Universitatea "Babeş-Bolyai" din Cluj-Napoca

Facultatea de Matematică şi Informatică
FISA DISCIPLINEI

Algebră computaţională

Computational algebra

Cod	Semes- trul	Ore: C+S+L	Credite	Tipul	Sectia
MA026	4	2+1+0	5	optionala	Informatică (Computer Science)

Cadre didactice indrumatoare

Teaching Staff in Charge

Lect. Dr. CRIVEI Septimiu, crivei@math.ubbcluj.ro

Obiective	Aims
O introducere in teoria moderna a modulelor, prin studiul unor clase speciale de module.	An introduction to modern Module Theory, by studying certain special classes of modules.

Continut

1. Notiuni de complexitatea algoritmilor. Notatia O, clase de complexitate. 2. Congruente si clase de resturi. Algoritmul lui Euclid, functia lui Euler, teorema chineza a restului, resturi patratice, simbolul lui Legendre. 3. Teste de primalitate. Testele de primalitate Fermat, Solovay-Strassen si Miller-Rabin, teste deterministice. 4. Metode de factorizare. Metode elementare, metoda Rho, metoda bazei de factori, metoda fractiilor continue, metoda sitei patratice. Aplicatii in criptografie. 5. Polinoame peste corpuri finite. Corpuri finite, logaritm discret, polinoame ireductibile, algoritmul lui Berlekamp de factorizare a polinoamelor. Aplicatii in criptografie 6. Alti algoritmi. Adunare rapida, transformarea Fourier rapida.

Bibliografie

1. W. Bosma, A. van der Porten, Computational Algebra and Number Theory, Kluwer 1995. 2. D. Bressoud, S. Wagon, A Course in Computational Number Theory, Springer-Verlag 2000. 3. H. Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag, 2000. 3. H. Cohen, A.M. Cuypers, H. Sterk, Some Tapas of Computer Algebra, Springer-Verlag, 1999. 4. R. Crandall, C. Pomerance, Prime Numbers. A Computational Perspective, Springer-Verlag, 2001. 5. K. Ireland, M. Rosen, A Classical Introduction to Number Theory, Springer-Verlag, 1990. 6. N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 1994. 7. R. Lidl, G. Pilz, Applied Abstract Algebra, Springer-Verlag, 1998. 8. A.J. Menezes, P.C. van Oorschot, S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997. 9. B. Schneier, Applied Cryptography, John Wiley & Sons, New York, 1996. 10. H.S. Wilf, Algorithmes et complexite, Masson, Paris, 1989.

Evaluare	Assessment
Examen.	Exam.