MB104 Discrete mathematics

Faculty of Informatics
Spring 2020
Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Mgr. Martin Dzúrik (seminar tutor)
Mgr. Jonatan Kolegar (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
Mgr. Tomáš Svoboda (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Mgr. Andrej Tokarčík (seminar tutor)
Mgr. Dominik Trnka (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
doc. RNDr. Martin Čadek, CSc. (assistant)
Mgr. Martin Panák, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 17. 2. to Fri 15. 5. Wed 8:00–9:50 D1
  • Timetable of Seminar Groups:
MB104/01: Mon 17. 2. to Fri 15. 5. Wed 10:00–11:50 B204, L. Vokřínek
MB104/02: Mon 17. 2. to Fri 15. 5. Thu 8:00–9:50 A320, J. Kolegar
MB104/03: Mon 17. 2. to Fri 15. 5. Thu 10:00–11:50 A320, J. Kolegar
MB104/04: Mon 17. 2. to Fri 15. 5. Tue 12:00–13:50 B204, T. Svoboda
MB104/05: Mon 17. 2. to Fri 15. 5. Tue 14:00–15:50 B204, T. Svoboda
MB104/06: Mon 17. 2. to Fri 15. 5. Tue 18:00–19:50 B204, M. Dzúrik
MB104/07: Mon 17. 2. to Fri 15. 5. Wed 16:00–17:50 B204, M. Dzúrik
MB104/08: Mon 17. 2. to Fri 15. 5. Wed 18:00–19:50 B204, M. Dzúrik
MB104/09: Mon 17. 2. to Fri 15. 5. Thu 12:00–13:50 A320, D. Trnka
MB104/10: Mon 17. 2. to Fri 15. 5. Thu 16:00–17:50 A320, D. Trnka
MB104/11: Mon 17. 2. to Fri 15. 5. Thu 18:00–19:50 A320, D. Trnka
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 53 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2019
Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Mgr. Jonatan Kolegar (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Mgr. Andrej Tokarčík (seminar tutor)
Mgr. Dominik Trnka (seminar tutor)
doc. Lukáš Vokřínek, PhD. (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
Mgr. Martin Panák, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 19. 2. to Tue 14. 5. Tue 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/01: Mon 12:00–13:50 B204, L. Vokřínek
MB104/02: Mon 14:00–15:50 B204, L. Vokřínek
MB104/03: Wed 8:00–9:50 B204, M. Šimková
MB104/04: Thu 21. 2. to Thu 16. 5. Thu 14:00–15:50 B204, M. Šimková
MB104/05: Wed 16:00–17:50 B204, J. Kolegar
MB104/06: Wed 18:00–19:50 B204, J. Kolegar
MB104/07: Wed 12:00–13:50 A320, R. Penčevová
MB104/08: Mon 10:00–11:50 A320, R. Penčevová
MB104/09: Tue 19. 2. to Tue 14. 5. Tue 16:00–17:50 B204, A. Tokarčík
MB104/10: Tue 19. 2. to Tue 14. 5. Tue 18:00–19:50 B204, A. Tokarčík
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2018
Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Mgr. Jonatan Kolegar (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
doc. Lukáš Vokřínek, PhD. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 D2, Mon 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/01: Tue 16:00–17:50 A320, J. Slovák
MB104/02: Tue 10:00–11:50 B204, R. Penčevová
MB104/03: Thu 14:00–15:50 A320, M. Šimková
MB104/04: Tue 12:00–13:50 A320, L. Vokřínek
MB104/05: Tue 14:00–15:50 A320, L. Vokřínek
MB104/06: Wed 8:00–9:50 A320, J. Kolegar
MB104/07: Wed 10:00–11:50 A320, J. Kolegar
MB104/08: Tue 18:00–19:50 A320, J. Volaříková
MB104/09: Wed 12:00–13:50 A320, J. Volaříková
MB104/10: Thu 12:00–13:50 B204, R. Penčevová
MB104/11: Wed 14:00–15:50 A320, R. Penčevová
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2017
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Bc. Martin Baláž (seminar tutor)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
RNDr. Jiří Pecl, Ph.D. (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
RNDr. Vladimír Sedláček, Ph.D. (seminar tutor)
Mgr. Jaroslav Šeděnka, Ph.D. (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
