Matrices, Graphs and Convexity

Uitgebreide vaknaam	Matrices, Graphs and Convexity
Leerdoelen	Upon completion of the course the student is able to: 1. Compute the Kronecker product, a Singular Value Decomposition, all left/right/generalized inverses and the Moore-Penrose inverse. 2. Check, prove and apply certain properties of (un)directed graphs. 3. Check and prove that a non-negative matrix is irreducible/primitive. 4. Check and prove that a set is convex and determine its extreme points. 5. Check and prove that a function is (quasi-)convex. 6. Compute all supporting/separating hyper-planes of convex sets.
Omschrijving	The students will acquire knowledge and skills of mathematical methods used in econometrics and operations research. Topics: Kronecker product, singular value decomposition, one-sided inverses and generalized inverses of matrices, (un)directed graphs, irreducible non-negative matrices, convex sets, convex and quasi-convex functions, supporting hyper-planes of a convex set and separating hyper-planes of two convex sets.
Uren per week	4
Onderwijsvorm	-hoorcollege ,  -practicum (lectures, practices)
Toetsvorm	-actieve deelname,  -groepsopdracht,  -schriftelijk tentamen (open vragen)
Vaksoort	bachelor
Coördinator	dr. W. Romeijnders
Docent(en)	dr. W. Romeijnders , student-assistants , L.M. van der Heide
Verplichte literatuur	Titel Auteur ISBN Prijs Lecture Notes on Matrices, Graphs, and Convexity (info during first lecture) Nusse, H.E. and Romeijnders, W.
Entreevoorwaarden	The contents of: Mathematics I for EOR, Mathematics II for EOR, Multivariate Calculus, Linear algebra for EOR
Opmerkingen	Info: Dr Ward Romeijnders, phone: +3150 36 33923. Secr: Operations, phone: +3150 36 37491, e-mail: secr.operations.feb@rug.nl.
Opgenomen in	Opleiding Jaar Periode Type BSc Econometrics and Operations Research/EOR  (basisprogramma BSc EOR) 2 semester I a verplicht Courses Exchange (BSc)  (Courses Exchange Students (BSc) without limited access) 2 semester I a keuze Pre-MSc-programma’s FEB  (Pre-MSc EORAS) 1 semester I a verplicht