CORE004 Mathematics as a part of culture

Faculty of Science
Autumn 2023
Extent and Intensity
2/0/0. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 A,01026
Prerequisites
Interest in deductive thinking
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Tho course consisting of twelve more or less independent lectures will show the way in which some problems - scientific, philosophical, political, of art ones - have inspired the formation and development of mathematical methods. And, vice versa, how the inner progress has influenced patterns of the western way of thinking. Mathematics is presented as a specific kind of language and a practice of relating to the world.
Learning outcomes
After completing the course, a student will: • obtain an insight into mathematics as a specific language making a formalization of "common sense" possible, • have a rough image of European mathematics history, • be oriented in terms such as mathematical proof and mathematical model, • be aware of a part of mathematics that may be useful for her/his field of study or interest.
Syllabus
  • 1. A quest for certainty: geometry and deductive thinking 2. A power of symbols: algebra and equations solution 3. A yearning for infinity: sets 4. A unification: analytic geometry 5. A motion and a change: infinitesimal calculus 6. An uncertainty: probability and game theory 7. An induction and experience: statistical inference 8. Out of experience: non-euclidean and differential geometry 9. A challenge of quantum mechanics: functional analysis 10. A challenge of ecology and sociology: mathematical modeling and dynamical systems 11. A challenge of economy: mathematical programing and optimization 12. The loss of certainty: mathematical logic and incompleteness
Literature
    recommended literature
  • L. Kvasz: Patterns of change, Linguistic innovations in the Development of Classical Mathematics, Birkhäuser Verlag AG, Basel 2008
  • K. Devlin: Jazyk matematiky, Argo 2011
  • HARDY, G. H. Obrana matematikova. Praha: Prostor, 1999, 138 s. ISBN 8072600249. info
  • Jakákoliv “matematika pro nematematiky” (např. od autorů z MU: Z. Došlá, P. Liška: Matematika pro nematematické obory, Grada 2014.
    L. Bauer, H. Lipovská, M. Mikulík, V. Mikulík: Matematika v ekonomii a ekonomice, Grada 2015)
Teaching methods
The lecture supplemented by class discussion of the two lectors and/or invited specialists and students. The references to study resources will be provided with advance for enabling students to participate in discussions in an active way. The students will elaborate projects in the form of essay or reviews (each student at least one project).
Assessment methods
Mutual evaluation of elaborated essays/presentations/projects supervised by a teacher. In particular, a measure of activity in discussions and the ability to understand some themes will be assessed.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is also listed under the following terms autumn 2021, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/CORE004