Course: History and Philosophy of Mathematics

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Course title History and Philosophy of Mathematics
Course code KFI/SHFM
Organizational form of instruction Lecture
Level of course Master
Year of study 2
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Dostálová Ludmila, Mgr. Ph.D.
  • Demjančuk Nikolaj, Doc. PhDr. CSc.
Course content
1. Introduction to philosophy and history of mathematics; particularization of European and non-European knowledge; phenomena and mathematical objects; evidence and calculus 2. Euclid's Elements; Axioms, postulates, basic notions in Elements. 3. Parallelism; infinity, horizon and geometry. The Pythagorean Theorem 4. Rationality and irrationality; the Golden Section. Space, perspective and modern geometry. 5. Solids, body; bodiness; volume; the Platonic solids; 6. Non-Euclidean geometries; topology; evidence in mathematics (and sciences). 7. Hindu and Arabic mathematics; cultural and religious presuppositions. 8. Algorithm; Arabic medieval arithmetics and algebra. 9. European medieval arithmetics and algebra. 10. Renaissance European mathematics; perspective; logarithm; the Cartesian turn. 11. Calculus infinitesimalis. 12. Abel classical and modern algebra; boundaries of mathematics. 13. Existence; modality; temporality; mathematics and logic. Reading texts are different for each academic year.

Learning activities and teaching methods
Interactive lecture, Textual studies
  • Contact hours - 26 hours per semester
  • Preparation for an examination (30-60) - 30 hours per semester
  • Graduate study programme term essay (40-50) - 22 hours per semester
prerequisite
Knowledge
to list the most important representatives of the field
to describe the most significant discoveries in the field and their role in European cultural development
Skills
to identify the problem (thesis) and reproduce the argumentation contained in the text
to use modern technologies, especially information databases
Competences
N/A
N/A
learning outcomes
Knowledge
to list key characters and topics from the history and philosophy of mathematics
to explain concrete terms and apparatuses related to the history and philosophy of mathematics
to describe problems that were solved in the field of history and philosophy of mathematics
Skills
to use the terminology of history and philosophy of mathematics with understanding
to reproduce the argumentation contained in the given text from the field of history and philosophy of mathematics
to interpret and discuss selected period mathematic texts
Competences
N/A
N/A
teaching methods
Knowledge
Interactive lecture
Textual studies
Skills
Interactive lecture
Textual studies
Competences
Interactive lecture
Textual studies
assessment methods
Knowledge
Seminar work
Continuous assessment
Kolokvium
Skills
Continuous assessment
Kolokvium
Competences
Continuous assessment
Kolokvium
Seminar work
Recommended literature
  • Základy. Knihy XI-XII. 1. vyd. Nymburk : OPS, 2011. ISBN 978-80-87269-24-4.
  • Abel, Niels Henrik. O algebraických rovnicích. 1. vyd. Kanina : OPS, 2011. ISBN 978-80-87269-23-7.
  • Boyer, Carl B. A history of mathematics. 3rd ed. Hoboken : John Wiley & Sons, 2010. ISBN 978-0-470-52548-7.
  • Calinger, Ronald S. A contextual history of mathematics : to Euler. Upper Saddle River : Prentice Hall, 1999. ISBN 0-02-318285-7.
  • Eukleidés. Základy. Kniha X. 1. vyd. Kanina : OPS, 2012. ISBN 978-80-87269-26-8.
  • Eukleidés. Základy. Knihy I-IV. 3., opr. vyd. Plzeň : Západočeská univerzita, 2010. ISBN 978-80-7043-974-6.
  • Eukleidés. Základy. Knihy VII-IX. 1. vyd. Nymburk : OPS, 2010. ISBN 978-80-87269-11-4.
  • Eukleidés. Základy. Knihy V-VI. 1. vyd. Nymburk : OPS, 2009. ISBN 978-80-87269-05-3.
  • Fauvel, John,; Gray, Jeremy. The history of mathematics : A reader. Hampshire : Palgrave Macmillan, 1987. ISBN 0-333-42791-2.
  • Hanke, M., Kastnerová, M., Švantner, M., Větrovcová, M. Stopování sémiotiky. Červený Kostelec: Pavel Mervart. ISBN 978-80-7465-142-7.
  • Husserl, Edmund. Krize evropských věd a transcendentální fenomenologie : úvod do fenomenologické filozofie. 2. vyd., reprint 1. vyd., Academia 1972. Praha : Academia, 1996. ISBN 80-200-0561-7.
  • Kůrka, P.; Matoušek, A. a Velický, B. Spor o matematizaci světa. 2011. ISBN 978-80-7465-012-3.
  • Patočka, Jan. Sebrané spisy 1-14. Praha : OIKOYMENH.
  • Vopěnka, P., Větrovcová, M., Ostřanský, B. Al-Chvárizmí. Aritmetický a algebraický traktát. Nymburk: OPS, 2009.
  • Vopěnka, P., Větrovcová, M. Uvedení do obecné topologie a jejích dějin do roku 1960. Praha: Vyšehrad, 2015.
  • Vopěnka, Petr; Novotná, Anna. Vyprávění o kráse novobarokní matematiky : souborné vydání Rozprav o teorii množin. Praha : Práh, 2004. ISBN 80-7252-103-9.
  • Vopěnka, Petr. Úhelný kámen evropské vzdělanosti a moci : souborné vydání Rozprav s geometrií. 4. vyd. Praha : Práh, 2011. ISBN 978-80-7252-338-2.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Arts Study plan (Version): European Cultural Studies (17-4) Category: Philosophy, theology 2 Recommended year of study:2, Recommended semester: Summer
Faculty: Faculty of Arts Study plan (Version): European Cultural Studies (17-4) Category: Philosophy, theology 2 Recommended year of study:2, Recommended semester: Summer