# MAT2500 - Geometry

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## Course content

The course is an introduction to geometry in the plane and in 3-space.  Central geometric topics that were not included in the beginner courses are emphasised.  The course contains a classification of symmetries (rigid motions) in the plane and in 3-space, considerations on triangles and circles of the ancient greek plane geometry, geometric and analytic descriptions of conic sections, and geometry in the projective plane.  The course is especially well suited for teacher students and is meant to build geometric intuition in preparation for more abstract mathematics.

## Learning outcome

After having completed the course:

• you can compute properties of elementary geometric objects in a way that supports intuition and understanding in mathematical and science studies and give necessary background for high school teaching.
• you know the different rigid motions in Euclidean spaces and the symmetries of the plane and can analyse and compute them in specific instances.
• you know the different wall paper patterns and their symmetry groups.
• you know the relation between the Platonic solids and symmetries in 3-space.
• you can use the classical plane geometric theorems, including the theorems of Menelaos and Ceva, in the study of triangles and conic sections in the plane.
• you can use analytic methods to determine loci of points in the plane, including conic sections.
• you know the properties of the projective plane and can use linear algebra both to deduce geometric propositions in the projective and the Euclidean plane.
• you can give a written presentation of a selected geometric topic in the form of a project assignment.

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.

## Prerequisites

### Formal prerequisite knowledge

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 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).

## Teaching

4 hours of lectures per week.

## Examination

From autumn 2015, a project paper (pass / fail). Written exam.

Mandatory assignments from previous years will have normal validity period (see website mandatory assignments).
Written examination at the end of the semester.

### 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.

### Resit an examination

This course offers both postponed and resit of examination. Read more:

### 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.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

10

Bachelor

Every autumn

Every autumn

Norwegian

## Contact

Department of Mathematics