MAs07 Selected Topics in Mathematics 3

Faculty of Education
Autumn 2018
Extent and Intensity
0/0/3. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
doc. RNDr. Eduard Fuchs, CSc. (lecturer)
Guaranteed by
Mgr. Helena Durnová, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is the enhancement of students' knowledge of logical foundations of mathematics, history of mathematics, and statistics.
Syllabus
  • 1. Logical architecture of mathematics: differences between intuitive and axiomatic structure of mathematics. Propositional calculus, basics of predicate calculus. Basics of axiomatic architecture of mathematics. Relationship between an axiomatic theory and a model of a theory. Gödel's incompleteness theorem. 2. Set theory. Actual and potential infinity, origins of set theory. Construction of natural numbers in set theory. Basics of the theory of cardinal and ordinal numbers. Transfinite induction. Axiom of choice and its role. 3. History of mathematics: reading selected original mathematical writings (Ancient Egypt, Alcuin, Euclid's Elements) 4. History of mathematics in high school mathematics teaching: role of history in mathematics teaching. Possibilities to use historical sources for teaching mathematics. 5. Hypothesis testing. Parametric and non-parametric tests. Errors of first and second kind. 6. Basics of regression analysis (method of least squares and linear regression)
Literature
  • FUCHS, Eduard. Teorie množin pro učitele. 1st ed. Brno: Masarykova univerzita, 1999. info
  • STRUIK, Dirk J. Dějiny matematiky. 1. vyd. Praha: Orbis, 1963, 250 s. URL info
Teaching methods
Theoretical lectures. Homework.
Assessment methods
Written assignment.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: in blocks.
Information on the extent and intensity of the course: 36 hodin.
The course is also listed under the following terms Autumn 2017, Autumn 2019, autumn 2020, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2018/MAs07