Linear Algebra (KMD/E-LAG)

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  • 6 credits
  • Lecturer: Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 1 + 0 + 1 [hours/week]
  • Semester: Winter / Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.): Bc., Mgr.
  • Method of completion: Examination

Synopsis / description / annotation:

The aim of the course is to introduce basic concepts of linear algebra, e.g. binary operations, groupoids, groups, rings, fields, matrices defined in a number field, elementary matrix operations, determinants and their properties, methods of computing them, regular and singular matrices, inverse matrices, vector spaces, linear independent vectors, a vector space basis, the dimension of a vector space, an isomorphism between vector spaces, subspaces, linear systems of equations, the rank of a matrix. Some of the exercises will take part in PC-rooms. Students will learn to solve some problems using mathematical software, e.g. MATLAB, MAPLE, MATHCAD there.

Requirements on student:

An active participation in the full-time form of the education, an active approach to solving tasks, the successful passing of the written test of the final exam.

Content:

Overview of lecture topics:

  • Basic concepts.
  • Matrices and determinants.
  • Vector spaces.
  • Linear systems of equations and their solutions.

Overview of exercise topics:

  1. Mappings between sets, permutations.
  2. Binary operations, groups, rings, fields.
  3. Matrices, adding and subtracting of matrices.
  4. Operations with matrices using specialized software.
  5. Determinants of matrices of the order 2 and 3.
  6. Determinants of matrices of the higher orders.
  7. Inverse matrices.
  8. Expressing of determinants and inverse matrices using specialized software.
  9. Linear systems of equations of Cramerian type.
  10. The rank of a matrix.
  11. Linear systems of equations of a general type.
  12. Homogenous linear systems of equations.
  13. Solving of linear systems of equations using specialized software.

Time requirements:

  • Being present in classes - 26 h.
  • Self-tutoring - 30 h.
  • Consultation of work with the teacher/tutor (incl. electronic) - 5 h.
  • Preparation for an exam - 30 h.

Prerequisites:

The secondary school knowledge of mathematics is assumed.

Course results:

After finishing the course, in which an understanding of topics of the linear algebra is offered, students will have knowledge about the advanced aspects of these parts of mathematics. Student will have abilities to solve problems using a software support for mathematics.

Assessment methods:

  • Written examination
  • Continuous analysis of student’s achievements

Teaching methods:

  • Computer-based tutoring
  • Dialogic (discussion, dialogue, brainstorming)
  • Individual tutoring

Literature:

  • Curtis, Ch., W. Linear Algebra: an introductory approach. Springer New York, 1997. ISBN 0-387-90992-3.
  • Robert, A., M. Linear Algebra: examples and applications. World Scientific, Hackensack, 2005. ISBN 981-256-499-3.

Updated: 03. 10. 2022