This course introduces the participants to some of the fundamental parts of functional analysis, a discipline that is concerned with ubiquitous abstract structures in analysis. It covers the basic theory of Hilbert and Banach spaces and their operators.
Compulsory: “Linear Functional Analysis” by Rynne and Youngson, 2nd ed., Springer, 2008, ISBN: 978-1-84800-004-9.
For students, a paper version of this book is also available for approximately 25 euro via the MyCopy-option in SpringerLink. Alternatively, a free PDF can legally be obtained by students via SpringerLink. Please note that one has to use a computer at the Mathematical Institute for both these options.
Blackboard. Enrollment is compulsory.
Rather limited. Basic knowledge of linear algebra (hardly beyond the notion of abstract vector spaces and linear maps) and elementary topology (metric spaces) are required.
Understanding the language of functional analysis is indispensable for various parts of analysis and stochastics. Therefore, it is strongly recommended that students with an interest in analysis or stochastics follow Linear Analysis in their third year, as well as Measure Theory. For other students these courses may be a valuable addition in later years.
Linear Analysis contains the prerequisites (!) for the national master course Functional Analysis. The latter yearly course is intended for students who want to continue in this direction, and it is likewise taught in the fall semester. It is not uncommon that students follow Linear Analysis (and Measure Theory) in their third year, the national course Functional Analysis in their fourth year, and write a Master’s thesis in functional analysis in their final year.
It is strongly recommended that students with an interest in analysis or stochastics follow Linear Analysis in their third year, as well as Measure Theory. For other students these courses may also be a valuable addition in later years.
Lecture hours per week
During the course, individual students hand in seven assignments, according to a schedule that is provided in Blackboard at the start of the semester. The final grade is determined as the average of the best six result for these assignments.