MAT2400 – Real Analysis
Course description
Schedule, syllabus and examination date
Course content
This course is a generalization and continuation of the mathematical analysis from MAT1100 – Calculus and MAT1110 – Calculus and Linear Algebra, and the linear algebra from MAT1120 – Linear Algebra. The theory is generalized from finite-dimensional spaces to spaces that may be infinite-dimensional, and whose elements typically are functions, rather than numbers or what you are used to thinking of as vectors. Key concepts are convergence, continuity, differentiability, completeness, and compactness. The theory is applied to problems from differential equations and Fourier analysis. MAT2400 gives training in mathematical reasoning and lays the theoretical foundation for further studies in mathematical analysis.
Learning outcome
After completing the course you
- are familiar with the theory of metric spaces, you can give arguments related to convergence, continuity, completeness, and compactness in such spaces, and you are familiar with several ways in which the theory may be applied, to study sequences of functions and to show the existence of solutions to ordinary differential equations
- have a basic knowledge of normed vector spaces and continuous linear maps between such spaces, and you know the basic theory of differentiation of maps between normed vector spaces, including the theorems about inverse and implicit functions
- have knowledge about inner product spaces, and how to express elements as linear combinations of elements of an orthonormal basis, in particular how functions may be represented as Fourier series, and you can explain various forms of convergence of such series
- can present your own mathematical arguments in a clear and well-organized way, with correct notation and terminology, and you can relate abstract concepts to concrete examples.
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
Overlapping courses
- 10 credits overlap with MAT1300 – Analysis I (discontinued).
- 10 credits overlap with MA134.
- 10 credits overlap with MA200.
- 9 credits overlap with MA110.
Teaching
4 hours of lectures and 2 hours of exercises sessions per week throughout the semester.
The number of groups offered can be adjusted during the semester, depending on attendance.
Examination
Final written exam which counts 100 % towards the final grade.?
This course has 2 mandatory assignments that must be approved before you can sit the final exam.
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.