DISCRETE MATHEMATICS

Course Description

The objective of the course is to introduce the students fundamental principles: logic and Boolean algebra, set theory, relations( Partial ordering, Total ordering and Hasse diagrams, Equivalence relations and equivalence classes), functions(one-to-one, onto, identity, inverse and composition of functions), inductive proofs and recurrence relations, counting techniques(multiplication and addition rules, permutations, combinations, unordered samples with repetitions, principle of inclusion and exclusion, pigeonhole principle) and introduction to graph theory(basic terminology like vertex, edge, degree of a vertex in directed and undirected graphs, Eulerian and Hamiltonian graphs, trees and spanning trees, minimal spanning trees, Prim’s Algorithm, Kruskal Algorithms, Shortest Path Problems, Dijkstra’s Algorithm).

DISCRETE MATHEMATICS

Evaluation Tools (Active Term)

Course outcomes

1. 01 1. Explain the basic terminology of functions, relations and sets and write examples.
2. 02 2. Identify formal tools of logic theory .
3. 03 3. Use counting techniques in particular application problems.
4. 04 4. Exemplify graphs and trees in graph theory.
5. 05 5. Apply minimal spanning algorithms to real life problems.

Course Syllabus

Reference Books & Course Materials

1. 01 Susanna S. Epp; Discrete Mathematics with Applications, 4th edition, Brooks/Cole Cengage Learning, 2011(ISBN-13:978-0-495-82616-3)
2. 02 Rosen K.; Discrete Mathematics & Its Applications, Seventh edition, McGraw Hill, 2012(ISBN:978-0-07-338309-5)
3. 03 McEliece J.R., Ash B.R, Ash C.; Introduction to Discrete Mathematics, McGraw Hill, 1989(ISBN:0-07-100202-2
4. 04 Ferland K.; Discrete Mathematics, Brooks/Cole Cengage Learning, 2009(ISBN-13:978-0-495-83174-7)

Learning Outcomes

1. L01 1. Explain the basic terminology of functions, relations and sets and write examples.
2. L02 2. Identify formal tools of logic theory .
3. L03 3. Use counting techniques in particular application problems.
4. L04 4. Exemplify graphs and trees in graph theory.
5. L05 5. Apply minimal spanning algorithms to real life problems.

Program Outcomes

1. P01 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems.
2. P02 Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3. P03 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4. P04 Ability to devise, select, and use modern techniques and tools needed for analysing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively
5. P05 Ability to design and conduct experiments, gather data, analyse and interpret results for investigating complex engineering problems or discipline specific research questions.
6. P06 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7. P07 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8. P08 Recognition of the need for lifelong learning ; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9. P09 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10. P10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11. P11 Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.

Po-Lo Matrix