Mathematics in Political Science: An Introduction
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.
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
Βιβλιογραφία μαθήματος (Εύδοξος)
Χατζηπαντελής, Θ, & Ι. Ανδρεάδης, Μαθηµατικά στις Πολιτικές Επιστήµες, Εκδόσεις Ζήτη, 2005.
Aγγελής, E. και Γ. Mπλέρης, ∆ιακριτά µαθηµατικά, Tζιόλα,2003.
Επιπρόσθετη βιβλιογραφία για μελέτη
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.