470-2204/04 – Algebra (ALG)
Gurantor department | Department of Applied Mathematics | Credits | 6 |
Subject guarantor | RNDr. Pavel Jahoda, Ph.D. | Subject version guarantor | doc. Mgr. Petr Kovář, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | | Semester | winter |
| | Study language | English |
Year of introduction | 2019/2020 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
After passing the course the student will be familiar with the definitions of basic concepts selected theory of algebraic structures and relationships between them. He will understand their significance and will be able to take advantage of their knowledge to solve simple algebraic structures theory tasks. He will also understand the importance of these concepts for the solution of the selected application roles, so that he could formulate a practical role in the language of group theory, solve the problem using theory and tools to interpret the outcome in the context of the original task.
Teaching methods
Lectures
Tutorials
Summary
Selected topics of general algebra constitute content of course Algebra. Possibilities of using this knowledges to solve some practical problems are demonstrated here. Students have the opportunity to obtain basic familiarity with mathematical apparatus, which stands behind the above mentioned applications. So they can understand how these applications work in practice.
Compulsory literature:
J. GALLIAN: Contemporary Abstract Algebra, Cengage Learning; 8 edition (2012), ISBN13 978-1133599708.
Recommended literature:
Way of continuous check of knowledge in the course of semester
Midterm exam and final test.
E-learning
Other requirements
The student attending the course of Algebra is expected to be of decent behavior, to be attentive at the lectures and exercises and we expect his busy preparation for the exam.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures
1) introduction to the group theory: symmetry and dihedral groups
2) group: definition, basic properties
3) finite groups and subgroups, examples
4) cyclic groups, classification
5) group of permutations, definitions, cycles, properties and use
6) normal subgroups and Lagrange's theorem
7) factor groups
8) homomorphisms of groups, definitions, examples
9) isomorfisms: motivation, properties, Cayley's theorem
10) direct product of groups, definitions, examples, applications
11) rings and fields: definitions, finite and infinite examples, applications
12) fields, algebraic extensions, examples, applications
13) vector spaces: definition and examples, subspaces, linear independence
Cvičení:
1) examples of dihedral groups, geometric meaning, examples
2) examples of groups, verification of the axioms of groups
3) subgroups, examples, design and verification
4) cyclic groups, examples, properties, verification
5) group of permutations, cycles, solving the practical examples
6) factorisation the group by its subgroup
7) examples of factor groups, construction and verification
8) homomorfisms of groups, definitions, examples
9) isomorfisms, examples and counterexamples, verification of axioms
10) direct product of groups, examples
11) homomorfisms og groups
12) rings and fields: examples, verification
13) vector spaces: finite and infinite examples, verification of linear independence
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.