MM548: Measure and Integration and Banach spaces

In relation to the competence profile of the degree it is the explicit focus of the course to:

• Give the competence to handle complex situations in study.
• Give skills to:
1. apply the thinking and terminology from the subject's basic disciplines.
2. analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model.
• Give knowledge and understanding of:
1. basic knowledge generation, theory and methods in mathematics.
2. how to conduct analyses using mathematical methods and critically evaluate scientific theories and models.

• use methods from the theory to solve practical problems, especially related to the integral convergence theorems, Fubini’s theorem, and calculate Fourier series
• present statements and proofs of items from an a priori given list of topics
• Answer additional questions from teachers and examiners around the central concepts and results from the above list
• Understand the basic theory in this area, including in particular concepts of sigma-algebra, measurability, integral
• use methods from the theory to solve problems related to measure and integration and Banach space theory
• give an oral and written presentation in correct mathematical language

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

• Intro phase (lectures, class lessons) - 42 hours
• Training phase: 22 hours
• Studiefase: 15 hours

Teaching method
Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.

Educational activities