Course: Fundamentals of Algebra

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Course title Fundamentals of Algebra
Course code KMA/ZA
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 2
Semester Winter and summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Tesková Libuše, RNDr. CSc.
  • Teska Jakub, RNDr. Mgr. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Week 1-4: Groupoids, monoids, semigroups. Week 5-7: Groups, Abelian Groups, subgroups, Lagrange´s Theorem, normal subgroups, quotient groups. Week 8-9: Homomorphisms of groups, theorem about isomorphism of groups, cyclic groups and their structure. Week 10-11: Rings and fields, subrings, ideals, quotient rings, zero divisors, basic properties of fields. Week 12-13: Associative, commutative rings with an identity.

Learning activities and teaching methods
Lecture supplemented with a discussion, Lecture with practical applications, Discussion
  • Undergraduate study programme term essay (20-40) - 30 hours per semester
  • Contact hours - 39 hours per semester
  • Preparation for an examination (30-60) - 45 hours per semester
prerequisite
professional knowledge
No particular prerequisites specified.
learning outcomes
The student will be able to: actively understand concept of equivalence and of decomposition of a set into equivalence classes, solve simple problems in modular arithmetics, apply Theory of semigroups terms,apply Theory of groups terms, apply basic properties of groups to particular models, recognise the structure of a ring and a field.
teaching methods
Lecture supplemented with a discussion
Lecture with practical applications
Discussion
assessment methods
Combined exam
Seminar work
Recommended literature
  • Beran, Ladislav. Grupy a svazy. Vyd. 1. Praha : SNTL, 1974.
  • Procházka a kol. Algebra. Academia Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 2 Winter
Faculty of Education Studies in Mathematics (15) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 1 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Summer