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 Apply data science principles and techniques to challenges in real life situations, and effectively communicate their solutions.
2. P02 Identify and implement data analysis methodologies based on theoretical ideas, ethical code, and in-depth knowledge of the underlying data.
3. P03 Analyze the guiding concepts and assessment procedures for information analysis in real-life applications.
4. P04 Design and apply relevant data analysis models to find obscure solutions to business-related problems.
5. P05 Utilize modern computing techniques to handle real-world problems characterized by massive amounts of data, such as parallel and distributed computing and machine learning.
6. P06 Configure and administer the software tools required to efficiently produce usable information from any size of structured and unstructured datasets.
7. P07 Administer or manage data science tools and techniques to organize and complete projects aimed at gaining useful insight from complex data.
8. P08 Think critically and imaginatively, conceiving real-world issues from several angles, and work well in a variety of teams to solve issues cooperatively.
9. P09 Be able to effectively integrate data‐based solutions into the user environment and help non-technical professionals in exploring, visualizing, and using these solutions
10. P10 Understand their obligations under professional and ethical standards in relation to matters like data ownership and citation, data security and sensitivity and the privacy implications of data analysis.

Po-Lo Matrix