Teaching
    Past and current courses
    Logica Matematica (curs pentru anul I Matematica, Matematica-Informatica)
    Polinoame si Ecuatii Algebrice (Master Matematica Didactica)
    Algebra pentru Fizicieni (curs pentru anul I Facultatea de Fizica)
    Group Theory and Applications (Master)
    Representation Theory of Groups and Algebras (Master)
    Algebra (Bachelor)
    Computational algebra, Coding Theory and Cryptology (Master)
    Homological Algebra (Master)
    Modular Representation Theory of Finite Groups (Doctoral School)
    Algebraic Groups (Doctoral School)
    Introducere in Logica Matematica si Teoria Multimilor (2012-2022)
    Polinoame si Ecuatii Algebrice (2012-2022)
    Introducere in Algebra pentru Fizicieni (2011-2022)
    Group Theory and Applications (2015-2022)
    Representation Theory of Groups and Algebras (2018-2021)
    Numere complexe, cuaternioni, aplicatii
    (prezentare beamer 2012)
    ALGEBRA JEGYZET (1990-2011)
    Logika és halmazelmét
    (1994-2002)

    Jegyzet:
    Marcus Andrei-Szántó Csaba-Tóth László: Logika és halmazelmét. Scientia Kiadó, Kolozsvár, 2004.
    Computational Algebra, Coding Theory and Cryptology
    (1997-2011)

    1. Primality Testing and Factorization
    2. Fast Fourier Transform
    3. Polynomials over finite fields. The Berlekamp algorithm
    4. Aplications to Cryptology
    5. Introduction to Coding Theory
    6. Gröbner bases. The Buchberger algorithm
    7. Generators and relations in groups. The Todd-Coxeter algorithm
    8. Lattice reduction and the LLL algorithm

    Bibliography
    1. R. Lidl, G. Pilz - Applied Abstract Algebra, Springer-Verlag 1998
    2. N. Koblitz - A Course in Number Theory and Cryptography, Springer-Verlag 1994
    3. D. Bressoud, S. Wagon - A Course in Computational Number Theory, Springer-Verlag 2000
    4. A. M. Cohen, H. Cuypers, H. Sterk - Some Tapas of Computer Algebra, Springer-Verlag 1999
    5. H. Cohen - A Course in Computational Algebraic Number Theory, Springer-Verlag 2000
    6. D. Knuth - The Art of Computer Programming, Addison-Wesley
    7. T. H. Cormen, Ch. Leiserson, R. R. Rivest, C. Stein - Introduction to Algorithms, Second Edition, MIT Press Cambridge MA 2001
    8. The GAP Group, GAP -- Groups, Algorithms, and Programming, Version 4.4; 2005. (http://www.gap-system.org)
    Homological Algebra

    Homological algebra first arose as a language for describing topological properties of geometrical objects. Since then, it has expanded into subject on its own right, and its contemporary applications are many and diverse. A quick look at the Mathematics Subject Classification 2000 reveals application to Number Theory, Algebra and Differential Geometry, Lie Groups and Algebras, Finite Groups, Partial Differential Equations, Functional Analysis and Operator Theory. Therefore, the homological algebra methods must be in the toolbox of every mathematician.
    The aim of this cause is to introduce the basic concepts and techniques in the language of categories and functors, and to present examples coming from various fields.

    I. Simplicial sets
      1. Triangulated spaces
      2. Simplicial sets
      3. Simplicial topological spaces and the Eilenberg-Zilber theorem
      4. Sheaves
    II. Homology and Cohomology
      1. Complexes and morphisms of complexes
      2. Coefficient systems
      3. The long exact sequence
      4. Homotopy
    III. Examples
      1. The Cech complex
      2. The complex of singular chains
      3. Homology and cohomology of groups
      4. The de Rham complex
      5. Homology and cohomology of Lie algebras
      6. Hochschild (co)homology of algebras
      7. Cyclic homology
      8. The Koszul complex
    IV. Categories and functors
      1. Categories
      2. Functors and natural transformations
      3. Equivalences of categories
      4. Adjoint functors
      5. Additive and abelian categories
    V. Derived functors
      1. Injective modules and projective modules
      2. Resolutions
      3. Derived functors
      4. Tor and Ext
      5. Examples: (co)homology of sheaves, of groups, of Lie algebras, and of algebras
    Bibliography
    1. S.I. Gelfand and Yu.I. Manin - Methods of Homological Algebra, Springer-Verlag 1998
    2. Ch. Weibel - An Introduction to Homological Algebra, Cambridge University Press, 1994
    3. H. Cartan and S. Eilenberg - Homological Algebra, Princeton University Press, 1956
    4. P. Hilton and U. Stammbach - A Course in Homological Algebra, Springer-Verlag 1971
    5. S. Maclane - Homology, Springer-Verlag 1963
    6. J. L. Loday - Cyclic Homology, Springer-Verlag 1992
    Modular Representation Theory of Finite Groups

    SYLLABUS 2010-2011

    Algebraic Groups

    SYLLABUS 2010-2011