Geometry

Faculteit Science and Engineering
Jaar 2021/22
Vakcode WBMA034-05
Vaknaam Geometry
Niveau(s) bachelor
Voertaal Engels
Periode semester II a
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Geometry
Leerdoelen At the end of this course, the student is able to:

1. Apply linear algebra and multivariable analysis to give precise descriptions of geometric concepts such as points, lines, angles, parallelism and curvature.
2. Assess what is the appropriate type of geometry to use in solving a practical problem.
3. Carry out calculations to find coordinates, angles, lengths, volumes and other geometric quantities.
4. Construct proofs of simple geometric statements.
5. Explain the unifying role of isometries in geometry
Omschrijving Traditionally geometry refers the properties of straight lines, circles, planes, angles and distances as summarized in Euclid's Elements. Loosening Euclid's axioms one finds there exist many interrelated theories of geometry, each with its own distinct interpretation of the above elementary notions of lines, distance etc. For example, what if distances play no role? (Affine geometry). What if parallel lines are to meet 'at infinty'? (projective geometry). What if we are on the sphere or even just on some potato? (differential geometry). Following Felix Klein we focus on the unifying concept of 'isometries': the motions or symmetries that preserve all the relevant geometric properties of the theory.

Using linear algebra as a foundation we will study in turn affine, Euclidean, projective and differential geometry.
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
Titel Auteur ISBN Prijs
Lecture notes Geometry, available on the website. http://www.rolandvdv.nl/GM Roland van der Veen
"Geometry" (Springer, 2003) M. Audin 978-3-540-43498-6
Entreevoorwaarden Prerequisites are the first year courses on Calculus and Linear Algebra and the second year courses
Metric and topological Spaces, complex analysis and multivariable analysis.
Opmerkingen The course prepares for the course Analysis on Manifolds and the track Mathematics and Complex Dynamical Systems of the MSc Mathematics.
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