MAT4510 – Geometric Structures
Course description
Schedule, syllabus and examination date
Course content
The course gives an introduction to geometry and topology, with emphasis on classical geometries, topological classification of surfaces, and differential geometry for Riemannian surfaces.
Learning outcome
After completing the course you
- can describe axioms for planar geometry, and models realizing these in the hyperbolic, Euclidean and elliptic cases
- can work with M?bius-transforms, as well as distances, angles and areas in hyperbolic geometry
- know about topological, combinatorial and differentiable surfaces, and can classify combinatorial surfaces up to homeomorphism
- can describe Riemannian metrics and curvature, by means of the first and second fundamental forms, as well as the Theorema Egregium
- know about geodesic curves on Riemannian surfaces, and the Gauss-Bonnet theorem.
Admission to the course
Students admitted at UiO must?apply for courses?in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may?apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about?admission requirements and procedures for international applicants.
Recommended previous knowledge
- MAT1100 – Calculus
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- MAT2400 – Real Analysis
- MAT2200 – Groups, Rings and Fields
- MAT2410 – Introduction to Complex Analysis
- MAT3500 – Topology / MAT4500 – Topology (can be taken simultaneously)
Overlapping courses
- 10 credits overlap with MAT3510 – Geometric structures (discontinued).
Teaching
4 hours of lectures/exercises per 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 or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 1 October/1 March for the autumn semester and the spring semester respectively.
This course has 1 mandatory assignment that must be approved before you can participate in 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 submit your response 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.