Admission requirements
Linear algebra,
(Metric) topology,
basics of measure and integration theory
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 normed spaces and inner product spaces, in particular Banach spaces and Hilbert spaces, and continuous linear maps between such spaces.
Course objectives
Knowledge of the concepts of a normed space, Banach space, Hilbert space, orthonormal basis, linear operator, bounded operator, dual space.
Knowledge of the theorems of Hahn-Banach, Banach-Steinhaus, closed graph, and bounded inverse.
The ability to apply these concepts and theorems to solve problems in functional analysis.
Schedule
The timetables are available through My Timetable (see the button in the upper right corner).
Teaching method
One lecture of 2 hours per week.
Assesment method
Written exam and homework, where homework counts as a practical. The homework is not compulsory. To pass the course, the unrounded final grade must be at least 5.5 and the grade for the written exam must be at least 5.
For the final grade, the homework counts for 10% and the written exam for 90%, unless the grade for the written exam is higher than the aforementioned weighted average. In the latter case, the final grade is equal to the the grade for the written exam. The homework schedule will be made available through Brightspace.
Resit, review & feedback
There will be a resit for the written exam. There are no retake opportunities for the homework.
After the grades of the written exam are known and before the retake, an opportunity will be offered to see the exam work and discuss it with the instructor. Details will be announced on Brightspace.
Reading list
Compulsory: “Linear Functional Analysis” by Rynne and Youngson, 2nd ed., Springer, 2008, ISBN: 978-1-84800-004-9.
A free PDF can legally be obtained by students via the website of our university library from SpringerLink, after logging in with a ULCN account. On SpringerLink, there is also a MyCopy option available to buy a paper version of the book for approximately 40 euro.
Online resellers may offer better deals.
Registration
Enrolment through MyStudyMap (button in upper right corner) is mandatory. General information about course and exam enrolment is available on the website https://www.student.universiteitleiden.nl/en/your-study-programme/courses-and-exams/enrolment/leiden-university
Contact
Onno van Gaans,
Mathematical Institute, Gorlaeus BW1.15
Email: vangaans@math.leidenuniv.nl
Tel.: 071 527 7122
Remarks
None