Mgr. Jan Fikejs (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 16:00–17:50 D2, Mon 16:00–17:50 D3
  • Timetable of Seminar Groups:
MB104/T01: Mon 14:30–16:05 116, Wed 22. 2. to Mon 22. 5. Wed 14:30–16:05 116, J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T02: Tue 21. 2. to Mon 22. 5. Tue 12:45–15:10 117, J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/01: Wed 8:00–9:50 B204, M. Panák
MB104/02: Wed 10:00–11:50 B204, M. Panák
MB104/03: Tue 8:00–9:50 B204, M. Panák
MB104/04: Wed 14:00–15:50 B204, L. Vokřínek
MB104/05: Wed 16:00–17:50 B204, L. Vokřínek
MB104/06: Tue 10:00–11:50 B204, L. Vokřínek
MB104/07: Wed 8:00–9:50 A320, J. Volaříková
MB104/08: Wed 12:00–13:50 A320, J. Volaříková
MB104/09: Wed 12:00–13:50 B204, R. Penčevová
MB104/10: Fri 10:00–11:50 B204, R. Penčevová
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2018, Spring 2019, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2016
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Bc. Martin Baláž (seminar tutor)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
RNDr. Jiří Pecl, Ph.D. (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
RNDr. Vladimír Sedláček, Ph.D. (seminar tutor)
Mgr. Jaroslav Šeděnka, Ph.D. (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
Mgr. Jan Fikejs (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 D3, Mon 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/T01: Mon 12:10–13:45 110, J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T02: Mon 15:00–16:35 117, Tue 23. 2. to Fri 20. 5. Tue 14:40–16:15 110, J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T03: Tue 13:00–14:35 110, Thu 14:00–15:35 110, J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/01: Wed 8:00–9:50 B204, M. Panák
MB104/02: Wed 10:00–11:50 B204, M. Panák
MB104/03: Tue 12:00–13:50 A320, M. Panák
MB104/04: Tue 8:00–9:50 C511, J. Volaříková
MB104/05: Thu 18:00–19:50 B204, J. Volaříková
MB104/06: Tue 14:00–15:50 A320, R. Penčevová
MB104/07: Thu 18:00–19:50 A320, R. Penčevová
MB104/08: Mon 16:00–17:50 A320, M. Baláž
MB104/09: Mon 18:00–19:50 A320, M. Baláž
MB104/10: Wed 18:00–19:50 A320, V. Sedláček
MB104/11: Fri 8:00–9:50 A320, V. Sedláček
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2015
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
RNDr. Jiří Pecl, Ph.D. (seminar tutor)
Mgr. Jaroslav Šeděnka, Ph.D. (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
Mgr. et Mgr. Tomáš Sklenák (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 D3, Mon 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/T01: Mon 16. 2. to Fri 15. 5. Mon 8:00–9:35 108, Thu 19. 2. to Fri 15. 5. Thu 14:40–16:10 106, J. Pecl, T. Sklenák, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T02: Thu 19. 2. to Fri 15. 5. Thu 12:00–13:35 116, J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/01: Tue 16:00–17:50 A320, J. Slovák
MB104/02: Tue 8:00–9:50 A320, M. Panák
MB104/03: Tue 10:00–11:50 A320, M. Panák
MB104/04: Wed 8:00–9:50 A320, M. Panák
MB104/05: Wed 10:00–11:50 A320, M. Panák
MB104/06: Fri 8:00–9:50 A320, M. Panák
MB104/07: Fri 10:00–11:50 A320, M. Panák
MB104/08: Thu 12:00–13:50 A320, J. Šilhan
MB104/09: Tue 12:00–13:50 A320, J. Šilhan
MB104/10: Tue 14:00–15:50 A320, J. Šilhan
MB104/11: Tue 8:00–9:50 B204, J. Šeděnka
MB104/12: Wed 8:00–9:50 B204, J. Šeděnka
MB104/13: Mon 8:00–9:50 B204, J. Komárková
MB104/14: Mon 10:00–11:50 B204, J. Komárková
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2014
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Mgr. Marek Filakovský, Ph.D. (seminar tutor)
Mgr. Bc. Tomáš Janík (seminar tutor)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
