Algebra (121001-1160):
  • Lecture - Mondays 11:40-13:20 in room G-111,
  • Classes - Mondays 13:30-15:10 in room G-111.


  • S. Dorosiewicz, J. Kłopotowski, D. Kołatkowski, H. Sosnowska - Matematyka, Oficyna Wydawnicza SGH, 2004
  • M. Ekes, J. Kłopotowski - Zbiór zadań z algebry liniowej cz. I, Oficyna Wydawnicza SGH, wyd. II, 2007
  • M. Ekes, J. Kłopotowski - Zbiór zadań z algebry liniowej, cz. II, BEL Studio, Warszawa 2004
  • J. Kłopotowski - Algebra liniowa, Oficyna Wydawnicza SGH, wyd. III 2006
  • I. Kostrykin - Wstęp do algebry. Algebra liniowa. PWN, Warszawa 2004
  • T. Kostrykin, J. I. Manin - Algebra liniowa i geometria, PWN, Warszawa 1993
  • A. Ostoja-Owsiany - Matematyka w ekonomii, część pierwsza, Algebra elementarna, PWN, 2006
  • M. Krych - Analiza matematyczna dla ekonomistów, Wydawnictwa Uniwersytetu Warszawskiego, 2010r.
  • W. Krysicki, L. Włodarski - Analiza matematyczna w zadaniach, część I i II, Państwowe Wydawnictwo Naukowe, Warszawa 1986r.
  • J. Banaś, S. Wędrychowicz - Zbiór zadań z analizy matematycznej, Wydawnictwo Naukowo-Techniczne, Warszawa 2001r.

  • Links:

    Ważniak - mathematical analysis
    Ważniak - linear algebra
    Octave and its extension Octave-Forge with the exemplary manual

    Grading Regulations:

    • The test for 50 points. The test covers the first part of the material. There is no possibility to retake the test.
    • The exam for 50 points. The exam covers the second part of the material. If someone did not write the test, then the exam covers the whole material from the lecture and is graded for 100 points.
    • In the second term the exam covers the whole material from the lecture and is graded for 100 points.
    • The grade (on the basis of the sum of the test and the exam or only the exam) by the conversion table:
      < 502
      from 503
      from 603.5
      from 704
      from 804.5
      from 905
    • Cheating on tests and exams will not be tolerated. If a student get caught cheating, the test/exam will be confiscated and rated to zero points.

    Course overview:

    1. Sets, realtions, groups, fields, complex numbers.
    2. Vector spaces and subspaces.
    3. Basis, dimension, coordinate systems.
    4. Linear mapping and a matrix of a linear mapping in a coordinate system.
    5. Kernel and rank of a mapping. Determinant. Characteristic polynomials.
    6. Invariant subspaces, eigenvalues and eigenvectors.
    7. Bilinear forms, quadratic forms,
    8. Inner product, norm, unitary space.
    9. Linear isometry and orthogonal matrices. Gram-Schmidt procedure.
    10. Orthogonal projection, properties. Geometric interpretation of least squares procedure.
    11. Convex sets, convex functions, Jensen's inequality.
    12. Multi-facet convex sets. Vertices.
    13. Cones and convex cones.
    14. Multi-facet convex cones. Dual cones and Farkas' lemma.
    Contact: [email protected]