Discrete Mathematics

The course introduces students to Discrete Mathematics, often referred to as the mathematics of computing. It covers fundamental concepts and methods from number theory, combinatorics, discrete calculus, and graph theory, with an emphasis on their applications in Computer Science. The course provides essential tools for algorithm analysis, data structure design, and the development of problem-solving techniques based on discrete structures. In addition, suitable software tools and web-based applications are presented to support the solution of practical problems.

Upon successful completion of the course the student will be able to:

• understand the basics of prime numbers theory
• solve modular arithmetic problems
• solve linear Diophantine equations
• understand the basic concepts and methods of combinatorial analysis
• understand basic elements of discrete calculus
• calculate sums
• solve recurrence relations
• use generating functions
• understand the basics of graph theory

Divisibility – Prime numbers – Modular Arithmetic - Linear Diophantine equations – Summation techniques – Discrete calculus - Stirling numbers of the first kind – Harmonic numbers – Sum and product rules – Permutations – Combinations – Pascal’s triangle – Inclusion-exclusion principle - Stirling numbers of the second kind - Recurrence relations – Fibonacci numbers – Catalan numbers - Generating functions – Basic concepts and theorems of graph theory – Euler graphs – Hamilton graphs

• Panagiotopoulos, A., Discrete Mathematics, Stamoulis Publications, 1999, ISBN: 960-351-227-3.
• Liu, C. L., Elements of Discrete Mathematics, ITE-Crete University Press, 2009, ISBN: 978-960-524-072-1.
• Scheinerman, E., Discrete Mathematics and Its Applications, P.Ch. Paschalidis Publications, 2023, ISBN: 978-9925-575-75-6.

• Lectures
• Tutorial exercises
• Student participation in tutorials

• Support of the educational process via the e-learning platform Opencourses
• Use of ICT in teaching and education (specialized software, electronic lecture notes)
• Use of ICT for communication with students

Written final examination with problem-solving questions