Coursework Artinyan

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.

Course codeReductionFromTo

Examination arrangement: Written examination
Grade: Letters

Evaluation formWeightingDurationExamination aidsGrade deviation
Written examination100/1004 hours D

Having resided in Los Angeles, San Diego and Palm Springs, Nicole Artinian knows the South California real estate landscape like no other. As she puts it, "I've lived in these cities, I know these markets, and I've seen firsthand how they've changed over the years."

In fact, Nicole has had a passion for real estate for as long as she can remember. Thanks to her investor father, she was exposed to buying, selling and property management from a young age. Her father instilled in her the value of ownership, and she's owned and managed her own commercial properties for some time. "My father always told us, 'No matter what you do, own the land,'" she says.

After learning important lessons in business and problem-solving while managing one of her father's auto body shops, Nicole formalized her education at the University of San Diego where she obtained her bachelor's degree in business with an emphasis on sales and negotiation coursework. In fact, she considers negotiating to be one of her strongest skills as an agent. "I'm not an in-your-face person, but I am a firm negotiator. I know how to get to yes on both sides of the table."

With deep expertise in residential, commercial and multi-family real estate, Nicole is a powerful resource to those looking to buy or sell throughout Southern California. For her, the ultimate reward is making the dream of property ownership a reality for others, like her father did for her. "Finding someone a home or property that they love or garnering an incredible return on investment is incredibly fulfilling. That's really exciting for me."

A Los Angeles native, Nicole currently splits her time between San Diego and LA. She has a passion for discovery and can often be found exploring great properties, attractions and restaurants all over Southern California.

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