XALA Linear Algebra

Moravská vysoká škola Olomouc
zima 2024

Předmět se v období zima 2024 nevypisuje.

Rozsah
2/2/0. 5 kr. Ukončení: zk.
Vyučující
doc. RNDr. Martina Pavlačková, Ph.D. (cvičící)
doc. RNDr. Martina Pavlačková, Ph.D. (přednášející)
Garance
doc. RNDr. Martina Pavlačková, Ph.D.
Moravská vysoká škola Olomouc
Dodavatelské pracoviště: Moravská vysoká škola Olomouc
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Cíle předmětu
The aim of the course is to familiarise students with the basics of abstract algebra, linear algebra, numerical sequences and numerical series. After completing the course, the student is able to define the basic concepts of mathematical logic and set operations, understand the logical construction in mathematics, and is able to evaluate the truth values of compound statements. They have knowledge of algebraic structures and relations. They are also able to define and understand basic concepts of linear algebra, explain matrix and determinant operations and use basic methods to solve systems of equations. They are able to define a numerical sequence, determine its terms and draw its graph. They understand the concept of limit of a sequence and are able to explain and visualise it, manage its calculation while developing their numerical skills. They are also able to describe the numerical series construction and, based on the convergence criteria, they are able to decide on the convergence or divergence of the numerical series.
Osnova
  • 1. Logic and mathematics statements. (Mathematics statements and their truth value.)
  • 2. Sets. (Definition. Operations on sets. Numerical sets and their cardinality.)
  • 3. Vector calculus. (Vector operations. Linear dependence and independence of vectors. Dimension of vector space.)
  • 4. Matrix. (Matrix types. Matrix operations. Matrix rank.)
  • 5. Determinants. (Properties of determinants. Determinant value calculation. Determination of inverse matrix.)
  • 6. Systems of linear equations. (Geometric solution of systems of two equations and two unknowns. Frobenius theorem.)
  • 7. Solving systems of linear equations. (Gaussian elimination. Cramer’s rule.)
  • 8. Numerical sequences. (Definition of a sequence. Input methods and graphical representation of a sequence. Properties of a sequence. Geometric and arithmetic sequences.)
  • 9. Limit of a sequence. (Definition of limit of a sequence, convergence theorems.)
  • 10. Numerical series. (Convergence of numerical series. Geometric series.)
  • 11. Convergence criteria for series with non-negative terms.
  • 12. Series with arbitrary terms. (Alternating series. Leibniz criterion. Absolute convergence of series with arbitrary terms.)
Literatura
    povinná literatura
  • STRANG, G. Introduction to Linear Algebra. 5th ed. Wellesley - Cambridge Press, 2016, 584 s. ISBN 978-0-9802327-7-6. info
  • LAY, D. C., S. R. LAY a J. J. MCDONALD. Linear Algebra and its Applications. 5th ed. Pearson, 2015, 576 s. ISBN 978-0-321-98238-4. info
    doporučená literatura
  • HALMOS, P. R. Finite-Dimensional Vector Spaces. 2nd ed. Dover Publications, 2017, 208 s. ISBN 978-0-486-81486-5. info
  • SINGH, L. Linear Algebra: Step by Step. 1st ed. Oxford University Press, 2013, 528 s. info
Metody hodnocení
Course credit: active participation in seminars, credit assignment. Examination: written examination (50% of the final assessment), oral examination (50% of the final assessment).
Vyučovací jazyk
Angličtina
Další komentáře
Předmět je vyučován každoročně.
Výuka probíhá každý týden.
Předmět je zařazen také v obdobích zima 2021, zima 2023.