Course syllabus - Applied Algebraic Structures

Objectives

The course aims to provide students with broad knowledge of how the most important algebraic and operator algebraic structures, ideas, concepts, methods and calculation tools arise and applied in science and technology, and in this context to develop the ability to master logic, algorithms, modeling and calculations in a useful way.
 

Learning outcomes

After completing the course the student is expected to be able to
- Explain the basic ideas and principles of symmetry analysis and the main applications of symmetry in science, engineering and life sciences
- Use solution methods and properties of systems of polynomial equations and relevant basics of algebraic geometry and commutative algebra in applications, particularly in robotics, computer vision and mechanics
- Explain initial ideas and examples of non-commutative analysis, operator algebra and non-commutative geometry and their fundamental role in mathematics and science
- Explain and explore the most important examples, concepts, ideas and generalizations of Lie analysis, Lie algebra, related non-associative structures, deformations of algebraic and geometric structures and their applications in physics and engineering
- Formulate and apply fundamental principles and models for rewriting systems and operads in computer science and physics
 

Course content

- Symmetry Analysis and symmetries in science, engineering and life sciences
- Systems of polynomial equations, algebraic geometry and commutative algebra in robotics, computer vision and mechanics
- Algebraic analysis of differential equations, integral equations, difference equations, recursive equations, functional equations and applications
- Non-commutative matrix equations in the stability analysis, optimization, control engineering and physics
- Lie analysis, Lie algebra, generalized Lie structures, hom-algebraic structures, non-associative algebra, deformations of algebraic and geometric structures in physics and engineering
- Non-commutative algebra and linear representations in physics and engineering
- Rewriting Systems and operads in computer science and physics
 

Tuition

Lectures and classes with both individual work and group work.
 

Specific requirements

120 credit points in one or several of the following subject areas: Engineering, Natural Science, Economics  or Business Administration with at least 60 credits in engineering and natural sciences including 30 credits in Mathematics / Applied Mathematics which must include either Applied Matrix Analysis, 7.5 credits or equivalent, or Abstract Algebra, 7.5 credits or equivalent. In addition Swedish B / Swedish 3 and English A / English 6 are required. In cases where the course is taught in English the requirement of Swedish B / Swedish 3 is excluded.
 

Examination

Project (PRO1), 4,5 credits, marks Pass (G) or Pass with distinction (VG)
Seminar (SEM1), 3 credits, marks Pass (G) or Pass with distinction (VG)
 

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail