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Linear Analysis (BM)


Admission requirements

Linear algebra (Metric) topology (required)
Basics of measure and integration theory (required)


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.

Course Objectives

Knowledge of the concepts of 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.


You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

Mode of instruction

Lecture (2 hours) and question hour (non-compulsory).

Assessment method

Written exam and homework. During the course, there will be six homework assignments to be handed in at predetermined dates. Out of these, the five best count towards the final grade. For the final grade, the homework counts for 25% and the written exam for 75%, 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.

Reading list

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.


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.