Description
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.
Literature
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.
Homepage
Brightspace. Enrollment is compulsory.
Prerequisites
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.
Knowledge of measure and integration theory is not necessary.
Possible sequels
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 Advanced 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 Advanced 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.
Remark
It is strongly recommended that students with an interest in analysis or stochastics follow Linear Analysis in their third year, as well as Advanced Measure Theory. For other students these courses may also be a valuable addition in later years.
Lecture hours per week
2
Assessment
During the course, individual students can hand in a number of assignments, according to a schedule that is provided in Blackboard at the start of the semester. The lowest grade for these is stricken, and the homework grade is determined as the (unrounded) average of the remaining grades for these assignments.
The unrounded final grade for the course is the maximum of:
the weighted average of the homework grade (25%) and the maximum of the (unrounded) grades for the written exam and the resit (75%), and
the (unrounded) grade for the written exam, and
the (unrounded) grade for the resit.
This maximum is then rounded to the nearest half-integer, but not to 5.5, to obtain the final grade for the course. If the result is 6.0 or higher, this is a "pass", provided that a grade of at least 5.0 (unrounded) has been obtained for the written exam and/or the resit. If the result is 5.0 or lower, or if no grade of at least 5.0 (unrounded) has been obtained for the written exam and/or the resit, this is a "fail".
During the written exam and the resit you can use the textbook of the course and the notes that you may have taken.
Although it is, in principle, possible to pass the course without participating in the homework, it is strongly recommended to use the homework assignments as a preparation for the written exam and/or the resit.
The grades for the homework, the written exam, and the resit are valid only for the current academic year.