XALA Linear Algebra

Moravian Business College Olomouc
winter 2023
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martina Pavlačková, Ph.D. (seminar tutor)
doc. RNDr. Martina Pavlačková, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martina Pavlačková, Ph.D.
Moravian Business College Olomouc
Supplier department: Moravian Business College Olomouc
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
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.
Syllabus
  • 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.)
Literature
    required literature
  • STRANG, G. Introduction to Linear Algebra. 5th ed. Wellesley - Cambridge Press, 2016, 584 pp. ISBN 978-0-9802327-7-6. info
  • LAY, D. C., S. R. LAY and J. J. MCDONALD. Linear Algebra and its Applications. 5th ed. Pearson, 2015, 576 pp. ISBN 978-0-321-98238-4. info
    recommended literature
  • HALMOS, P. R. Finite-Dimensional Vector Spaces. 2nd ed. Dover Publications, 2017, 208 pp. ISBN 978-0-486-81486-5. info
  • SINGH, L. Linear Algebra: Step by Step. 1st ed. Oxford University Press, 2013, 528 pp. info
Assessment methods
Course credit: active participation in seminars, credit assignment. Examination: written examination (50% of the final assessment), oral examination (50% of the final assessment).
Language of instruction
English
Further Comments
Study Materials
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms winter 2021.
  • Enrolment Statistics (recent)
  • Permalink: https://is.mvso.cz/course/mvso/winter2023/XALA