MAT4510 – Geometric structures
Schedule, syllabus and examination date
The course gives an introduction to geometry and topology, with emphasis on classical geometries, topological classification of surfaces, and differential geometry for Riemannian surfaces.
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 Möbius-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.
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
MAT1100 – Calculus, MAT1110 – Calculus and Linear Algebra, MAT1120 – Linear algebra, MAT2400 – Real Analysis, MAT2200 – Groups, Rings and Fields and MAT2410 – Introduction to Complex Analysis. Should be taken together with or after MAT3500 – Topology/MAT4500 – Topology.
10 credits overlap with MAT3510 – Geometric structures (discontinued)
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department.
4 hours of lectures/exercises per week.
Final written examination.
Examination support material
No examination support material is allowed.
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.
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.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.