MU06108 Theoretical Arithmetics

Mathematical Institute in Opava
Summer 2017
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Hynek Baran, Ph.D.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is offered to students of any study field.
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)
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.
The course is also listed under the following terms Summer 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2017, recent)
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