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Introduction to Discrete Mathematics

General data

Course ID: 103A-CTxxx-ISA-EIDMA Erasmus code / ISCED: (unknown) / (unknown)
Course title: Introduction to Discrete Mathematics Name in Polish: Introduction to Discrete Mathematics
Department: The Faculty of Electronics and Information Technology
Course groups: ( Courses in English )--eng.-EITI
( Mathematics )--B.Sc.-EITI
( Technical Courses )---EITI
( Technical Courses )--eng.-EITI
ECTS credit allocation (and other scores): 6.00
Language: English
(in Polish) Jednostka decyzyjna:

(in Polish) 103000 - Wydział Elektroniki i Technik Informacyjnych

(in Polish) Kod wydziałowy:

(in Polish) EIDMA

(in Polish) Numer wersji:

(in Polish) 1

Short description:

The lecture covers mathematical logic including quantifiers, set theory, basic combinatorial principles and foundations of recursion theory.

Full description:

The lecture covers mathematical logic including quantifiers, set theory, basic combinatorial principles and foundations of recursion theory.

Lecture contents

  1. Introduction (4h): Propositions, prepositional calculus,
    tautologies. Propositional functions and quantifiers. Sets, operations
    on sets, generalized union and intersection of sets

  2. Relations (6h): Cartesian product of sets. Relations as subsets
    of the Cartesian product of sets. Equivalence relations,
    equivalence classes. Ordering relations, partial and total orders,
    minimal, maximal, least and largest elements, chains and antichains.
    Well ordered sets. The Induction Theorem.

  3. Congruence modulo n (4h): Remainder lemma, residues modulo n.
    Addition and multiplication modulo n. Properties of addition and
    multiplication mod n.

  4. Functions (4h): Functions as relations. One-to-one and onto
    functions. Image and inverse image of a set by a function. Order
    preserving (increasing) functions. The concept of a fixed point.

  5. Combinatorics (6h): Basic combinatorial principles. Newton
    binomial formula. Pigeon-hole principle. Inclusion-exclusion principle.
    Generating functions. Number of subsets of a set, number of fixed-size
    subsets, number of permutations, number of functions from one set into
    another.

  6. Graphs (4): Graphs, subgraphs, induced and spanning subgraphs,
    paths and cycles. Connectivity, Menger theorem. Eulerian graphs,
    Hamilton graphs. Planar graphs, Kuratowski theorem. Coloring of graphs.

  7. Recurrence relation (2): Recursive equations. Recursive methods
    in enumeration


Tutorial contents
Tutorials will follow lectures step by step.

Assessment methods and assessment criteria:

Two midterm exams for the maximum of 20 point each


  • Up to 10 points for classroom activity

  • Final exam for up to 50 points


The final result is based on the following pattern:

5.0: 91-100 points

4.5: 81-90 points

4.0: 71-80 points

3.5: 61-70 points

3.0: 51-60 points

2.0: ..0-50 points

Classes in period "Summer Semester 2019/2020"

Time span: 2020-02-22 - 2020-09-30

Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2019/2020" (past)

Time span: 2019-10-01 - 2020-02-21
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 120 places more information
tutorials, 30 hours, 120 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2018/2019" (past)

Time span: 2019-02-18 - 2019-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2018/2019" (past)

Time span: 2018-10-01 - 2019-02-17
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 120 places more information
tutorials, 30 hours, 120 places more information
Coordinators: Tomasz Traczyk
Group instructors: (unknown)
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2017/2018" (past)

Time span: 2018-02-19 - 2018-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2017/2018" (past)

Time span: 2017-10-01 - 2018-02-18
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 120 places more information
tutorials, 30 hours, 120 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2016/2017" (past)

Time span: 2017-02-20 - 2017-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 50 places more information
tutorials, 30 hours, 50 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2016/2017" (past)

Time span: 2016-10-01 - 2017-02-19
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 70 places more information
tutorials, 30 hours, 70 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2015/2016" (past)

Time span: 2016-02-23 - 2016-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2015/2016" (past)

Time span: 2015-10-01 - 2016-02-22
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2014/2015" (past)

Time span: 2015-02-23 - 2015-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 40 places more information
tutorials, 30 hours, 40 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2014/2015" (past)

Time span: 2014-09-29 - 2015-02-22
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2013/2014" (past)

Time span: 2014-02-24 - 2014-09-28
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2013/2014" (past)

Time span: 2013-10-01 - 2014-02-23
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2012/2013" (past)

Time span: 2013-02-20 - 2013-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2012/2013" (past)

Time span: 2012-10-01 - 2013-02-19
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

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Copyright by Warsaw University of Technology.