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Course Catalog 2012-2013
MAT-53756 Introduction to Geometric Algebras and their Applications, 7 cr |
Additional information
Suitable for postgraduate studies
Person responsible
Sirkka-Liisa Eriksson
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Written final examination or two partial exams
Completion parts must belong to the same implementation
Principles and baselines related to teaching and learning
During the course there are instructed exercises that helps learning. Moodle study platform is used during the course and extra material may be handed out through that there and students may discuss about there problem.-
Learning outcomes
After completion of the course the students knows geometric products and their importance. The student is capable of applying them in geometric problems. The student knows the foundations of the analysis in higher dimensions. using geometric algebras and the special case quaternions. The student can apply them for solving systems of partial differential equations.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Introduction to geometric or Clifford algebras and their basic elements scalars, vectors, bivectors and multivectors | ||
| 2. | Exterior product, contraction and geometric product and their calculation rules. | ||
| 3. | Calculation of vector derivatives and integrals using geometric algebras | ||
| 4. | Cauchy theorem in higher dimensions. Dirac and Maxwell equations |
Evaluation criteria for the course
The grade of the course is based on the final exam or two partial exams. When the points for the final exam or the partial exams are 30% of the maximum, the grade of the course may be improved by bonus points collected from the instructed exercises and homework. The passing limit is 50% of the maximum. If the student is mastering the concepts, results, short proofs and examples type of problems the evaluation is 3. For the grade 4 the student should in addition to the previous level be able to independenly apply theory more. For the grade 5 the student should independently deduce results, invent solutions and compare results more than in the previous levels.
Assessment scale:
Numerical evaluation scale (1-5) will be used on the course
Partial passing:
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Summary of lectures | An Introduction to geometric algebras | Janne Pesonen | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-41150 Algebra 1 | Advisable |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
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Contact teaching: 0 % Distance learning: 0 % Self-directed learning: 0 % |