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  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


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, GramSchmidt 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, halflines, abscissas. 11.Oriented affine spaces, halfspaces. 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 

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 