Geometry Including Project

The course includes a literature and a project component.

The literature module consists of lectures and exercises on:

The axioms of Euclidean geometry

• points, plane, space, straight lines, circles and other curves in the plane

The Cartesian axes in the plane and in Euclidean space

• Euclidean geometry in the plane and in the space

The Euclidean scalar product in the space

• norms of vectors, lengths and angles, the groups of Euclidean isometries in the plane and in the space

Straight lines and curves of degree two in the plane

• the equation of the plane and surfaces of degree two in the space

Quadratic forms in two and three variables

• the classification of curves of second degree in the plane and of surfaces of second degree in the space by means of the theory of quadratic forms
• The history of non-Euclidean geometry, the history of hyperbolic geometry, model construction,

Smooth curves in the space

• curvature and torsion of a smoooth curve, Frenet-Serret formulas for smooth curves

The fundamental theorem of the differential geometry of smooth curves in the space

Progressive specialisation: A1N (has only first‐cycle course/s as entry requirements)

Education level: Master's level

Admission requirements: Mathematics 60 ECTS cr, including Linear Algebra 7.5 ECTS cr, Analysis B1 7.5 ECTS cr, and Analysis B2 7.5 ECTS cr or equivalent

Selection: Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.