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FF:PLIN004 Elementary mathematics and sta - Course Information

## PLIN004 Elementary mathematics and statistics for Humanities, Pt. I

**Faculty of Arts**

Autumn 2011

**Extent and Intensity**- 1/1. 4 credit(s). Type of Completion: z (credit).
**Teacher(s)**- RNDr. Vojtěch Kovář, Ph.D. (lecturer)

doc. Mgr. Pavel Rychlý, Ph.D. (lecturer)

RNDr. Miloš Jakubíček, Ph.D. (seminar tutor)

Mgr. Dana Hlaváčková, Ph.D. (assistant) **Guaranteed by**- doc. PhDr. Zdeňka Hladká, Dr.

Department of Czech Language - Faculty of Arts

Contact Person: Jaroslava Vybíralová **Timetable**- Tue 9:10–10:45 G24
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.

The capacity limit for the course is 40 student(s).

Current registration and enrolment status: enrolled:**0**/40, only registered:**0**/40, only registered with preference (fields directly associated with the programme):**0**/40 **Fields of study the course is directly associated with**- Czech Language with Orientation on Computational Linguistics (programme FF, B-FI)

**Course objectives**- The course is aimed at students of humanities (especially Czech Language with Orientation on Computer Linguistics) who for their studies need also essentials of mathematics and statistics. Students will get acquainted with necessary essentials of mathematics and statistics that will be used in their courses from the field of humanities. Attention is paid especially o the theory of sets, linear equations, descriptive statistics, theory of probability, random entities and their distribution of probabilities.
**Syllabus**- Main areas: 1) Mathematical principles (definition-theorem-proof), types of proofs. 2) Propositional logic, mathematical induction. 3) Essentials of set theory: sets, enumeration of elements, basic operation with sets, Cartesian product. 4) Sets of numbers: natural numbers, integral numbers, rational numbers, real numbers, arithmetic operations, sequences and series. 5) Relation an function. 6) Equivalence and orders. 7) Introduction to formal linguistics, language as set of words/sentences, formal grammar, Chomsky hierarchy of grammars and corresponding computational models (finite state automata, push-down automata, Turing machines). 8) Equivalence of DFA-NFA-regular grammar-regular expression, undecidable problems. 9) Combinatorics and selections of elements: independent selections, combinatorial numbers, permutations and factorial. Combinatorial probability: throwing the dice and shuffling cards, finite space of probability. 10) Descriptive statistics: statistic file, average, medians, diffusion, correlation.

**Literature**- Základy matematiky (Rosický): http://www.math.muni.cz/~rosicky/lectures/zm.pdf
- Formální jazyky a automaty (Černá, Křetínský, Kučera): http://is.muni.cz/elportal/estud/fi/js06/ib005/Formalni_jazyky_a_automaty_I.pdf
- ANDĚL, Jiří.
*Statistické metody*. 2. přeprac. vyd. Praha: Matfyzpress, 1998. 274 s. ISBN 80-85863-27-8. info

**Teaching methods**- One-hour lecture and subsequent one-hour tutorial.
**Assessment methods**- Mid-term test (25 %) and final written exam (75 %). Unexcused absence at most 3 times.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- Study Materials

The course is taught annually. **Teacher's information**- http://www.pocitacova-lingvistika.cz

- Enrolment Statistics (Autumn 2011, recent)
- Permalink: https://is.muni.cz/course/phil/autumn2011/PLIN004