Geometry
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WBMA17001 
Vaknaam  Geometry 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Geometry  
Leerdoelen  1. The student is able to reproduce basic concepts and theorems from Differential Geometry, such as curvature and torsion of curves in threespace, lengths of curves on surfaces in threespace, the First and Second Fundamental Form and the Gaussmap of surfaces in threespace, principal curvatures, principal directions and curvature lines on surfaces in threespace, asymptotic directions and asymptotic curves on surfaces in threespace, geodesics, Christoffel symbols, the intrinsic geometry of abstract surfaces, parallel transport and covariant differentiation, the Theorema Egregium. 2. The student is able to understand and apply the theory from textbooks and elementary papers on Differential Geometry autonomously. He/she has developed a critical learning attitude regarding theory and problems in Differential Geometry. He/she is able to assess the validity and scope of definitions and theorems in Differential Geometry. 3. The student is able to give a clear and coherent written presentation on parts of Differential Geometry. 4. The student can solve problems strategically 

Omschrijving  Differential geometry of curves and surfaces is the central theme of this course. Both local and global aspects will be discussed. After a discussion of regular surfaces in threespace the local theory of surfaces will be discussed, emphasizing the role of the Gaussmap in the definition of curvature. Elementary aspects of Riemannian Geometry will play a central role in the intrinsic properties of surfaces.  
Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(Assessment takes place through 3 homework assignments and a written exam. The final grade is obtained by taking the following weighted average: the average of the 3 homework assignments counts for 30% and the grade of the final exam counts for 70%. In case the grade of the final exam is larger than this weighted average the final grade is just the exam grade.) 

Vaksoort  bachelor  
Coördinator  dr. R.I. van der Veen  
Docent(en)  dr. R.I. van der Veen  
Verplichte literatuur 


Entreevoorwaarden  Prerequisites are the first year courses on Calculus and Linear Algebra, and the course Metric Spaces.  
Opmerkingen  The course prepares for the course Analysis on Manifolds and the track Mathematics and Complex Dynamical Systems of the MSc Mathematics  
Opgenomen in 
