Mathematics: Linear Functional Analysis
Course · 7.5 credits
The course presents the principles of functional analysis and their applications. These include the basic properties of Banach and Hilbert spaces as well as the spectral theory of bounded and compact linear operators.
The course treats fundamental properties of Banach and Hilbert spaces and the bounded linear operators defined on them:
- Banach spaces, the Hahn-Banach Theorem, weak convergence and weak precompactness of the unit ball.
- Hilbert spaces. Examples including L2 spaces. Orthogonality, orthogonal complement, closed subspaces, projection theorem. Riesz Representation Theorem.
- Orthonormal sets, Bessel's inequality. Complete orthonormal sets, Parseval's identity.
- Baire Category Theorem and its consequences for operators on Banach spaces (uniform boundedness, open mapping, inverse mapping and closed graph theorems). Strong convergence of sequences of operators.
- Bounded and compact linear operators on Banach spaces and their spectra.
- The spectral theorem for compact self-adjoint operators on Hilbert spaces.
Closed for applicationsApplication opportunities
Mathematics (Faculty of Sciences)
Sölvegatan 18A, 223 62 Lund
Box 118, 221 00 Lund
+46 46 222 85 41
kjell [dot] elfstrom [at] math [dot] lu [dot] se
Requirements and selection
At least 90 credits in pure mathematics including knowledge corresponding to a course in Integration Theory, 7.5 credits (Lebesgue integral). English 6/English course B.
English language requirements
Most of Lund University’s programmes require English Level 6 (unless otherwise stated under 'Entry requirements'). This is the equivalent of an overall IELTS score of 6.5 or a TOEFL score of 90. There are several ways to prove your English language proficiency – check which proof is accepted at the University Admissions in Sweden website. All students must prove they meet English language requirements by the deadline, in order to be considered for admission.
Check if there are any country-specific eligibility rules for you to study Master's studies or Bachelor's studies in Sweden.
Start Autumn Semester 2022
Day-time Lund, part time 25%
29 August 2022 - 15 January 2023
Closed for applications
How to apply
Lund University uses a national application system run by University Admissions in Sweden. It is only possible to apply during the application periods.
Step 1: Apply online
- Check that you meet the entry requirements of the programme or course you are interested in (refer to the section above on this webpage).
- Start your application – go to the University Admissions in Sweden website where you create an account and select programmes/courses during the application period.
Visit the University Admissions in Sweden website
- Rank your programme/course choices in order of preference and submit them before the application deadline.
Step 2: Submit documents
- Read about how to document your eligibility and how to submit your documents at the University Admissions in Sweden website. Follow any country-specific document rules for Master's studies or Bachelor's studies
Country-specific requirements for Bachelor's studies – universityadmissions.se
Country-specific requirements for Master's studies – universityadmissions.se
- Get all your documents ready:
- official transcripts and high school diploma (Bachelor's applicants)
- official transcripts and degree certificate or proof of expected graduation (Master's applicants)
- passport/ID (all applicants) and
- proof of English proficiency (all applicants).
- Prepare programme-specific documents if stated in the next paragraph on this webpage.
- Upload or send all required documents to University Admissions before the document deadline.
- Pay the application fee (if applicable – refer to the section below on this webpage) before the document deadline.
* Note that the process is different if you are applying as an exchange student or as a part of a cooperation programme (such as Erasmus+).
* If you have studied your entire Bachelor's programme in Sweden and all of your academic credits are in Ladok, you do not have to submit transcripts or your diploma when applying for a Master's programme. However, there may still be other documents you need to submit! See the link below.
* Svensk student?
Läs instruktionerna om att söka till ett internationellt masterprogram på lu.se
Full programme/course tuition fee: SEK 18 125
First payment: SEK 18 125
Citizens of a country outside of the European Union (EU), the European Economic Area (EEA) and Switzerland are required to pay tuition fees. You pay one instalment of the tuition fee in advance of each semester.
EU/EEA citizens and Switzerland
There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.
If you are required to pay tuition fees, you are generally also required to pay an application fee of SEK 900 (approximately EUR 100) when you apply at the University Admissions in Sweden website. You pay one application fee regardless of how many programmes or courses you apply to.
*Note that there are no tuition or application fees for exchange students or PhD students, regardless of their nationality.
Scholarships & funding
Lund University Global Scholarship programme
The Lund University Global Scholarship programme is a merit-based and selective scholarship targeted at top academic students from countries outside the EU/EEA.
Swedish Institute Scholarships
The Swedish Institute offers scholarships to international students applying for studies in Sweden at Bachelor's, Master's, PhD and post-doctoral levels.
Country-specific scholarships and funding options
Lund University has agreements with scholarship organisations and funding bodies in different countries, which may allow applicants to apply for funding or scholarships in their home countries for their studies at Lund University.
- Scholarships/funding for students from Indonesia, Mexico, Colombia, Russia and Chile, among other countries
- US student finance
- Canada student finance