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Lecturer(s)
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Andres Jan, prof. RNDr. dr hab. DSc.
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Benešová Martina, Mgr. Ph.D.
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Matlach Vladimír, Mgr. Ph.D.
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Course content
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(1) Basic mathematical framework (terminology, number domains, set theory) (2) Fundamental terminology of mathematical logic and set theory (basics of logic, propositions, hypotheses) (3) Introduction to function theory - basic qualities of functions (definitions, domain of definition, range of values, one-to-one function, monotonic function) (4) Linear, quadratic function (description, qualities, solution of related equations) (5) Rational, power function (description, qualities, solution of related equations) (6) Exponential, logarithmic function (description, qualities, solution of related equations) (7) Inverse function (definition, qualities, application) (8) Graphs of functions, practical usage in statistics and linguistics (9) Basics of combinatorics (variations, permutations, combinations - examples of application in linguistics) (10) Basics of probability theory - definitions (event, trial, result; examples of application in linguistics) (11) Basics of statistics for evaluating experiment validity - basic terminology, graphs (histograms) (12) Basics of statistics (population and sample, applications in linguistics) (13) Basics of statistics (characteristics of a sample)
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Methods of Written Work
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Learning outcomes
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The course aims to introduce students to rudiments of mathematics and its instruments which are crucial for quantitative linguistic sample processing and subsequent validation of experiments performed in this way. The course is aimed at students of philological studies and other humanities. The course is the platform of theoretical preparation for attending the practical course Mathematical Modelling of Text, wherein the knowledge and skills gained in this course should be applied in a more practical manner.
The course is introduced by revision of basic tools of mathematics, e.g. mathematical terminology, number domains, their qualities and graphs (linear, quadratic, exponential, logarithmic). From basic qualities of functions, qualities of inverse functions are derived. This is demonstrated using valid linguistic laws (e.g. Zipf and Menzerath-Altmann) and examples of applying mathematics in linguistics. The second half of the course covers basics of combinatorics and probability theory so that the fundamentals of statistics crucial for assessing validity of linguistic experiments can follow. The course is complemented by short practical applications of the knowledge acquired.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam, Written exam, Student performance, Systematic Observation of Student
(1) Regular attendance (no more than 2 unexcused absences) (2) Creation of encyclopaedic entry (3) Final test
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Recommended literature
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Jirásek, F. a kol. Sbírka řešených příkladů z matematiky I, II. Praha 1989.
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Polák, J. (1998). Přehled středoškolské matematiky. Prometheus, Praha.
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Rektorys, K. (2000). Přehled užité matematiky II. Praha.
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Rektorys, K. (2000). Přehled užité matematiky I. Praha.
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Šalát, T a kol. Malá encyklopédia matematiky. Bratislava 1967.
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Škrášek, J.,-Tichý, Z. Základy aplikované matematiky I, II. Praha 1983.
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