The course explores introductory concepts, algorithms and examples from probability theory, combinatorial theory (combinatorics), graph theory and set theory including relations and functions in sets.

With regard to combinatorial theory, the course examines the techniques of enumeration (enumerative combinatorics), the concepts of combinations, and permutations with or without repetitions.

With regard to probability theory, the course examines the concepts of probability and conditional probability. For graph theory, the course explores concepts, definitions, properties and algorithms with emphasis on planar and connected graphs.

The course also offers descriptions of the relations determined by finite sets and interpretations of the functions and graphic representations defined by them.

In the final part, we focus on understanding and creating voting advise applications and political compasses

Objectives of the course is that students gain the following capabilities:

• Ability to understand and apply an algorithm.
• Ability to calculate the probability so that they can take political decisions based on real facts
• Ability to reach useful conclusions using the results of the elections. (method of bounds)
• Ability to abstract complex relationships and find the solution with the help of graph theory.
• Ability to study social networks and analyze network effects on the formation of political views.
• Ability to understand and create voting advise applications and political compasses

Students need to have a 12-digit calculator (using your mobile phone as calculator is not permitted) and their book with them which they can consult during the exams to solve problems similar to those in the book.
The final grade of students can be the result of a combination of evaluations:

1. Assignments, quizzes or exercises prepared during the semester according to the procedures defined in the course (eg submission deadlines, assessment methods, etc.).
2. Oral exams with emphasis on the assignments that have been prepared during the semester according to the procedures defined in the course
3. Written exams The weight of the individual assessments is shaped by the special circumstances of each academic year and it is announced in the elearning of the course.

Course Bibliography (Eudoxus)
Χατζηπαντελής, Θ, & Ι. Ανδρεάδης, Μαθηµατικά στις Πολιτικές Επιστήµες, Εκδόσεις Ζήτη, 2005. Κωδικός Βιβλίου στον Εύδοξο: 11093
Aγγελής, E. και Γ. Mπλέρης, ∆ιακριτά µαθηµατικά, Tζιόλα,2003. Κωδικός Βιβλίου στον Εύδοξο: 18548932

Additional bibliography for study
Aldous, J. M. και R. J. Wilson, Graphs and Applications: An Introductory Approach, Springer Verlag, 2000.
Biggs, N. L., Discrete Mathematics (αναθεωρηµένη έκδοση),Oxford Science Publications, 1990.
Grinstead, C. M. και J. L. Snell, Introduction to Probability (δεύτερη αναθεωρηµένη έκδοση), American Mathematical Society, 1997.
Paulos, J.Α., A Mathematician Reads the Newspaper, Turtleback Books-Demco Media, 1996.
Garzia, D., & Marschall, S. (Eds.). (2014). Matching Voters with Parties and Candidates: Voting Advice Applications in Comparative Perspective. ECPR Press.