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| MATH0468-1 | Algebraic Analysis
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Number of credits : |
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| Lecturer : | Jean-Pierre Schneiders |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| This course presents first the basic results of the theory of sheaves and then deals with the theory of modules over the sheaf of linear differential operators with holomorphic coefficients. One then shows how the study of these modules is related to the one of systems of partial differential equations in the complex domain. Finally, one shows how to apply some results of homological algebra and sheaf theory to obtain local and global informations on the solutions of systems of this kind. |
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Learning outcomes of the course :
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| At the end of the course, the students should be able to understand recent works on algebraic analysis and to begin a research work in this field. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Good knowledge of algebra, topology, geometry, analysis and of algebraic topology. |
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Planned learning activities and teaching methods :
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| The course consists of blackboard lessons, exercises sessions and a personal work.
During the lessons, the main theoretical results are introduced, established and illustrated with examples.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons
The personal work consists of the preparation of a short paper presenting and establishing a result related to the course but not considered during the lessons. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face course. |
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Recommended or required readings :
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| Reference texts are pointed out at the beginning of the course. |
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Assessment methods and criteria :
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| An examination comprising an oral part on the theory and a presentation of the personal work is organized during the first session. A similar examination is organized during the second session. |
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Work placement(s) :
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Organizational remarks :
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| The course follows the official schedule handed out to the students at the beginning of the academic year. |
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Contacts :
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| Jean-Pierre Schneiders
Département de Mathématique (Bât. B37, Bureau 1/60)
Grande Traverse 12 - 4000 Liège (Sart-Tilman)
Phone: (04) 366.94.01 - E-Mail: jpschneiders@ulg.ac.be
Web page: http://www.analg.ulg.ac.be/jps/ |
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| Items online : |
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| Course web page |
| Web page giving access to various informations on the course and to the electronic version of the notes. |
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