Course: Algebra

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Course title Algebra
Course code KAG/ALN
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Emanovský Petr, doc. RNDr. Ph.D.
  • Švrček Jaroslav, RNDr. CSc.
  • Calábek Pavel, RNDr. Ph.D.
  • Botur Michal, doc. Mgr. Ph.D.
Course content
1. Introduction: Elements of mathematical logic, sets, relations, mappings, algebraic structures. 2. Matrices: Operations with matrices, vector space of matrices, ring of square matrices. 3. Determinants: Definition, calculation of determinants. 4. Vector spaces: Subspace, subspace generated by a set, basis, dimension. 5. Systems of equations: Homogeneous and nonhomogeneous systems and their solutions, the Frobenius theorem, Gauss elimination, the Cramer rule. 6. Homomorphisms and isomorphisms of vector spaces: Arithmetical vector spaces and their importance for description of vector spaces, coordinates of vectors according to a given basis, transformation of coordinates as consequense of change of basis, matrix of transformation, matrix of endomorphism. 7. Inner product spaces: Inner product, length of a vector, angle between vectors, orthogonal and orthonormal basis, Gram-Schmidt orthogonalization, isomorphism of inner product spaces. 8.Affine spaces, affine coordinates, affine subspaces, expression of subspaces by means of equations, relative position of affine subspaces. 9.Barycentric coordinates. 10.Oriented affine lines, ordered affine lines, half-lines, abscissas. 11.Oriented affine spaces, half-spaces. 12.Affinity. 13.Euclidean spaces, metric, distance of subspaces. 14.Angle of subspaces. 15. Volume of a simplex. 16. Isometry.

Learning activities and teaching methods
Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
Learning outcomes
Understand the principles linear algebra.
1. Knowledge List of the fundamental knowledge from the algebra for students of the physical courses.
Prerequisites
Understanding of mathematics on secondary school level.

Assessment methods and criteria
Oral exam, Written exam

Credit: the student has to participate in seminars actively and do homework assignments. He/She has to pass a written test successfuly. Exam: the student has to pass a written part successfuly. He/She has to understand the problems and interpret them correctly.
Recommended literature
  • Bartsch, H. J. (1996). Matematické vzorce. Praha: Mladá fronta.
  • Bican L. (1979). Lineární algebra. SNTL Praha.
  • Borůvka O. (1971). Základy teorie matic. Academia Praha.
  • Jukl M. (2006). Lineární algebra. UP Olomouc.
  • Klucký D. (1989). Kapitoly z lineární algebry I. VUP Olomouc.
  • Rektorys K. (1981). Přehled užité matematiky. SNTL Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (1) Physics courses 1 Winter
Faculty of Science Molecular Biophysics (2015) Physics courses 1 Winter
Faculty of Science Optics and Optoelectronics (1) Physics courses 1 Winter
Faculty of Science Applied Physics (1) Physics courses 1 Winter
Faculty of Science Biophysics (2015) Physics courses 1 Winter