Mathematics: Specialised Course in Linear Functional Analysis

This course explores how core principles from functional analysis can be applied to a wide range of problems in mathematical analysis. You’ll learn how abstract concepts like weak convergence, compactness, and spectral theory are used to understand and solve complex mathematical challenges.

The course is alternative-compulsory within the Master’s Programme in Mathematics at Lund University and is also offered as a standalone course. It is given in parallel with MATP35 Linear Functional Analysis, offering the possibility to dive deeper into the subject. We strongly recommend students to take both courses during the same semester for a comprehensive understanding of functional analysis.

Topics include

• Hahn–Banach Theorem
• Weak convergence and compactness
• Riesz Representation Theorem
• Orthonormal bases
• Boundedness, compactness, and spectra of integral operators
• Spectral theorem for compact, self-adjoint operators

You’ll gain both theoretical insight and practical skills that are relevant for advanced studies and research.

Teaching is based on lectures and seminars. The focus is on problem-solving and presenting key results. You’re expected to actively participate in discussions and presentations. Assessment includes oral presentations of problems or proofs and a final problem-solving project.

The grading scale is: Fail, Pass, Pass with Distinction. To earn a distinction, you need at least 75% of the total points, with the project is weighted six times more than the oral presentations.

This course prepares you for advanced studies and research in mathematics and physics. You will develop the ability to solve complex problems using functional analysis, work independently on advanced tasks, and understand the role of functional analysis in modern research. Completing the course provides a strong foundation for doctoral studies or careers in academia, data science, theoretical physics, or any field where deep mathematical understanding is essential.

Entry requirements

At least 90 credits in mathematics. In addition it is required that the student has either completed a course in Linear functional analysis or is taking the course MATP35 Linear functional analysis, 7.5 credits, in parallel to the present course. English 6/English course B.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.