematik / PO 2019 Master (research-oriented) / Artificial Intelligence / PO 2022 Bachelor (research-oriented) / Informatik / PO 2008 Master (research-oriented) / Informatik / PO 2008 Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2023 Bachelor (research-oriented) - Co-Op Programme with Practical Placement / Wirtschaftsmathematik - dual / PO 2023 Remarks: Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“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 extendStudy 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" Module Components: Lecture Algebra: Structures and Algorithms, with integrated exerciseRelated examination Components to be offered in the Current Semester: no assignment