Course Catalog 2012-2013
International

Basic Pori International Postgraduate Open University

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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
Lectures
Excercises


 


 
 4 h/per
 3 h/per
+3 h/per
+3 h/per


 
MAT-53756 2012-01 Monday 12 - 14, TB214
Tuesday 10 - 12, TB214
Monday 9 - 12, TB216

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:

Completion parts must belong to the same implementation

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 
MAT-53756 Introduction to Geometric Algebras and their Applications, 7 cr MAT-53750 Introduction to Geometric Algebras and their Applications, 7 cr  

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-53756 2012-01       Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified07.03.2012