# Linear Analysis (BM)

Course
2024-2025

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 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.

## Timetable

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, where homework counts as a practical. To pass the course, the grade for the written exam must be at least 5, regardless of what the homework grade is. 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. The homework is not compulsory. 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.

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.

## Registration

Please register for the course in 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 note that it is compulsory to register 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. Not being registered for an exam means your grade will not be processed.

## Contact

b.mesland[at]math.leidenuniv.nl