Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MMX1006	Computer aided learning	

Section	Sem.	Hours: C+S+L	Category	Type	
Didactic Mathematics	1	1+1+1	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. ANISIU Valeriu, Ph.D., anisiu@math.ubbcluj.ro	
Aims	Problem solving in several mathematical fields by using symbolic calculus. The Maple system is the main tool (and secondary Derive)

	
Content	The Maple system. Graphical interfaces. Expression representation. Types.
Operators, statements, mathematical functions, evaluation and simplification in Maple.
Maple structures: strings numbers, sequences, tabes, procedures, modules.
Graphics in 2 and 3 dimensions Curves and surfaces given explicitely, parametrically or implicitely.
Polinomials, algebraic extensions, Groebner bases.
Limits, derivatives, integrals, extremums.
Linear algebra: matrices, vectors, decompositions.
Numerical sequences, recurrences, series, infinite products. Convergence and divergence.
Ecuations an systems of equations.
ODEs and PDEs.
Combinatorics and group theory.
Asymptotics and generating functions.
Numerical computations with arbitrary precision.
Solving complex problems.

	
Bibliography	1. V. Anisiu: Calcul simbolic cu Maple. Presa Universitară Clujeană, 2006
2. C. Gomez, B. Salvi, P. Zimmermann: Calcul formel: Mode d@emploi; Exemples en Maple. Masson, Paris 1995
3. E. Scheiber, M. Lupu: Rezolvarea asistată de calculator a problemelor de matematică. Editura Matrix Rom, Bucureşti 2003
4. D. E. Knuth: Arta programării calculatoarelor, vol. 1, Ed. Teora, Bucureşti 1999
5. J. von zur Gathen, J. Gerhard: Modern Computer Algebra. 2nd ed, Cambridge University Press 2003
6. P. Dumas, X. Gourdon: Maple - Son bon usage en mathématiques. Springer 1997
7. R. Varga: Scientific Computation on Mathematical Problems and Conjectures. SIAM, Philadelphia 1990
8. J. Borwein, D. Bailey: Mathematics by Experiment, A. K. Peters Ltd., 2003

	
Assessment	Midterm test and Final Exam.