Course: Elementary Algebra

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Course title Elementary Algebra
Course code KMT/ELA
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 1
Semester Winter and summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Honzík Lukáš, PhDr. Ph.D.
Course content
1. Binary relations: Relation, complementary, inverse, reflexive, symetric and transitive relation. Equivalence and decomposition over a set. Linear ordered relation, partially ordered relation. Well ordered relation, well ordered set and the mathematical induction principle. Mapping relation, equivalency of sets. Countable and uncountable sets. 2. Binary operations, algebraic structures: Binary operations and their basic characteristics. Examination of binary operations. Algebraic structures. Mapping of algebraic struktures. Groups and semigroups. Ring, integral domain and field. 3. Congruences and Diophantine equations: Congruences and their basic properties. Euler's theorem and Fermat's little theorem. Methods for solving linear congruencies. 4. Classical polynomial theory. Polynomial, the zero of polynomial. Division of polynomials. The Horner scheme. Decomposition of polynomials.

Learning activities and teaching methods
One-to-One tutorial, Students' self-study, Textual studies, Lecture, Practicum
  • Preparation for an examination (30-60) - 30 hours per semester
  • Contact hours - 52 hours per semester
  • Preparation for formative assessments (2-20) - 30 hours per semester
prerequisite
professional knowledge
ovládat matematický jazyk a postupy na úrovni předmětu KMT/MMM1
professional skills
ovládat matematický jazyk a postupy na úrovni předmětu KMT/MMM1
learning outcomes
professional knowledge
vysvětlit pojem binární relace a vymezit její vlastnosti
popsat princip důkazu matematickou indukcí
vysvětlit pojem binární operace a vymezit její vlastnosti a významné prvky
vyjmenovat vlastnosti algebraických struktur s jednou a se dvěma binárními operacemi
vymezit pojem kongruence
vymezit pojem diofantické rovnice
popsat princip Hornerova schématu a vysvětlit možnosti jeho použití
vymezit pojem největšího společného dělitele
vymezit pojem nejmenšího společného násobku
professional skills
vyšetřit binární relaci a rozhodnout o jejích vlastnostech
umět použít matematickou indukci pro důkaz jednoduchých tvrzení
vyšetřit binární operaci a určít její základní vlastnosti a význačné prvky
rozlišit různé typy algebraických struktur s jednou a dvěma binárními operacemi
zvolit vhodný postup pro řešení jednoduchých kongruencí
zvolit vhodný postup pro řešení jednoduchých diofantických rovnic
provést v jednoduchých případech rozklad polynomu na jeho faktory
užít Hornerovo schéma
určit největší společný dělitel
určit nejmenší společný násobek
teaching methods
professional knowledge
Lecture
Practicum
Textual studies
Students' self-study
One-to-One tutorial
Group discussion
Individual study
Self-study of literature
Task-based study method
professional skills
Lecture
Seminar
Textual studies
Students' self-study
One-to-One tutorial
Group discussion
Individual study
Self-study of literature
Task-based study method
assessment methods
professional knowledge
Test
Seminar work
Individual presentation at a seminar
Oral exam
professional skills
Test
Seminar work
Skills demonstration during practicum
Individual presentation at a seminar
Oral exam
Recommended literature
  • Drábek, Jaroslav; Hora, Jaroslav. Algebra. Polynomy a rovnice. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-787-4.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Education - (16) Pedagogy, teacher training and social care 1 Winter
Faculty of Education Chemistry in Education (15) Chemistry courses 2 Winter
Faculty of Education Geography in Education (15) Pedagogy, teacher training and social care 2 Winter
Faculty of Education Geography in Education (13) Pedagogy, teacher training and social care 2 Winter
Faculty of Education Biology in Education (17) Biology courses 1 Winter
Faculty of Education Information Technologies in Education (17) Informatics courses 1 Winter
Faculty of Education - (17) Pedagogy, teacher training and social care 1 Winter
Faculty of Education Chemistry in Education (16) Chemistry courses 1 Winter
Faculty of Education Physics in Education (15) Physics courses 2 Winter
Faculty of Education Geography in Education (1) Pedagogy, teacher training and social care 2 Winter
Faculty of Education Physical Education in Education (1) Physical education and sport 2 Winter
Faculty of Education Physics in Education (17) Physics courses 1 Winter
Faculty of Education Information Technologies in Education (14) Informatics courses 2 Winter
Faculty of Education Chemistry in Education (17) Chemistry courses 1 Winter
Faculty of Education Physical Education in Education (17) Physical education and sport 1 Winter
Faculty of Education Chemistry in Education (14) Chemistry courses 2 Winter
Faculty of Education Information Technologies in Education (15) Informatics courses 2 Winter
Faculty of Education Physics in Education (13) Physics courses 2 Winter
Faculty of Education Studies in Mathematics (15) Mathematics courses 2 Winter
Faculty of Education Studies in Mathematics (13) Mathematics courses 2 Winter
Faculty of Education Biology in Education (16) Biology courses 1 Winter
Faculty of Education Biology in Education (15) Biology courses 2 Winter
Faculty of Education Studies in Mathematics (1) Mathematics courses 2 Winter
Faculty of Education Geography in Education (17) Pedagogy, teacher training and social care 1 Winter
Faculty of Education Physics in Education (16) Physics courses 1 Winter
Faculty of Education Geography in Education (16) Pedagogy, teacher training and social care 1 Winter
Faculty of Education Biology in Education (14) Biology courses 2 Winter
Faculty of Education Information Technologies in Education (13) Informatics courses 2 Winter
Faculty of Education Studies in Mathematics (17) Mathematics courses 1 Winter
Faculty of Education Physics in Education (14) Physics courses 2 Winter
Faculty of Education Chemistry in Education (13) Chemistry courses 2 Winter
Faculty of Education Biology in Education (13) Biology courses 2 Winter
Faculty of Education Studies in Mathematics (16) Mathematics courses 1 Winter
Faculty of Education Information Technologies in Education (16) Informatics courses 1 Winter
Faculty of Education Geography in Education (14) Pedagogy, teacher training and social care 2 Winter
Faculty of Education Studies in Mathematics (14) Mathematics courses 2 Winter