Course title  Algebra 

Course code  UMB/567 
Organizational form of instruction  Lecture + Lesson 
Level of course  Bachelor 
Year of study  not specified 
Frequency of the course  In each academic year, in the winter semester. 
Semester  Winter 
Number of ECTS credits  6 
Language of instruction  Czech 
Status of course  Compulsory 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
We study algebraic structures with one and two binary operations. We give basic definitions and properties and we study important cases of these structures. Summary: Algebraic structures with one operation  grupoids, semigropus, groups. Subgroups, homomorphisms, isomorphisms. Group of permutations. Symmetry groups. Cyclic and dihedral groups. Congruence relation and groups of congruence classes. Divisibility of integers. Euklid agorithm. Bezout equality and consequences. Primes. Linear congruence equations. Euller theorem. Applications in crypthography. Algebraic structures with two operations  rings, domains, fields. Rings/fields of numbers. Rings/fields of congruence classes. Polynomials, roots of polynomials, irreducibility. Complex polynomias, fundamental theorem of algebra. Rational and real polynomials. Eisenstein criterion.

Learning activities and teaching methods 
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam

Learning outcomes 
The goal of the course is the introduction into elementary algebraic structures.
The student will acquire the basic knowledge of abstract algebra and number theory. 
Prerequisites 
The knowledge of mathematics on the level of secondary school and the theory of matrices and their properties.

Assessment methods and criteria 
Combined exam, Seminar work
Active participation in the course, project focusedon mathematic olympiad and applied algebra (including programming), passing both written and oral part of the exam (50%). 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Category of Branch/Specialization  Recommended semester  

Faculty: Faculty of Science  Study plan (Version): Applied Mathematics (2010)  Category: Mathematics courses  2  Recommended year of study:2, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Mathematics for future teachers (1)  Category: Mathematics courses  2  Recommended year of study:2, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Mathematics for future teachers (1)  Category: Mathematics courses  2  Recommended year of study:2, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012)  Category: Pedagogy, teacher training and social care    Recommended year of study:, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Secondary Schools Teacher Training in Mathematics (1)  Category: Pedagogy, teacher training and social care    Recommended year of study:, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Secondary Schools Teacher Training in Mathematics (1)  Category: Pedagogy, teacher training and social care    Recommended year of study:, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Mathematics for future teachers (1)  Category: Mathematics courses  2  Recommended year of study:2, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Secondary Schools Teacher Training in Mathematics (1)  Category: Pedagogy, teacher training and social care    Recommended year of study:, Recommended semester: Winter 
Faculty: Faculty of Science  Study plan (Version): Mathematics for future teachers (1)  Category: Mathematics courses  2  Recommended year of study:2, Recommended semester: Winter 