MATA2520 Set theory and graphs (5 cr)

• Basic concepts of set theory.
• Relations and functions, including properties of relations and equivalence classes.
• Binary trees.
• Undirected and directed graphs, including connected and strongly connected components.
• Isomorphism and bisimilarity. 

After completing the course, the student:

• Understands the Cartesian product and its connection to data structures composed of multiple parts.
• Is familiar with the concept of a power set.
• Can calculate the sizes of finite sets using the inclusion-exclusion principle, as well as the sizes of product sets and power sets.
• Can use the definitions of reflexivity, symmetry, antisymmetry, and transitivity in simple reasoning regarding binary relations.
• Masters the concepts of equivalence and order relations, as well as the relationship between equivalence classes and partitions.
• Is familiar with the concepts of function, function composition, bijection, inverse function, injection, and surjection.
• Is familiar with the concept of a binary tree and knows how to traverse a binary tree in pre-order, in-order, and post-order.
• Knows the definitions of undirected and directed graphs.
• Masters concepts related to graphs: node, edge, path, loop, cycle, connected component, and strongly connected component.
• Has been introduced to graph isomorphism and bisimilarity, and knows their connection to equivalence classes and the behavior of computer programs.
• Recognizes when a case involves a graph according to its formal definition versus an equivalence class of isomorphic graphs. 

2) Johdatus verkkoteoriaan                                                 

3) Johdatus kombinatoriikkaan

Jos sisällytät kurssin MATA2520 Joukko-oppi ja graafiteoria  matematiikan opintokokonaisuuteen, et voi sisällyttää siihen edellä mainittuja kursseja. 

MATA2700 Proof and Deduction Methods for Engineering