Mathematics: Fourier Analysis

This course introduces key techniques of modern Fourier analysis and demonstrates how they are applied in different areas of mathematics and science. You’ll learn how to break down complex functions into simpler components using Fourier series and transforms, and explore how these methods apply to areas such as dynamical systems, number theory, and partial differential equations.

Topics include

• Fourier series, the Fourier transform in one and several variables, and the Fourier transform on finite commutative groups
• L^2 convergence of Fourier series, pointwise convergence
• Cesàro means and Fejer’s theorem, Weyl’s criterion
• The Fourier inversion theorem, Parseval’s and Plancherel’s theorem, Poisson summation formula, and the Heisenberg inequality
• Examples of applications in physics and in other areas of mathematics, including dynamical systems, number theory, and partial differential equations.

The course is an alternative-compulsory course within the Master’s Programme in Mathematics at Lund University. Students in the Bachelor’s Programme in Mathematics may take it as an elective, and it is also offered as a standalone course.

Teaching is based on lectures and seminars, with assignments that support your learning. You will work both independently and in groups to solve problems and present your reasoning clearly, both in writing and orally.

Assessment includes a written exam and an oral exam at the end of the course. Bonus points from completed assignments may count toward your final score on the written exam. The oral exam is only available to students who pass the written exam. Re-examinations are offered shortly after the regular ones.

Fourier analysis is a cornerstone ofin many advanced areas of mathematics and theoretical physics. After completing the course, you will be equipped to apply these techniques in research or further studies, especially in fields like harmonic analysis, signal processing, quantum mechanics, dynamical systems and PDEs. The course also strengthens your foundation for doctoral studies or analytical roles in academia and industry.

Entry requirements

To be admitted to the course, the student must have completed at least 90 credits, of which 75 credits must be in mathematics, including knowledge equivalent to the course MATB34 Linear Analysis (7.5 credits). The courses MATC21 Complex Analysis 1 (7.5 credits) and MATM39 Integration Theory (7.5 credits) are recommended but not compulsory.

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.