273049.0 Advanced Analysis I (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Grading scale:
0-5
Description
The courses Advanced analysis 1-2 pertain to the formalization of mathematical structures that in some sense generalize R^n and hence exhibit some similar properties. Such structures lay the foundation of, e.g., modern real and functional analysis as well as probability theory.
Part 1: metric, normed and unitary spaces; briefly on topological spaces. Linear maps. Open and closed sets, convergence, continuity, completeness.
Learning outcomes
By the end of the course, a student should
-know, understand and be able to apply foundational concepts within analysis and functional analysis; and
-be able to study independently typical contemporary graduate-level literature within these areas.
Additional information
The course is taught roughly every second year
Description of prerequisites
BSc level analysis and calculus.