This course is designed to help the students to develop basic technical proficiency in discrete mathematics that is used in natural sciences and engineering and to solve everyday problems. The course aims also to help students to develop and apply logic for quantified statements, precision and language to achieve mathematical certainty in problem-solving. Content that is brought up:
· The concept of discrete mathematics
· Arithmetic algorithms
· Modulo calculations
· Polynomials
· Set theory
· Functions and relations
· Number sequences (arithmetic or geometric)
· Basic combinatorial methods
· Algebraic structures
· Basic graph theory
After passing the course, the student should be able to:
1. perform operations on functions Use Euclid's algorithm to calculate the greatest common divisor to two integers a and b and I see solve the Diophantine equation ax + by = c
2. Use Euclid's algorithm to calculate the greatest common divisor to two polynomials
3. Use knowledge in discrete mathematics to solve combinatorial problems and permutations
4. Use Lagrange's theorem for groups
5. Explain the concepts of sub-groups, coset and the order of elements
6. Explain basic concepts in graph theory such as: isomorphism, degree (valency), coherence, path, cycle, Hamiltonian cycle and Eulerian circuit