Mgr. Bc. Jaromír Kuben (seminar tutor)
Mgr. Lenka Mžourková Macálková (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
RNDr. Jiří Pecl, Ph.D. (seminar tutor)
Mgr. Milan Werl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 14:00–15:50 D3, Mon 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/T01: Tue 18. 2. to Sat 31. 5. Tue 13:00–14:35 Učebna S2 (36b), Thu 20. 2. to Sat 31. 5. Thu 13:00–14:35 Učebna S6 (20), Fri 21. 2. to Sat 31. 5. Fri 8:00–9:35 Učebna S10 (56), J. Pecl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T02: Thu 27. 2. to Sat 31. 5. Thu 8:00–9:35 Učebna S6 (20), M. Werl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T03: Tue 25. 2. to Sat 31. 5. Tue 9:40–11:15 Učebna S4 (35a), Fri 28. 2. to Sat 31. 5. Fri 13:30–15:10 Učebna S4 (35a), M. Werl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/01: Wed 8:00–9:50 G331, M. Panák
MB104/02: Wed 10:00–11:50 G331, M. Panák
MB104/03: Thu 14:00–15:50 G331, D. Kruml
MB104/04: Wed 8:00–9:50 G125, D. Kruml
MB104/05: Thu 10:00–11:50 B410, M. Panák
MB104/06: Thu 12:00–13:50 G330, D. Kruml
MB104/07: Thu 16:00–17:50 G331, M. Filakovský
MB104/08: Thu 18:00–19:50 G331, M. Filakovský
MB104/09: Tue 16:00–17:50 G331, T. Janík
MB104/10: Tue 18:00–19:50 G331, T. Janík
MB104/11: Fri 12:00–13:50 G331, J. Komárková
MB104/12: Fri 14:00–15:50 G331, J. Komárková
MB104/13: Thu 16:00–17:50 G125, J. Kuben
MB104/14: Thu 18:00–19:50 G125, J. Kuben
MB104/15: Fri 8:00–9:50 G331, M. Werl
MB104/16: Fri 10:00–11:50 G330, M. Werl
MB104/17: Thu 14:00–15:50 G330, L. Mžourková Macálková
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2013
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Mgr. Petr Pupík (lecturer)
Mgr. Bc. Tomáš Janík (seminar tutor)
Mgr. Eva Janoušková, Ph.D. (seminar tutor)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. Jan Meitner (seminar tutor)
Mgr. Lenka Mžourková Macálková (seminar tutor)
doc. Mgr. Aleš Návrat, Dr. rer. nat. (seminar tutor)
Mgr. Jaroslav Šeděnka, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (seminar tutor)
Mgr. Milan Werl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 18:00–19:50 D1, Wed 16:00–17:50 D1
  • Timetable of Seminar Groups:
MB104/T01: Tue 9:00–10:55 Učebna S8 (17), Fri 8:00–9:55 Učebna S6 (20), E. Janoušková, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/T02: Tue 15:00–16:55 Učebna S6 (20), M. Werl, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
MB104/01: Mon 12:00–13:50 G124, L. Mžourková Macálková
MB104/02: Mon 14:00–15:50 G124, L. Mžourková Macálková
MB104/03: Tue 16:00–17:50 G125, J. Komárková
MB104/04: Tue 18:00–19:50 G125, J. Komárková
MB104/05: Mon 8:00–9:50 G124, M. Werl
MB104/06: Mon 10:00–11:50 G124, M. Werl
MB104/07: Fri 12:00–13:50 G125, J. Meitner
MB104/08: Fri 14:00–15:50 G125, J. Meitner
MB104/09: Thu 12:00–13:50 G124, J. Šeděnka
MB104/10: Thu 14:00–15:50 G124, J. Šeděnka
MB104/11: Thu 16:00–17:50 M5,01013, T. Janík
MB104/12: Thu 18:00–19:50 G124, T. Janík
MB104/13: Tue 16:00–17:50 G124, T. Janík
MB104/14: Tue 18:00–19:50 G124, T. Janík
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101. The main objectives can be summarized as follows: to understand basic concepts and tools of Algebra; to understand basic concepts and tools of Probability and Statistics.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ZVÁRA, Karel and Josef ŠTĚPÁN. Pravděpodobnost a matematická statistika. Vyd. 3. Praha: Matfyzpress, 2002, 230 s. ISBN 80-85863-93-6. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are theoretical lectures, practical demonstration of the computational aspects, and standard tutorial accompanied by homework assessment.
