MAT3400 – Linear Analysis with Applications
Course description
Schedule, syllabus and examination date
Course content
The course gives a thorough introduction to measure and integration theory together with a basic introduction to functional analysis. Covered topics include Banach and Hilbert spaces, Hahn-Banach theorem, dual spaces, orthonormal bases, measure spaces, Lebesgue integration, convergence theorems, Lp-spaces and their duals, construction and decomposition of measures, Lebesgue and Lebesgue-Stieltjes measures, Littlewood’s principles, Riesz-Markov theorem, product measures and Fubini-Tonelli theorems, fundamental theorem of calculus, Fourier transform and Plancherel theorem, conditional expectations and martingales.
Learning outcome
After completing the course you
are used to work with measure spaces and integration of measurable functions
have a good understanding of the most frequently used tools of Lebesgue integration such as convergence theorems and Fubini-Tonelli theorems
have a good understanding of various function spaces and their duals
are acquainted with basic notions of functional analysis
are familiar with fundamental tools of Fourier analysis
are prepared for more advanced courses on differential equations, harmonic, stochastic and functional analysis
Admission to the course
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.
Special admission requirements
In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:
- Mathematics R1 (or Mathematics S1 and S2) + R2
And in addition one of these:
- Physics (1+2)
- Chemistry (1+2)
- Biology (1+2)
- Information technology (1+2)
- Geosciences (1+2)
- Technology and theories of research (1+2)
The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).
Recommended previous knowledge
- MAT1100 – Calculus
- MAT-INF1100 – Modelling and Computations
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- MAT2400 – Real Analysis
Overlapping courses
- 10 credits overlap with MAT4400 – Linear Analysis with Applications.
- 5 credits overlap with MAT4300 – Measure and integration (discontinued).
- 5 credits overlap with MAT4340 – Elementary functional analysis (discontinued).
- 5 credits overlap with MAT3300 – Measure and integration (discontinued).
- 5 credits overlap with MA141.
- 5 credits overlap with MA154.
- 5 credits overlap with MA254.
- 5 credits overlap with MA254.
- 5 credits overlap with MA354.
- 5 credits overlap with MA354.
Teaching
6 hours of lectures/exercises every week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Examination
Final written exam which counts 100 % towards the final grade.
This course has 1 mandatory assignment that must be approved before you can sit the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4400 – Linear Analysis with Applications
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.