# Linear Analysis (BM)

Vak
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

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## 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

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

b.mesland[at]math.leidenuniv.nl

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.