Assessment methods
Two hours of lectures, two hours of presentations of typical problem solutions. Homeworks supported by tutorials. Written test exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2012
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Martin Panák, Ph.D. (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Mgr. Marek Filakovský, Ph.D. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
Mgr. Jan Meitner (seminar tutor)
Mgr. Jaroslav Šeděnka, Ph.D. (seminar tutor)
doc. Mgr. Josef Šilhan, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (seminar tutor)
Mgr. Milan Werl, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Mon 18:00–19:50 D1, Tue 8:00–9:50 D1
  • Timetable of Seminar Groups:
MB104/01: Wed 8:00–9:50 G124, M. Panák
MB104/02: Wed 10:00–11:50 G124, M. Panák
MB104/03: Thu 12:00–13:50 G125, D. Kruml
MB104/04: Thu 14:00–15:50 G125, D. Kruml
MB104/05: Thu 16:00–17:50 G125, D. Kruml
MB104/06: Wed 12:00–13:50 G124, J. Šilhan
MB104/07: Wed 14:00–15:50 G124, J. Šilhan
MB104/08: Fri 8:00–9:50 G125, J. Šeděnka
MB104/09: Fri 10:00–11:50 G125, J. Šeděnka
MB104/10: Fri 12:00–13:50 G125, J. Meitner
MB104/11: Fri 14:00–15:50 G125, J. Meitner
MB104/12: Wed 8:00–9:50 G125, M. Filakovský
MB104/13: Wed 10:00–11:50 G125, M. Filakovský
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101. The main objectives can be summarized as follows: to understand basic concepts and tools of Algebra; to understand basic concepts and tools of Probability and Statistics.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ZVÁRA, Karel and Josef ŠTĚPÁN. Pravděpodobnost a matematická statistika. Vyd. 3. Praha: Matfyzpress, 2002, 230 s. ISBN 80-85863-93-6. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are theoretical lectures, practical demonstration of the computational aspects, and standard tutorial accompanied by homework assessment.
Assessment methods
Two hours of lectures, two hours of presentations of typical problem solutions. Homeworks supported by tutorials. Written test exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2011
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. Lenka Mžourková Macálková (seminar tutor)
Mgr. et Mgr. Alena Novotná (seminar tutor)
Mgr. Petr Pupík (seminar tutor)
Mgr. Milan Werl, Ph.D. (seminar tutor)
Mgr. Silvie Zlatošová, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Tue 16:00–17:50 D1, Wed 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/01: Tue 18:00–19:50 G125, P. Pupík
MB104/02: Thu 8:00–9:50 G125, S. Zlatošová
MB104/03: Thu 10:00–11:50 G125, S. Zlatošová
MB104/04: Mon 8:00–9:50 G125, M. Werl
MB104/05: Mon 10:00–11:50 G125, M. Werl
MB104/06: Fri 8:00–9:50 G124, L. Mžourková Macálková
MB104/07: Fri 10:00–11:50 G124, L. Mžourková Macálková
MB104/08: Tue 12:00–13:50 G124, J. Komárková
MB104/09: Wed 12:00–13:50 G124, J. Komárková
MB104/10: Wed 8:00–9:50 G125, A. Novotná
MB104/11: Wed 10:00–11:50 G125, A. Novotná
MB104/12: Mon 14:00–15:50 G101, S. Zlatošová
MB104/13: Thu 18:00–19:50 G123, L. Mžourková Macálková
MB104/14: Mon 12:00–13:50 G123, J. Komárková
MB104/15: Fri 8:00–9:50 M3,01023, P. Pupík
MB104/16: Mon 12:00–13:50 G101, M. Werl
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 19 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101. The main objectives can be summarized as follows: to understand basic concepts and tools of Algebra; to understand basic concepts and tools of Probability and Statistics.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ZVÁRA, Karel and Josef ŠTĚPÁN. Pravděpodobnost a matematická statistika. Vyd. 3. Praha: Matfyzpress, 2002, 230 s. ISBN 80-85863-93-6. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are theoretical lectures, practical demonstration of the computational aspects, and standard tutorial accompanied by homework assessment.
