University of West Bohemia in Pilsen
Study programmes & Course catalogue
for academic year 2025/2026
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Course: Introduction to the Study of Mathematics

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Course title Introduction to the Study of Mathematics
Course code KMT/USM
Organizational form of instruction Lecture + Seminar
Level of course Master
Year of study 1
Semester Winter and summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Posová Veronika, Mgr. et Mgr. Ph.D.
  • Bílá Margita, PhDr. Ph.D.
Course content
1. Propositional calculus 2. Mathematization of real situation, propositional analysis of word text 3. Predicate calculus 4. Introduction to set theory, set operations 5. Venn diagrams, word problems 6. Quantified propositions 7. Proofs of mathematical theorems 8. Proofs of mathematical theorems 9. Carthesian product and binary relations on a set 10. Properties of binary relations 11. Order relations 12. Inverse and complement relations, composition of relations 13. Transformation

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, E-learning, Collaborative instruction, Cooperative instruction, Seminar classes
  • Contact hours - 39 hours per semester
  • Preparation for formative assessments (2-20) - 8 hours per semester
  • Preparation for an examination (30-60) - 40 hours per semester
  • unspecified - 15 hours per semester
prerequisite
Knowledge
achieve a high school level of mathematical knowledge
Skills
modify an algebraic expression
solve linear equations (including absolute value equations and equations with a parameter)
solve systems of linear equations
Competences
N/A
learning outcomes
Knowledge
explain the concept of propositional form
clarify the difference between a propositional form and a proposition
distinguish between a general and an existential proposition
define the basic properties of binary operations in a set
specify different types of representations in a set and between sets
Skills
determine the type of propositional formula
solve word problems using knowledge of sets, set operations and Venn diagrams
prove mathematical theorems using different types of proofs
identify properties of specific types of relations
Competences
N/A
teaching methods
Knowledge
Lecture supplemented with a discussion
Interactive lecture
Collaborative instruction
Practicum
Skills
Practicum
Skills demonstration
Collaborative instruction
Competences
Task-based study method
assessment methods
Knowledge
Combined exam
Test
Continuous assessment
Skills
Combined exam
Test
Skills demonstration during practicum
Competences
Combined exam
Skills demonstration during practicum
Recommended literature
  • Učebnice, pracovní sešity a metodické příručky matematiky pro 1. st. ZŠ.
  • Coufalová, Jana. Matematika s didaktikou pro 1. ročník učitelství 1. stupně ZŠ. 5. vydání. 2016. ISBN 978-80-261-0649-4.
  • Jirotková, Darina; Kaslová, Michaela. Sbírka úloh z elementární matematiky pro studující učitelství 1. stupně ZŠ : Určeno pro posl. fak. pedagog. Díl 1.. 1. vyd. Praha : SPN, 1985.
  • Panáčová, Jitka; Beránek, Jaroslav. Základy elementární matematiky s didaktikou pro učitelství 1. stupně ZŠ. 1. vydání. 2020. ISBN 978-80-210-9863-3.
  • Pisklák, Bohuslav. Matematika pro učitele primárního vzdělávání : binární relace a zobrazení :distanční text. Vyd. 1. Ostrava : Universitas Ostraviensis, 2004. ISBN 80-7368-013-0.
  • Wells.D. G. Prime numbers: the most mysterious figures in math. Hoboken, 2005. ISBN 0-471-46234-9.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (15) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (16) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (16) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (13) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (14) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (15) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Teacher Training for BSPL Teachers (12) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
University of West Bohemia in Pilsen, date of update: 24.04.2025 23:52. Data created for academic year 2025/2026