The course builds further on the course TMA4150 Algebra. It gives a basis for further studies in algebra by discussing central classes of rings, and by giving an introduction to the theory of modules. An alternative approach to Jordan canonical form is given as an application of module theory. The course includes Artinian and Noeterian rings and modules, structure
theorems for modules over principal ideal domains and for simple and semisimple rings. Jordan canonical form of matrices with application to systems of differential equations is also discussed.
1. Knowledge. The student has knowledge of fundamental properties of rings and modules, and examples of such. In particular, the student is familiar with the key properties and examples of noetherian, artinian and semisimple rings and modules.
2. Skills. The student is able to decide whether a given ring or module, or a class of rings or modules, is noetherian/artinian/semisimple, by applying the characterizations discussed in the course. The student is able to calculate the Jordan canonical form of a matrix, and use this to solve systems of linear differential equations.
Lectures. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. If the course is taught in English, the exam will be given only in English. Students may answer either in Norwegian or English. Retake of examination may be given as an oral examination.
see «Teaching methods and activities».
The course is based on MA1201 Linear algebra and geometry, MA1202 Linear algebra with applications and MA2201 Algebra, or equivalent knowledge.
Will be announced at the start of the course.
Examination arrangement: Written examination
|Evaluation form||Weighting||Duration||Examination aids||Grade deviation|
|Written examination||100/100||4 hours||D|
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