Assessment methods
Two hours of lectures, two hours of presentations of typical problem solutions. Homeworks supported by tutorials. Written test exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2010
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
RNDr. Jana Komárková, Ph.D. (seminar tutor)
Mgr. Jitka Kühnová, Ph.D. (seminar tutor)
Mgr. Lenka Mžourková Macálková (seminar tutor)
Mgr. Petr Pupík (seminar tutor)
Mgr. Veronika Trnková (seminar tutor)
Mgr. Milan Werl, Ph.D. (seminar tutor)
prof. RNDr. Radan Kučera, DSc. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Mon 12:00–13:50 D1, Wed 12:00–13:50 D1
  • Timetable of Seminar Groups:
MB104/01: Mon 16:00–17:50 B007, J. Kühnová
MB104/02: Thu 18:00–19:50 B007, P. Pupík
MB104/03: Fri 8:00–9:50 B007, V. Trnková
MB104/04: Fri 10:00–11:50 B007, V. Trnková
MB104/05: Wed 8:00–9:50 B003, M. Werl
MB104/06: Wed 10:00–11:50 B003, M. Werl
MB104/07: Mon 18:00–19:50 B007, J. Kühnová
MB104/08: Tue 12:00–13:50 B003, P. Pupík
MB104/09: Mon 18:00–19:50 B011, L. Mžourková Macálková
MB104/10: Tue 18:00–19:50 B007, L. Mžourková Macálková
MB104/11: Fri 10:00–11:50 B011, J. Komárková
MB104/12: Fri 12:00–13:50 B007, J. Komárková
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 16 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101. The main objectives can be summarized as follows: to understand basic concepts and tools of Algebra; to understand basic concepts and tools of Probability and Statistics.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ZVÁRA, Karel and Josef ŠTĚPÁN. Pravděpodobnost a matematická statistika. Vyd. 3. Praha: Matfyzpress, 2002, 230 s. ISBN 80-85863-93-6. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are theoretical lectures, practical demonstration of the computational aspects, and standard tutorial accompanied by homework assessment.
