Discrete Mathematics and Set Theory 2600-ABdz1MDTM
The course will present the principles of formal logic and review the rules of mathematical logic. Various types of valid deductive and inductive reasoning will also be discussed. Logical operations will be linked to set-theoretic operations: union, intersection, and the Cartesian product of sets. These topics will primarily concern finite sets. Formal set operations will be used in the construction of relational algebra – a tool fundamental to understanding business databases and organizing data retrieval.
Topics related to enumerating finite sets will include the rules of multiplication and addition, the Dirchlet box rule, and the inclusion-exclusion method.
Mathematical graph theory facilitates understanding the principles governing supply chain management and logistics. This theory will cover planar graphs, including Kuratowski's characterization and Euler's theorem, cyclicity in graphs – Euler's and Hamilton's cycles, and issues related to counting spanning trees (Cayley's theorem and Prüfer's code).
Type of course
Course coordinators
Learning outcomes
K_W02 – The student demonstrates a thorough understanding of the complex processes and phenomena occurring in various types of organizations and the world around them. He/she utilizes management theory to identify, diagnose, and solve problems related to the organization's operations and their integration into the organization's strategy based on analytical findings.
K_W05 – The student demonstrates a thorough understanding of complex technological, social, legal, economic, ethical, and ecological processes and phenomena, including those related to the use of numerical data, and their impact on the functioning of the organization and the entire economy.
K_U09 – The student is able to improve acquired skills and support others in this regard and is capable of self-education.
K_K02 – The student is willing to recognize the importance and value of scientific knowledge in the context of solving complex problems involving analytical methods used in business environments, and to seek expert advice in this process.
Assessment criteria
The final test consists of short open-ended and multiple-choice questions. A pass score of at least 60% is required.
passing the test with a grade.
Practical placement
Professional practice is not required.
Bibliography
1. Ryan T. White, Archana Tikayat Ray, Matematyka dyskretna dla praktyków, Helion, Gliwice 2022,
2. Robin J. Wilson, Wprowadzenie do teorii grafów, Wydawnictwo Naukowe PWN, Warszawa 2012,
3. Andrzej Kisielewicz, Logika i argumentacja, Wydawnictwo Naukowe PWN, Warszawa 2017,
4. Kenneth A. Ross, Charles R.B. Wright, Matematyka dyskretna, Wydawnictwo Naukowe PWN, Warszawa 2012,
Stephen Barnett, Diascrete Mathematics, Addison Wesley Longman, Harlow 1998
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Term 2025Z:
1.Ryan T. White, Archana Tikayat Ray, Matematyka dyskretna dla praktyków, Helion, Gliwice 2022, |
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: