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Combinatorics for bioinformatics - NDMI089

Title:	Kombinatorika pro bioinformatiky
Guaranteed by:	Computer Science Institute of Charles University (32-IUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015 to 2016
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Ondřej Pangrác, Ph.D.
Class:	Informatika Bc.
Classification:	Informatics > Discrete Mathematics

Annotation -

Last update: IUUK (09.03.2015)

An introductionary course on combinatorics and graph theory for students of bioinfomatics.

Literature -

Last update: RNDr. Ondřej Pangrác, Ph.D. (01.10.2019)

J. Matoušek, J. Nešetřil: An Invitation to Discrete Mathematics

Syllabus -

Last update: RNDr. Ondřej Pangrác, Ph.D. (01.10.2019)

Basic notions, binary relations, equivalences and partially ordered sets.

Functions and their properties, permutations.

Combinatorial counting, Binomial theorem.

Principle of inclusion and exclusion and its applications.

Discrete probability.

Graphs - notions and examples. Paths and circuits in graphs, connectivity.

Trees, spanning trees of graphs.

Planar graphs, Euler's formula, max. number of edges.

Graph colorings, d-degenerate graphs. Five color theorem for planar graphs.

Flows in networks.

Hall's theorem and its applications, matchings in bipartite graphs.

Higher connectivity, Menger's and Ford-Fulkerson's theorems.