Assessment methods
Two hours of lectures, two hours of presentations of typical problem solutions. Homeworks supported by tutorials. Written test exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2009
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Martin Panák, Ph.D. (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer), Mgr. Martin Panák, Ph.D. (deputy)
RNDr. Mgr. Jana Dražanová, Ph.D. (seminar tutor)
Mgr. Jan Gregorovič, Ph.D. (seminar tutor)
Mgr. et Mgr. Alena Novotná (seminar tutor)
doc. Lukáš Vokřínek, PhD. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Mon 16:00–17:50 D1, Mon 16:00–17:50 D3, Tue 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB104/01: Wed 8:00–9:50 B003, M. Panák
MB104/02: Wed 10:00–11:50 B003, M. Panák
MB104/03: Wed 14:00–15:50 B003, M. Panák
MB104/04: Thu 10:00–11:50 B007, J. Gregorovič
MB104/05: Thu 12:00–13:50 B007, J. Gregorovič
MB104/06: Fri 8:00–9:50 B007, J. Dražanová
MB104/07: Fri 10:00–11:50 B007, J. Dražanová
MB104/08: Wed 8:00–9:50 B007, A. Novotná
MB104/09: Wed 10:00–11:50 B007, A. Novotná
MB104/10: Thu 14:00–15:50 B011, L. Vokřínek
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 14 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101. The main objectives can be summarized as follows: to understand basic concepts and tools of Algebra; to understand basic concepts and tools of Probability and Statistics.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ZVÁRA, Karel and Josef ŠTĚPÁN. Pravděpodobnost a matematická statistika. Vyd. 3. Praha: Matfyzpress, 2002, 230 s. ISBN 80-85863-93-6. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods
Two hours of lectures, two hours of presentations of typical problem solutions. Homeworks supported by tutorials. Written test exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2008
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
Mgr. Jan Herman (lecturer)
Mgr. Jitka Kühnová, Ph.D. (lecturer)
Ing. Mgr. Dávid Dereník (seminar tutor)
RNDr. Jiří Glozar (seminar tutor)
Mgr. Petr Liška, Ph.D. (seminar tutor)
Mgr. Miloš Přinosil, Ph.D. (seminar tutor)
Mgr. Petr Pupík (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Mon 8:00–9:50 D1, Wed 8:00–9:50 D1
  • Timetable of Seminar Groups:
MB104/01: Tue 14:00–15:50 B007, J. Glozar
MB104/02: Tue 16:00–17:50 B007, J. Glozar
MB104/03: Wed 18:00–19:50 B003, P. Liška
MB104/04: Tue 14:00–15:50 B003, M. Přinosil
MB104/05: Tue 18:00–19:50 B003, J. Herman
MB104/06: Thu 14:00–15:50 B003, P. Pupík
MB104/07: Thu 12:00–13:50 B003, P. Pupík
MB104/08: Thu 18:00–19:50 B003, P. Liška
MB104/09: Tue 18:00–19:50 B011, P. Pupík
MB104/10: Wed 14:00–15:50 B011, J. Kühnová
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 15 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods (in Czech)
Dvouhodinová přednáška a dvouhodinová přednášená ukázková řešení s řešením vzorových příkladů. Povinná je docházka do cvičení, součástí zkoušky budou 2-3 průběžně psané písemky. Zakončení písemnou zkouškou na konci semestru.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2007
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Mgr. Josef Šilhan, Ph.D. (lecturer)
Ing. Mgr. Dávid Dereník (seminar tutor)
RNDr. Ing. Hana Kotoučková, Ph.D. (seminar tutor)
Mgr. Tomáš Lipenský (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
Mgr. Eva Pellarová (seminar tutor)
Mgr. Michaela Vokřínková (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Mon 14:00–15:50 D3, Tue 16:00–17:50 D3
  • Timetable of Seminar Groups:
MB104/01: Tue 8:00–9:50 B007, M. Vokřínková
MB104/02: Tue 10:00–11:50 B007, M. Vokřínková
MB104/03: Wed 10:00–11:50 B007, H. Kotoučková
MB104/04: Wed 12:00–13:50 B007, H. Kotoučková
MB104/05: Thu 8:00–9:50 B007, T. Lipenský
MB104/06: Thu 10:00–11:50 B007, T. Lipenský
MB104/07: Wed 8:00–9:50 B007, E. Pellarová
Prerequisites
Recommended: Calculus and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 10 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101.
Syllabus
  • Abstract mathematical structures: groups, algebras, lattices, rings, fields, divisibility, prime numbers decompositions, Euler theorem. Introduction to probability theory and statistics: Probality functins and their properties, conditional probability, Bayes formula, random quantities, mean value, median, quantil, variance, sequences of random quantities, law of large numbers, examples of discrete and continuous distributions, selected applications.
Literature
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
  • ROSICKÝ, J. Algebra, grupy a okruhy. 3rd ed. Brno: Masarykova univerzita, 2000, 140 pp. ISBN 80-210-2303-1. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods (in Czech)
Dvouhodinová přednáška a dvouhodinová přednášená ukázková řešení úloh, spolu s povinnostmi samostatného řešení a odevzdávání úloh se zázemím cvičení. Zakončení písemnou zkouškou na konci semestru a dvě další krátké písemné zkoušky během semestru.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2006
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
prof. Mgr. Petr Hasil, Ph.D. (seminar tutor)
RNDr. Gabriela Kraváčková (seminar tutor)
Mgr. Tomáš Lipenský (seminar tutor)
Mgr. Petra Ovesná, Ph.D. (seminar tutor)
Mgr. Jaroslava Sidorová (seminar tutor)
RNDr. Jitka Vacková, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Timetable
Mon 18:00–19:50 D1
  • Timetable of Seminar Groups:
MB104/sc1: No timetable has been entered into IS. P. Ovesná
MB104/sc2: No timetable has been entered into IS. T. Lipenský
MB104/01: Tue 12:00–13:50 B003, J. Sidorová
MB104/02: Tue 14:00–15:50 B003, J. Sidorová
MB104/03: Fri 8:00–9:50 B003, P. Hasil
MB104/04: Fri 10:00–11:50 B003, P. Hasil
MB104/05: Tue 16:00–17:50 B007, J. Vacková
MB104/06: Tue 18:00–19:50 B007, J. Vacková
MB104/07: Mon 9:00–10:50 B007, G. Kraváčková
MB104/08: Mon 11:00–12:50 B007, G. Kraváčková
Prerequisites
Recommended: Calculus of functions of one real variable and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 10 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101.
Syllabus
  • Multivariable calculus. Partial derivatives, differential, tangent plane and normal vector. Extrema of functions of several variables. Elements of probability theory. Probability function and its properties, conditional probability, Bayes formula. Random quantities, mean value, variance, sequences of random quantities, law of large numbers.
Literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vyd. 2. přeprac. Brno: Masarykova univerzita, 1999, iv, 143. ISBN 8021020520. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods (in Czech)
Two-hour lectures and practising, two-hour written final exam. Dvouhodinová přednáška a cvíčení zakončené písemnou zkouškou.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2005
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
RNDr. Martina Jarošová, Ph.D. (seminar tutor)
RNDr. Gabriela Kraváčková (seminar tutor)
Mgr. Daniel Marek, Ph.D. (seminar tutor)
Mgr. Zdeněk Opluštil, Ph.D. (seminar tutor)
Mgr. Stepan Sukovych (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Faculty of Informatics
Timetable
Mon 18:00–19:50 D3
  • Timetable of Seminar Groups:
MB104/01: Fri 9:00–10:50 B007, S. Sukovych
MB104/02: Fri 11:00–12:50 B007, S. Sukovych
MB104/03: Wed 10:00–11:50 B011, Z. Opluštil
MB104/04: Wed 12:00–13:50 B011, M. Jarošová
MB104/05: Thu 8:00–9:50 B003, G. Kraváčková
MB104/06: Thu 10:00–11:50 B003, G. Kraváčková
MB104/07: Thu 14:00–15:50 B003, D. Marek
Prerequisites
Recommended: Calculus of functions of one real variable and linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101.
Syllabus
  • Multivariable calculus. Partial derivatives, differential, tangent plane and normal vector. Extrema of functions of several variables. Elements of probability theory. Probability function and its properties, conditional probability, Bayes formula. Random quantities, mean value, variance, sequences of random quantities, law of large numbers.
