1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Combinatorial Analysis of Discrete Structures

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Combinatorial Analysis of Discrete Structures - opis przedmiotu

Cel przedmiotu

Learning about selected discrete structures, various techniques for counting them and proofs of their existence.

Wymagania wstępne

Zapisz zmiany

Discrete Mathematics 1, Linear Algebra 1.

Zakres tematyczny

Lecture

1. Partitions of a set, Stirling numbers of the second kind, Bell numbers (3 hours).
2. Stirling numbers of the first kind, combinatorial interpretation of these numbers and relations with Stirling numbers of the second kind (4 hours).
3. Partitions of numbers, generating functions for partitions of numbers (3 hours).
4. Combinatorial configurations, finite projective planes (12 hours).
5. General principles of encoding and decoding (8 hours).

Exercises

1. Recognizing, in tasks involving the content of partition problems for sets and numbers, using the known recursive relationships and explicit formulas to estimate objects of this type, proving simple theoretical facts related to the numbers of divisions of sets and numbers (12 hours).
2. Proving simple theoretical facts for combinatorial configurations using relationships between combinatorial configurations and finite projective planes, relating these concepts to practical issues, differential set as a method for constructing quadratic configurations, systems of Steiner triples (10 hours).
3. Testing the detectability and possibility of correcting errors for given codes and their perfection, finding dictionaries and systems of control equations, examining the matrices generating codes (6 hours).
4. Colloquium (2 hours).

Metody kształcenia

Conversation lecture, traditional lecture, discussion exercises.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Conditions for passing classes:

1. Checking the level of students' preparation and their activity during the exercises.
2. A test during exercises, with tasks of varying difficulty, allowing the assessment of whether and to what extent the student has achieved the above-mentioned learning outcomes, mainly in terms of skills and competences.
3. Conversation during a lecture to verify higher levels of educational outcomes in the field of knowledge and skills.
4. Conversation during a lecture to verify higher levels of educational outcomes in the field of knowledge and skills.of knowledge and competences presented during the lecture.

 

The grade for the course consists of the grade for the exercises (50%) and the grade for the lecture (50%). The condition for passing the course is obtaining positive grades from exercises and lectures.

Literatura podstawowa

1. John Riordan, Introduction to Combinatorial Analysis, Dover publication Inc, 2002,
2. Any book containing above mentioned classical topics.

Literatura uzupełniająca

Uwagi

The subject is also offered in the 6th semester.

Zmodyfikowane przez dr Ewa Synówka (ostatnia modyfikacja: 29-12-2023 18:58)