Mathematics for Informatics I-E2

Numbering Code U-LAS30 20041 LE10 Year/Term 2021 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year All students Target Student For all majors
Language English Day/Period Thu.5
Instructor name EVEN,Jani Juhani luc (Graduate School of Informatics Program-Specific Senior Lecturer)
Outline and Purpose of the Course This course is an introduction to graph theory. Graph theory is a field of mathematics that studies graphs. A graph is a way to represent relationships. For example, graphs can be used to represent a train map or a social network. Graphs and graph theory play an important role in computer science.

The purpose of this course is as follows:
・ Learn the mathematical definitions of graphs,
・ Understand the important theorems of graph theory,
・ Discover some practical applications of graphs,
・ Get familiar with graph based algorithms.
Course Goals The students should be able to use graph theory to proposed efficient models for real-world problems and efficiently solve them using graphs based algorithms.
Schedule and Contents The course starts by the definition of graph and some basic concepts.
・ Common families of graphs
・ Graph operations
・ Graph isomorphism
・ Subgraphs
・ Matrix representation

Then, the following topics are discussed with a focus on applications and algorithms:
・ Trees: tree transversal, binary search tree
・ Spanning trees: depth-first search, depth-first search, minimum spanning tree
・ Graph traversals: Eulerian trails and tours, Hamiltonian paths and cycles
・ Network flow: maximum flow
・ Bipartite graphs: maximum bipartite matching,
・ Planar graphs: Planarity testing
・ Graph coloring: vertex coloring, edge coloring

The schedule and contents are subject to change based on class progress.

Total:14 classes, 1 Feedback session.
Evaluation Methods and Policy The evaluation will be based on assignments given after some of the classes (30%) and a final examination during the last class (70%).
For each task, the evaluation criteria will be presented and a raw score grade [0-100] will be used.

In addition, some classes will have self-evaluation exercises. These will not contribute to the evaluation.
Course Requirements This course does not require special knowledge. However, many of the algorithms and examples are from the field of computer science. Some basic programming skill is an advantage. But, no specific programming language knowledge is necessary as the algorithms will be presented in pseudo-code.
Study outside of Class (preparation and review) The students are expected to review the handouts before the next class in order to smoothly follow the course.
Textbooks Textbooks/References No textbook, handouts.
References, etc. [1] Jonathan L. Gross, Jay Yellen, ”Graph theory and its applications, second edition” (Chapman and Hall) ISBN:978-1584885054