Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMA1024 | The Role of Counterexamples in Teaching of Mathematical Analysis |
| Teaching Staff in Charge |
Prof. KASSAY Gabor, Ph.D., kassay math.ubbcluj.ro |
| Aims |
|
Systematization and classification of the main concepts of calculus for real functions of one real viariable using different kind of counterexamles. Presentation of wrong solutions in order to avoid them. |
| Content |
|
Course and tutorial 1: Counterexamples relative to sequences.
Course and tutorial 2: Counterexamples relative to series and their convergence criteria. Course and tutorial 3: Counterexamples relative to the limit and continuity of real functions. Course and tutorial 4: Properties of differentiable functions. Course and tutorial 5: Counterexamples relative to the mean-value theorems of differential calculus. Course and tutorial 6: Counterexamples relative to convex functions. Course and tutorial 7: Counterexamples relative to graphical representations of functions. Course and tutorial 8: Functions with Darboux property. Course and tutorial 9: Riemann integrable functions. Course and tutorial 10: Set with zero measure (Jordan or Lebesgue. Lebesgue criterium for Riemann integrability. Course and tutorial 11: Monotone, odd/even, periodics and linear functions. Primitives. Course and tutorial 12: Mean-value theorems of integral calculus. Course and tutorial 13: Improper integrals. Course and tutorial 14: Counterexamples relative to sequences and series of functions. |
| References |
|
1. Balázs M. - Hatházi A. : Matematika, Erdélyi Tankönyvtanács, Kolozsvár, 2006.
2. Balázs M. : Matematika analízis, Erdélyi Tankönyvtanács, Kolozsvár, 2006. 3. Crăciun C.V. : Analiză matematică (Materiale pentru perfecţionarea profesorilor de liceu), Universitatea din Bucureşti, Facultatea de Matematică, Bucureşti, 1992. 4. Crăciun C.V. : Contraexemple în analiza matematică, Universitatea din Bucureşti, Facultatea de Matematică, Bucureşti, 1989. 5. Crăciun C.V. : Teoreme de medie din analiza matematică, Universitatea din Bucureşti, Facultatea de Matematică, Bucureşti, 1986. 6. Gelbaum B.R. – Olmsted J.M.H. : Contraexemple în analiză, Editura Ştiinţifică, Bucureşti, 1973. 7. Sireţchi Gh. : Calculul diferenţial şi integral, vol. I-II, Editura Ştiinţifică şi Enciclopedică, Bucureşti, 1985. 8. Sireţchi Gh. : Calculul diferenţial, Universitatea din Bucureşti, Facultatea de Matematică, Bucureşti, 1983. 9. Sireţchi Gh. : Funcţii cu proprietatea Darboux, Universitatea din Bucureşti, Facultatea de Matematică, Bucureşti, 1986. 10)Rădulescu S. – Rădulescu M. : Teoreme şi probleme de analiză matemaitică, Editura Didactică şi Pedagogică, Bucureşti, 1982. |
| Assessment |
|
written exam 40%, homeworks 30%, presentations 30%. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |