MU:MU06108 Theoretical Arithmetics - Course Information
MU06108 Theoretical Arithmetics
Mathematical Institute in OpavaSummer 2011
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Hynek Baran, Ph.D. (lecturer)
RNDr. Petr Blaschke, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Hynek Baran, Ph.D.
Mathematical Institute in Opava - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Secondary School Teacher Training in Mathematics (programme FPF, M7504)
- Upper Secondary School Teacher Training in Mathematics (programme MU, N1101)
- Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)
- Course objectives
- It is one of the basic courses for future teachers. As part of this course the student will extend their knowledge of algebraic structures and linear algebra.
- Syllabus
- 1) Divisibility in integral domains(integral domains, divisibility, units, associated elements, the greatest common divisor, Euclidean rings, Euclidean algorithm)
2) Gaussian rings (irreducible elements and primes, decomposition into irreducible components, divisibility Gaussian ring)
3) Polynomials (divisibility of univariate and multivariate polynomials, symmetric polynomials)
4) Algebraic and transcendental extensions (field, subfield, extensions, algebraic and transcendental elements)
- 1) Divisibility in integral domains(integral domains, divisibility, units, associated elements, the greatest common divisor, Euclidean rings, Euclidean algorithm)
- Literature
- recommended literature
- P. Horák. Algebra a teoretická aritmetika II. Praha, 1988. ISBN 1112-5690. info
- P. Horák. Algebra a teoretická aritmetika. Brno, 1987. info
- J. Blažek, M. Koman, B. Vojtášková. Algebra a teoretická aritmetika, 2. díl. Praha, 1985. info
- J. Blažek, M. Koman, B. Vojtášková. Algebra a teoretická aritmetika, 1. díl. Praha, 1983. info
- S. Lang. Algebraic structures. Addision-Wesley Reading, 1967. info
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Teacher's information
- Active audience participation in solving problems in lectures and seminars.
- Enrolment Statistics (Summer 2011, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2011/MU06108