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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

Discrete Mathematics and Logic

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Code Completion Credits Range Language
BI-DML.21 Z,ZK 5 2P+1R+1C Czech
The course cannot be taken simultaneously with:
Mathematical Logic (BI-MLO)
Elements of Discrete Mathematics (BI-ZDM)
Lecturer:
Daniel Dombek (guarantor), Jan Spěvák
Tutor:
Daniel Dombek (guarantor), Jakub Čermák, Jitka Rybníčková, Jan Spěvák, Irena Šindelářová, Alena Šolcová, Kateřina Trlifajová
Supervisor:
Department of Applied Mathematics
Synopsis:

Students will get acquainted with the basic concepts of propositional logic and predicate logic and learn to work with their laws. Necessary concepts from set theory will be explained. Special attention is paid to relations, their general properties, and their types, especially functional relations, equivalences, and partial orders. The course also lays down the basics of combinatorics and number theory, with emphasis on modular arithmetics.

Requirements:

None.

Syllabus of lectures:

1. Propositional logic. Formulas. Truth tables. Logical equivalence. Basic laws.

2. Disjunctive and conjunctive normal forms. Full forms. Logical consequence.

3. Predicate logic. Formalization of language.

4. Sets and functions. Basic number sets. Cardinalities of sets.

5. Mathematical induction. Types of mathematical proofs.

6. Binary relations (properties, representations). Composition of relations.

7. Equivalence and ordering.

8. Enumerative combinatorics and its basic principles.

9. k-combinations with repetition, permutations with repetition, Stirling numbers, properties of binomial coefficients. Classical definition of probability.

10. Fundamentals of number theory, modular arithmetic.

11. Properties of prime numbers, Fundamental theorem of arithmetic.

12. Diophantine equations, linear congruences, Chinese remainder theorem.

Syllabus of tutorials:

1. Introduction to mathematical logics. Formulas, truth tables. Tautology, contradiction.

2. Consequence and equivalence. Universal systems of connectives.

3. Disjunctive and conjunctive normal forms.

4. Syntax of predicate logic. Language, terms, formulas. Formalization of language.

5. Mathematical induction.

6. Sets and maps.

7. Binary relation (properties, representation), composition of relations.

8. Equivalence and order.

9. Application of combinatorial principles, probability,

10. Advanced combinatorial principles.

11. Divisibility. Diophantine equations solution.

12. Solution of linear congruences and their systems.

Study Objective:
Study materials:

1. Mendelson E.: Introduction to Mathematical Logic (6th Edition); Chapman and Hall 2015; ISBN 978-1482237726

2. Chartrand G., Zhang P.: Discrete Mathematics; Waveland;2011; ISBN 978-1577667308

3. Graham R. L., Knuth D. E., Patashnik O.: Concrete Mathematics: A Foundation for Computer Science (2nd Edition); Addison-Wesley Professional; 1994; ISBN 978-0201558029

4. Trlifajová K., Vašata D.: Matematická logika; ČVUT2017; ISBN 978-80-01-05342-3

5. Nešetřil J., Matoušek J.: Kapitoly z diskrétní matematiky; Karolinum2007; ISBN 978-80-246-1411-3

Note:
Further information:
https://courses.fit.cvut.cz/BI-DML
Time-table for winter semester 2022/2023:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
roomT9:105
Dombek D.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
Tue
roomTH:A-1442
Dombek D.
09:15–10:00
(parallel nr.1)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
10:00–10:45
(parallel nr.2)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
11:00–11:45
(parallel nr.3)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
11:45–12:30
(parallel nr.4)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Rybníčková J.
12:45–13:30
(parallel nr.5)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Rybníčková J.
13:30–14:15
(parallel nr.6)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
14:30–15:15
(parallel nr.7)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
15:15–16:00
(parallel nr.8)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
16:15–17:00
(parallel nr.9)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Dombek D.
17:00–17:45
(parallel nr.10)
Thákurova 7 (FSv-budova A)
Wed
roomT9:346
Čermák J.
11:00–11:45
(parallel nr.11)
Dejvice
NBFIT učebna
roomT9:346
Čermák J.
11:45–12:30
(parallel nr.12)
Dejvice
NBFIT učebna
roomT9:346
Čermák J.
12:45–13:30
(parallel nr.13)
Dejvice
NBFIT učebna
roomT9:346
Čermák J.
13:30–14:15
(parallel nr.14)
Dejvice
NBFIT učebna
roomTH:A-942
Šolcová A.
14:30–15:15
(parallel nr.15)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Šolcová A.
15:15–16:00
(parallel nr.16)
Thákurova 7 (FSv-budova A)
roomT9:155
Dombek D.
11:00–12:30
(lecture parallel2)
Dejvice
Posluchárna
Thu
roomT9:343
Spěvák J.
09:15–10:00
(parallel nr.17)
Dejvice
NBFIT učebna
roomT9:343
Spěvák J.
10:00–10:45
(parallel nr.18)
Dejvice
NBFIT učebna
roomT9:343
Spěvák J.
11:00–11:45
(parallel nr.19)
Dejvice
NBFIT učebna
roomT9:343
Spěvák J.
11:45–12:30
(parallel nr.20)
Dejvice
NBFIT učebna
roomTH:A-1247
Šindelářová I.
12:45–13:30
(parallel nr.23)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Šindelářová I.
13:30–14:15
(parallel nr.24)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Šindelářová I.
14:30–15:15
(parallel nr.25)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Šindelářová I.
15:15–16:00
(parallel nr.26)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1442
Trlifajová K.
11:00–11:45
(parallel nr.21)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Trlifajová K.
11:45–12:30
(parallel nr.22)
Thákurova 7 (FSv-budova A)
roomT9:105
Spěvák J.
14:30–16:00
(lecture parallel3)
Dejvice
Posluchárna
Fri
roomTH:A-942
Šindelářová I.
07:30–08:15
(parallel nr.27)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Šindelářová I.
08:15–09:00
(parallel nr.28)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Šindelářová I.
09:15–10:00
(parallel nr.29)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Šindelářová I.
10:00–10:45
(parallel nr.30)
Thákurova 7 (FSv-budova A)
roomTH:A-1247
Trlifajová K.
11:00–11:45
(parallel nr.31)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Trlifajová K.
11:45–12:30
(parallel nr.32)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Trlifajová K.
12:45–13:30
(parallel nr.33)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Trlifajová K.
13:30–14:15
(parallel nr.34)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-942
Rybníčková J.
14:30–15:15
(parallel nr.35)
Thákurova 7 (FSv-budova A)
roomTH:A-942
Rybníčková J.
15:15–16:00
(parallel nr.36)
Thákurova 7 (FSv-budova A)
roomTH:A-1247
Šolcová A.
16:15–17:00
(parallel nr.39)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Šolcová A.
17:00–17:45
(parallel nr.40)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Šolcová A.
14:30–15:15
(parallel nr.37)
Thákurova 7 (FSv-budova A)
seminární místnost
roomTH:A-1247
Šolcová A.
15:15–16:00
(parallel nr.38)
Thákurova 7 (FSv-budova A)
seminární místnost
Time-table for summer semester 2022/2023:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-01-28
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6533606.html