Discrete Mathematics

The course is an introduction to discrete mathematics, a branch of mathematics which aims at counting discrete objects like, for instance, pixels on a screen, characters in a password, directions on how to drive from one place to another. Despite a strong correlation with Computer Science, Discrete Mathematics are used in practice for solving problems from various disciplines (engineering, physical sciences, social sciences, economics, operations research) and are essential for decision making in non continuous situations. Emphasis is placed on basic concepts of combinatorics (like combinations, permutations, distribution of objects, subsets, etc.) as well as on the principle of inclusion and exclusion so that students acquire the necessary background and skills for using Discrete Mathematics efficiently in practice for addressing a variety of issues relevant to the Management of Cultural Heritage, with or without the support of New Technologies. Does a curriculum in Cultural Heritage Management and New Technologies really need to include Discrete Maths? To get the answer just consider the “No” replies to the question: which of the tasks below you can handle? The more the “No” replies, the more intense the necessity of the course... • You are given 5 Greek, 7 English and 10 Spanish books. In how many ways you can chose 2 of them? • How many 7-character words (no character repetition allowed) you can generate using the Greek alphabet? • In how many ways you can schedule the exam of 3 courses in 5 days so that no 2 courses are scheduled on the same day? • In an ancient text, a 3-digit date is detected but only the first digit is a clear “1”; the next two digits are not recognizable. What is the range of dates that you should further investigate for your study? • There are 10 collections available in a museum. In how many ways you can organize a visit including 3 of them? • During an archeological excavation the group comes up with 10 clay pieces. The group knows that 3 of them form a figurine. How many trials are possibly needed for determining the figurine pieces? • In how many ways the 28 member-states of EU can form 7-member coalitions? • You are given a team of persons of 3 nationalities. How many pairs of persons of different nationality you can have? • You are given a gallery of 20 rooms. In how many ways your can order 18.000 items belonging to 4 different historic periods under the constraint that each room is devoted to a single historic period? • In how many ways you can read this 4-paragraph course description text?

Objectives

Emphasis is placed on basic concepts of combinatorics (like combinations, permutations, distribution of objects, subsets, etc.) as well as on the principle of inclusion and exclusion so that students acquire the necessary background and skills for using Discrete Mathematics efficiently in practice for addressing a variety of issues relevant to the Management of Cultural Heritage, with or without the support of New Technologies.

Prerequisites

Elementary arithemitic

Syllabus

The course is an introduction to discrete mathematics, a branch of mathematics which aims at counting discrete objects like, for instance, pixels on a screen, characters in a password, directions on how to drive from one place to another. Despite a strong correlation with Computer Science, Discrete Mathematics are used in practice for solving problems from various disciplines (engineering, physical sciences, social sciences, economics, operations research) and are essential for decision making in non continuous situations. Emphasis is placed on basic concepts of combinatorics (like combinations, permutations, distribution of objects, subsets, etc.) as well as on the principle of inclusion and exclusion so that students acquire the necessary background and skills for using Discrete Mathematics efficiently in practice for addressing a variety of issues relevant to the Management of Cultural Heritage, with or without the support of New Technologies.