Course: Language and Methods of Mathematics

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Course title Language and Methods of Mathematics
Course code KMA/JMM
Organizational form of instruction Tutorial
Level of course Bachelor
Year of study 1
Semester Winter and summer
Number of ECTS credits 2
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Girg Petr, Doc. Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Week 1: Introduction; necessity of formalisation in mathematics; examples and thorough study of misleading and invalid arguments; Week 2: Propositional calculus; Week 3: Predicate logic - an introduction; Week 4: Predicate logic - advanced examples; Week 5: Basic types of proofs and its principles; Sets; Real Numbers Week 6: Basic types of proofs by examples; Week 7: Selected theorems of mathematical analysis and algebra under microscope, revealing their structure; Week 8: Thorough analysis of selected proofs from other mathematical subjects; Week 9: Logical structure of a mathematical theory; Week 10: Exercise: a simple mathematical theory build from the ground up; Week 11: Diskussion on intuition and experiment in mathematics; publishing and scientific ethic; Week 12: Computer simmulations and experiments in mathematics; experimental mathematics; Week 13: Rigorous computer (and/or computer assisted) proofs. see also http://analyza.kma.zcu.cz.

Learning activities and teaching methods
Practicum
  • Contact hours - 26 hours per semester
  • Preparation for formative assessments (2-20) - 10 hours per semester
  • Preparation for comprehensive test (10-40) - 16 hours per semester
prerequisite
professional knowledge
There are no prerequisites for this course. Students should be familiar with a high school mathematics.
learning outcomes
At the end of the course, a succesfull student should be able to 1. Read mathematical text; 2. Deal with logical expressions (propositional calculus and predicate logic); 3. Distinguish between axiom, definition, theorem and conjecture; 4. Use basic methods of proofs.
teaching methods
Practicum
assessment methods
Test
Skills demonstration during practicum
Recommended literature
  • J. Polák. Přehled středoškolské matematiky. Prometheus, Praha, 2000.
  • R. Thiele. Matematické důkazy. SNTL, Praha, 1986.
  • R.M. Smulyan. Jak se jmenuje tahle knížka. Praha, 1986.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Winter
Faculty of Applied Sciences Information Technologies (2017) Informatics courses 3 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Winter
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 1 Winter
Faculty of Applied Sciences Information Technologies (2016) Informatics courses 3 Winter
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 1 Winter
Faculty of Applied Sciences Information Technologies (2015) Informatics courses 3 Winter
Faculty of Applied Sciences Information Technologies (2012) Informatics courses 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 1 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Winter