MAT4370 – Introduction to Fourier Analysis and Wavelet Theory
Schedule, syllabus and examination date
The subject encompasses classical and modern Fourier analysis. The material covered includes the Haar wavelet, elementary functional analysis and Hilbert space theory, Fourier series and Fourier transform, the Fourier inversion formula, Plancherel´s theorem, othonormal wavelet basises and tight frames, multiresolution analysis, classification of wavelets with compact support, pyramid algorithm, convergence of cascade approximants, transfer operators.
The subject gives basic mathematical understanding of fundamental subjects which has applications in the development of tools and techniques which may be used in signal theory, communication techniques, graphical algorithms and numerical analysis. The course is also an entrance to various concrete aspects of functional analysis which has interest for other parts of mathematics.
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Recommended previous knowledge
MAT2400 – Real Analysis and one or more of the following: MAT-INF1310 – Ordinary differential equations (discontinued), MAT-INF3300 – Partial differential equations and Sobolev spaces I (discontinued), MAT3300 – Measure and integration (discontinued), MAT2410 – Introduction to Complex Analysis, MAT4340 – Elementary functional analysis (discontinued)
4 hours of lectures per week
Oral exam. Letter grading (A-F)
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Explanations and appeals
Resit an examination
Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.
Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.