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Discrete mathematics

General data

Course ID:	1000-212bMD
Erasmus code / ISCED:	11.001 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0540) Mathematics and statistics, not further defined The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Discrete mathematics
Name in Polish:	Matematyka dyskretna
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Obligatory courses for 1st year Computer Science Obligatory courses for 2nd grade JSIM (3I+4M) Obligatory courses for 2nd grade JSIM (3M+4I)
ECTS credit allocation (and other scores):	7.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Requirements:	Foundations of mathematics 1000-211bPM Geometry with linear algebra 1000-211bGAL Mathematical analysis for computer science I 1000-211bAM1
Short description:	Mathematical concepts essential for design and analysis of algorithms: combinatorics, graph theory and number theory.
Full description:	* Mathematical induction and recursion * Finite sums * Binomial Coefficients * Permutations and partitions * Generating functions with application * Counting methods: - enumerators - inclusion-exclusion principle * Asymptotics: - asymptotic notation - Master theorem * Elementary number theory: - divisibility, primes, factorization - gcd and Euclid's algorithm * modular arithmetic: - Fermat's little theorem and Euler's theorem - Chinese remainder theorem - solving modular equations * Elements of the cryptography: Miller-Rabin primality and the RSA system * Graphs: - paths, trees and cycles - Euler and Hamilton cycles - bipartite graphs, transversals and Hall theorem - planarity - coloring
Bibliography:	1. R.L.Graham, D.E.Knuth, O.Patashnik, Matematyka Konkretna, Państwowe Wydawnictwo Naukowe, Warszawa 2013. 2. W.Lipski, Kombinatoryka dla programistów, Wydawnictwa Naukowo-Techniczne 2004. 3. Z.Palka, A.Ruciński, Wykłady z kombinatoryki, Wydawnictwa Naukowo-Techniczne 2009 4. R.J.Wilson, Wprowadzenie do teorii grafów, Państwowe Wydawnictwo Naukowe, Warszawa 2012.
Learning outcomes:	(in Polish) Wiedza - absolwent zna i rozumie: - ma wiedzę w zaawansowanym stopniu w zakresie kombinatoryki, teorii grafów i elementarnej teorii liczb dającą matematyczne podstawy projektowania algorytmów (K_W01), - rozumie i potrafi stosować notację asymptotyczną (K_W01), - rozumie rolę i znaczenie konstrukcji rozumowań matematycznych (K_W01). Umiejętności - absolwent potrafi: - zastosować wiedzę matematyczną do formułowania, analizowania i rozwiązywania związanych z informatyką zadań (K_U01), - samodzielnie planować i realizować własne uczenie się przez całe życie (K_U09). Kompetencje społeczne - absolwent jest gotów do: - uznawania znaczenia wiedzy w rozwiązywaniu problemów poznawczych i praktycznych oraz wyszukiwania informacji w literaturze oraz zasięgania opinii ekspertów (K_K03).
Assessment methods and assessment criteria:	Written tests during the course, written exam.

Classes in period "Summer semester 2024/25" (past)

Time span:	2025-02-17 - 2025-06-08	Selected timetable range: weekly course term Go to timetable MO WYK CW CW CW CW CW CW CW CW CW TU W TH WYK FR CW CW CW CW CW CW CW CW CW
Type of class:	Classes, 60 hours more information Lecture, 45 hours more information
Coordinators:	Adam Malinowski
Group instructors:	Łukasz Bożyk, Kunal Dutta, Soumik Dutta, Paweł Górecki, Mirosław Kowaluk, Adam Malinowski, Oskar Skibski
Students list:	(inaccessible to you)
Credit:	Examination

Classes in period "Summer semester 2025/26" (future)

Time span:	2026-02-16 - 2026-06-07	Selected timetable range: weekly course term Go to timetable
Type of class:	Classes, 60 hours more information Lecture, 45 hours more information
Coordinators:	Adam Malinowski
Group instructors:	Łukasz Bożyk, Tomasz Kazana, Mirosław Kowaluk, Adam Malinowski, Marcin Mucha, Wojciech Nadara
Students list:	(inaccessible to you)
Credit:	Course - Examination Lecture - Examination

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