Course syllabus

# Geometri

Geometry

## FMA135, 6 credits, G1 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Geometry

Valid for: 2014/15

Decided by: Education Board B

Date of Decision: 2014-04-08

Main field: Technology.

Elective for: C4, D4-bg, E4, F1, Pi1

Language of instruction: The course will be given in English on demand

The aim of the course is to introduce geometrical concepts which are of importance in modern engineering applications, e.g. computer aided design (CAD), computer aided manufacturing (CAM), computer graphics and computer vision, and to give examples of their use. A subgoal is to study how geometrical objects can be described numerically in a neat way.

Knowledge and understanding

For a passing grade the student must

- be able to explain the basic parts of the theory.
- exhibit understanding of some different algorithms in computer geometry.
- show knowledge of and understanding of the properties of different concepts in projective geometry, and be aware of how they appear in applications.

Competences and skills

For a passing grade the student must

- be able to integrate methods and views from different parts of the course to solve problems and answer questions within the framework of the course.
- be able to write Matlab programs to solve mathematical problems within the course.
- be able to explain the solution to a mathematical problem within the course, in writing and orally, with clear logic and using proper terminology.

- Curves and surfaces. Some basic differential geometry. Bezier curves. Interpolation.
- Projective geometry. Perspective.

Grading scale: TH

Assessment: First part of the course: Computer session and take-home exam.
Second part of the course: Home assignments. Oral exam for those students who want a higher grade than a pass.

Parts

Code: 0113. Name: Geometry, Laboratory Work.

Credits: 0. Grading scale: UG. Assessment: Take-home exam

Code: 0213. Name: Geometry, Geometrical Design.

Credits: 3. Grading scale: TH. Assessment: Take-home exam.

Code: 0313. Name: Geometry, Projective Geometry.

Credits: 3. Grading scale: TH. Assessment: Satisfactory solutions to homework problems are a necessary
and sufficient condition for the grade 3. To obtain a higher grade the student has to pass an oral examination.

Required prior knowledge: Linear algebra, and derivatives from one variable calculus.

The number of participants is limited to: No

The course overlaps following course/s: FMN100

- Ufnarovski, V: Kompendium i Geometri. Distributed by the department.
- Holmstedt, T: Föreläsningar i projektiv geometri. Distributed by the department.

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se

Teacher: Victor Ufnarovski, ufn@maths.lth.se

Course homepage: http://www.ctr.maths.lu.se/course/geometri/