Literature
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Diferenciální počet funkcí více proměnných. Vyd. 2. přeprac. Brno: Masarykova univerzita, 1999, iv, 143. ISBN 8021020520. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Popisná statistika. Třetí doplněné vydání. Brno: Masarykova univerzita, 1998, 48 stran. ISBN 8021018313. info
  • BUDÍKOVÁ, Marie, Štěpán MIKOLÁŠ and Pavel OSECKÝ. Teorie pravděpodobnosti a matematická statistika : sbírka příkladů [Budíková, 1996]. 1. vyd. Brno: Masarykova univerzita, 1996, 131 s. ISBN 80-210-1329-X. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods (in Czech)
Two-hour lectures and practising, two-hour written final exam. Dvouhodinová přednáška a cvíčení zakončené písemnou zkouškou.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2004
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
Mgr. Martina Bobalová, Ph.D. (seminar tutor)
Mgr. et Mgr. Lukáš Maňásek (seminar tutor)
Mgr. Hana Štěpánková, Ph.D. (seminar tutor)
Mgr. Magda Zemánková (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Faculty of Informatics
Timetable
Thu 8:00–9:50 D3
  • Timetable of Seminar Groups:
MB104/01: Mon 16:00–17:50 B007, H. Štěpánková
MB104/02: Wed 10:00–11:50 B003, M. Zemánková
MB104/03: Tue 10:00–11:50 B007, M. Zemánková
MB104/04: Thu 10:00–11:50 B003, L. Maňásek
MB104/05: Thu 12:00–13:50 B003, L. Maňásek
MB104/06: Tue 8:00–9:50 B007, M. Bobalová
Prerequisites (in Czech)
MB103 Mathematics III || M000 Calculus I || M500 Calculus I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101.
Syllabus
  • Elements of probability theory. Probability functions and their properties, conditional probability, Bayes formula. Random quantities, mean value, sequences of random quantities, law of large numbers. Partial derivatives, differential tangent plane and normal vector. Extrema of functions of several variables. First order differential equations. Second order linear equations with constant coefficients. Elements of graphs theory.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1983, 876 s. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1986, 896 s. URL info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods (in Czech)
Dvouhodinová přednáška a cvíčení zakončené písemnou zkouškou.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2022

The course is not taught in Spring 2022

Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Mgr. Martin Dzúrik (seminar tutor)
Mgr. Jonatan Kolegar (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
Mgr. Tomáš Svoboda (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Mgr. Andrej Tokarčík (seminar tutor)
Mgr. Dominik Trnka (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
doc. RNDr. Martin Čadek, CSc. (assistant)
Mgr. Martin Panák, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 53 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Discrete mathematics

Faculty of Informatics
Spring 2021

The course is not taught in Spring 2021

Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Mgr. Martin Dzúrik (seminar tutor)
Mgr. Jonatan Kolegar (seminar tutor)
Mgr. Radka Penčevová (seminar tutor)
Mgr. Tomáš Svoboda (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Mgr. Andrej Tokarčík (seminar tutor)
Mgr. Dominik Trnka (seminar tutor)
Mgr. Jana Volaříková, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant)
doc. RNDr. Martin Čadek, CSc. (assistant)
Mgr. Martin Panák, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
Prerequisites
! MB204 Discrete mathematics B && !NOW( MB204 Discrete mathematics B )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 53 fields of study the course is directly associated with, display
Course objectives
At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context;
model and solve simple combinatorial problems.
Syllabus
  • Number theory:
  • divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
  • Number theory applications:
  • short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
  • Combinatorics:
  • reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
Literature
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Teaching methods
There are standard two-hour lectures and standard tutorial.
Assessment methods
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.

MB104 Mathematics IV

Faculty of Informatics
Spring 2003

The course is not taught in Spring 2003

Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Helena Dvořáčková (assistant)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Faculty of Informatics
Prerequisites
MB103 Mathematics III
Mathematics III MB103
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The last part of the block Mathematics I-IV, for the brief content of the whole block see Mathematics I MB101.
Syllabus
  • Elements of probability theory. Probability functions and their properties, conditional probability, Bayes formula. Random quantities, mean value, sequences of random quantities, law of large numbers. Partial derivatives, differential tangent plane and normal vector. Extrema of functions of several variables. First order differential equations. Second order linear equations with constant coefficients. Elements of graphs theory.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1983, 876 s. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1986, 896 s. URL info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB104!
Assessment methods (in Czech)
Dvouhodinová přednáška a cvíčení zakončené písemnou zkouškou.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019, Spring 2020.
  • Enrolment Statistics (recent)