Subject: Computational Algebra	Code: MA026	

Semester	 Hours: C+S+L	Type	 Section	
6	2+1+0	optional	Applied Mathematics	

Teaching Staff in Charge	Assoc.Prof. CRIVEI Septimiu, Ph.D., crivei@math.ubbcluj.ro
Lect. SACAREA Cristian, Ph.D., csacarea@math.ubbcluj.ro
Lect. SZANTO Csaba Lehel, Ph.D., szanto@math.ubbcluj.ro	
Aims	An introduction to Computational Algebra by a survey of applications of algebraic algorithms in Cryptography, Coding Theory and Conceptual Knowledge Processing and Representation	
Content	1. Notions of algorithms complexity. The O notation, classes of complexity.
2. Congruences and residue classes. Euclid's algorithm, Euler's function, Chinese remainder theorem, public key cryptography: RSA, ElGamal. Electronic  signature. Cryptanalysis.
3. Primality tests. Fermat, Solovay-Strassen,  quadratic residues, Legendre's symbol.
4. Coding and  decoding systems. Linear codes, cyclic codes, Reed-Mulles codes. Factorizing  algorithms and applications in the construction of decoding   systems.
5. Conceptual Knowledge Processing, Conceptual Knowledge Representation, Conceptualll browsing of data bases, applications in    management and  economics. Algorithms for graphical representation of knowledge.	
Selective References	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 2001.
4. N. KOBLITZ : A Course in Number Theory and Cryptography, Springer-Verlag, Berlin 1994.
5. R.LIDL, G. PILZ : Applied Abstract Algebra, Springer-Verlag, Berlin1998. 
6. A. M. COHEN, H. CUYPERS, H. STERK: Some Tapas of Computer Algebra, Springer-Verlag 1999
7. THE GAP GROUP:  GAP - Groups, Algorithms, and Programming. Version 4.4.3. [http://www.gap-system.org]
8. T.H. CORMEN, C.E.  LEISERSON, R.L. RIVEST: Introduction to Algorithms.  MIT 1990.
9. D.E. KNUTH: The Art of Computer Programming,  Addison Wesley Longman 1998.	
Assessment	Continuous evaluation by homeworks. Project. Final exam