"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Algebra 1
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MML0001
1
2+2+0
6
compulsory
Matematică
MML0001
1
2+2+0
6
compulsory
Matematică informatică
MML0001
1
2+2+0
6
compulsory
Matematici aplicate
Teaching Staff in Charge
Prof. MARCUS Andrei, Ph.D.,  marcusmath.ubbcluj.ro
Prof. CALUGAREANU Grigore, Ph.D.,  calumath.ubbcluj.ro
Lect. SACAREA Cristian, Ph.D.,  csacareamath.ubbcluj.ro
Aims
Notions and results concerning linear algebra.
Content
The course presents elements of Linear Algebra: linear maps and matrices; change of bases-automorphisms; eigenvectors and eigenvalues, eigenspaces; diagonalizable and triangulable matrices; Jordan canonical form; hermitian and quadratic forms; unitary, hermitian and anti-hermitian matrices; spectral theorem; Sylvester's law of inertia; linear systems of equations: compatibility, Kronecker-Capelli and Rouche theorems.
References
1. G.PIC, I. PURDEA: Tratat de algebra moderna, vol.1, Editura Academiei, 1977.
2. I.PURDEA, Tratat de algebra moderna, vol.2, Editura Academiei, 1982.
3. I. PURDEA, I. POP, Algebra, Editura GIL, Zalau, 2003.
4. G. CALUGAREANU, Lectii de algebra liniara, Litografiat Univ. Babes-Bolyai, 1995.
5. I.D. ION, N. RADU, Algebra (ed.3-a), Editura Didactica si Pedagogica, 1981.
6. N. BOURBAKI, Algebre, chap.1 -3, Editura Hermann, 1970.
7. I.V. PROSKURIAKOV: Problems in linear algebra, Mir Publishers, Moscow 1978.
8. S. CRIVEI: Basic Abstract Algebra, Casa Cartii de Stiinta, Cluj-Napoca 2002.
9. P. HALMOS: Veges dimenzios vektorterek, Muszaki Konyvkiado, Budapest 1984.
10. A. MARCUS : Algebra [http://math.ubbcluj.ro/~marcus]
12. J. SZENDREI: Algebra es szamelmelet, Tankonyvkiado, Budapest1974.
13. P. GABRIEL: Matrizen, Geometrie, Lineare Algebra, Birkhauser-Verlag, Basel-Boston-Berlin 1996.
Assessment
Exam.