Course: Algebra I

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Course title Algebra I
Course code KMA/AL1
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 2
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Tlustý Pavel, prof. RNDr. CSc.
Course content
1. Relations and operations. 2. Basic algebraic structures. 3. Natural numbers 4. Divisibility 5. Primes. Prime factorisation. The greatest common divisor 6. The least common multiply 7. Euclidean algorithm 8. Kongruence 9. Euler's Theorem 10. Wilson Theorem 11. Number systeme 12. Divisibility kriteria 13. Diofant equations. Applications. 14. Revision

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Work with text (with textbook, with book), Projection, E-learning
  • Class attendance - 56 hours per semester
Learning outcomes
Relations and operations, Basic algebraic structures, group, ring, field. Divisibility, congruence and its properties, Diofant equations and its applications. Euclidian algorithm, Eisenstein criterion.
The student acquires the basic concept of the number theory and is capable of solving simple problems.
Prerequisites
none

Assessment methods and criteria
Oral examination, Written examination

Oral examination, Written examination,
Recommended literature
  • Crandell, R., Pomerance, C. Prime numbers: a computational perspective,.
  • Menezes, J. A.:. Handbook of applied cryptography, CRC Press, Boca Raton 1997.
  • Rosen, K. H.:. Elementary Number Theory and Its Applications, Addison-Wesley, 1999.
  • Tlustý. Obecná algebra pro učitele. České Budějovice. ISBN 80-7040-828-6.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter