EDG604 Discrete structures and combinatorics
Professor: Evi PAPAIOANNOU
The evolution of ancient civilizations was based on the use and understanding of numbers. Mathematics constitutes a global language for storing, disseminating and processing data with unprecedented efficiency. An important problem-solving skill is the ability to count or enumerate objects. Discrete objects and relationships between these objects are can be represented via discrete structures, which are the abstract mathematical structures including sets, permutations, relations, graphs, trees, finite-state machines.
Combinatorial analysis is used to solve counting problems. Enumeration, the counting of objects with certain properties, is an important part of combinatorics. Many counting problems can be phrased in terms of ordered or unordered arrangements of the objects of a set with or without repetitions. These arrangements, called permutations and combinations, are used in many counting problems.
In the context of this course we study introductory elements of set theory as well as basic and advanced methods of enumerating discrete objects (combinations, permutations, inclusion-exclusion). In addition, we examine basic types of practical arithmetic problems.
The course contributes to the development of “computational thinking” and offers the necessary background for the exploitation and use of methods, techniques and tools from the area of computer science and technology in the study of issues in the field of modern history-archaeology.