Course: Algebra 1

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Course title Algebra 1
Course code KMI/ALG1
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
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)
  • Kolařík Miroslav, doc. RNDr. Ph.D.
Course content
1. Binary relations. Functions. Equivalences and decompositions. Equivalences and functions. Closure systems. Basic algebraic structures. The rules for counting in the rings. 2. Vector spaces and subspaces. Linear dependence and independence. Steinitz theorem on exchange bases. Arithmetic vector spaces. Euclidean vector spaces. Orthogonalization process. 3. Matrices. Operations with matrices. 4. Permutations. Determinants. The rule of Sarrus. Laplace's theorem. Properties of determinants. 5. Systems of linear equations. Rank of matrix. Gaussian elimination. Frobenius theorem. Cramer's rule. Fundamental system of solutions of linear equations. 6. Ring of square matrices. Inverse matrices. Characteristic polynomial of matrix. Eigenvalue of matrix. 7. Linear transformation (homomorphism) of vector spaces. Monomorphism and epimorphism of vector spaces. Coordinate transformations. 8. Applications of linear algebra in computer science. Other examples of applications in computer science: foundations of group theory; foundations of affine and projective spaces; basics of computer graphics; transformation matrices.

Learning activities and teaching methods
Lecture, Demonstration
Learning outcomes
The students become familiar with basic concepts of algebra.
1. Knowledge Define basic concepts, describe and apply basic methods of linear algebra.
Prerequisites
unspecified

Assessment methods and criteria
Oral exam, Written exam

Active participation in class. Completion of assigned homeworks. Passing the oral (or written) exam.
Recommended literature
  • Bečvář, J. (2010). Lineární algebra. Praha: Matfyzpress.
  • Bican, L. (2009). Lineární algebra a geometrie. Praha: Academia.
  • Halmos P.R. (1995). Linear Algebra Problem Book. Cambridge University Press.
  • Chajda, I. (1999). Úvod do algebry. Olomouc: Univerzita Palackého.
  • Jukl, M. (2010). Lineární algebra: euklidovské vektorové prostory : homomorfizmy vektorových prostorů. Olomouc: Univerzita Palackého v Olomouci.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Bioinformatics (1) Informatics courses 1 Summer
Faculty of Science Computer Science (1) Informatics courses 1 Summer