Discrete Mathematics

Aim

• To be able to model and solve problem applying concepts and methods in combinatorics, recurrence, set theory, relations and maps.
• Apply number theory and graphs through projects
• Written and oral communication of relevant mathematical concepts and methods. Show acquaintance with applications.

Content

The course consists of two parts: Part 1 om 4 hp, and Part 2 om 2 hp

Part 1:

• Combinatorics: Permutations and combinations. The principle of inclusion and exclusion with applications in modeling. The pigeonhole principle. Sets.
• Relations and maps for efficient counting.
• Recursion: Recursive equations and mappings. Linear recursive equations and systems of linear recursive equations

Part 2:

• Number theory: Divisibility. Linear Diophantine equations. Modular Arithmetic
• Graphs: Basic concepts in graphs: graphs and networks, trees, bipartite graphs, planar graphs and colorings.

Observe that applications of number theory and graphs are examined by projects that include real life applications. Examples of such projects are: RSA-cryptography, cyphers for block chain, matching and optimisation (applications in social sciences), phylogenetic trees, decision trees, chromatic number and complexity of algorithms, adjacency matrices and data transmission.