# Bachelor's Thesis in Algebra and Geometry

On this page you will find information specific for the course SA104X, with specialization towards Algebra and Geometry.

### Course Structure

Prerequisities for writing a bachelor's thesis in Algebra and Geometry are covered by the course SF2729. The course SF2729 during 2012/13 is given in period 2 and 3. Those who are interested in writing a bachelor thesis in 2012/2013 in  Algebra and Geometry are encourage to take this course. Look at the web page for more information about the course.

If you are interested in writing a bachelor's thesis in Algebra and Geometry you are encouraged to take contact as soon as possible to discuss possible projects and get advice on needed background material for their particular project.

## MÖBIUS GROUP

The Möbius transformations are automorphisms of the sphere. The sphere is identified with the plane and a point at infinity, and as such the Möbius transformations are the length preserving transformations of hyperbolic geometry. Consult Wikipedia for more information.

## GAUSSIAN INTEGERS

By combining the integers and the square root of -1, one obtains the Gaussian integers. This integer lattice of the complex plane is only one of many possible ones. Other lattices have unexpected behavior, which raises several natural questions.

## APPLICATIONS OF PROJECTIVE GEOMETRY TO COMPUTER VISION

Projective geometry represents an important area in modern geometry, extending the basics of Euclidian geometry. Recently it has become an important tool in more applied disciplines like computer vision.

## CONJUGACY OF MATRICES

A matrix encodes the information about a linear mapping, and it is important to understand conjugacy of matrices. In particular if two matrices are conjugate over a given field, or ring, and the coefficients of the matrices belong to a subfield, are the two matrices then conjugate over the smaller field?