TY  - JOUR
T1  - MATEMATİK EĞİTİMİ PROGRAMLARINA ÇOK BOYUTLU BİR YAKLAŞIM: "LIE CEBİRİ" ÖRNEĞİ
TT  - A MULTI-DIMENSIONAL APPROACH IN MATHEMATICS TEACHER EDUCATION PROGRAMS: "COMPUTATIONS IN FREE AND FINITELY GENERATED LIE ALGEBRAS" EXAMPLE
AU  - Topak, Ebubekir
AU  - Aydın, Ela
AU  - Sönmez, Orhan
AU  - Temizyürek, Ahmet
PY  - 2014
DA  - March
DO  - 10.17152/gefd.98884
JF  - Gazi Eğitim Fakültesi Dergisi
JO  - GUJGEF
PB  - Gazi University
WT  - DergiPark
SN  - 1301-9058
SP  - 91
EP  - 103
VL  - 34
IS  - 1
LA  - tr
KW  - Matematik Eğitimi
KW  - Lie Cebirleri
KW  - Alan Bilgisi.
N2  - Let  be a finitely generated Lie algebra and  be an arbitrary subalgebra of . The maximal linearly independent set of the algebra  modulo the subalgebra  is called the modulo  basis of . In this article we apply computer techniques to compute the modulo  basis of  using an algorithm given by Aydın in her PhD thesis.
CR  - Andary, P. (1997). Finely homogeneous computations in free Lie algebras. Discrete Math. Theor. Comput. Sci, 1(1), 101–114.
CR  - Aydın, E. (1997). Subalgbras of Lie Algebras of Finite Codimension, PhD Thesis, Çukurova University.
CR  - Berry, J. (1997). Improving discrete mathematics and algorithms curricula with LINK. ITICSE’ 97 2nd Conference on Integrating Technology into Computer Science Education, 14-20. ACM: New York.
CR  - Bourbaki N. (1975). Lie groups and lie algebras, Part II., Addison-Wesley.
CR  - Cohen, A. M., & de Graaf, W. A. (1996). Lie algebraic computation. Comput. Phys. Comm. 97(1-2), 53–62.
CR  - Gerdt, V. P., & Kornyak, V. V. (1996). Construction of finitely presented Lie algebras and superalgebras. J. Symbolic Comput, 21(3), 337–349. de Graaf, W. A. (2000). Lie Algebras: Theory and Algorithms, North Holland.
CR  - Goldhaber, D., & Anthony, E. (2003). Indicators of Teacher Quality. Retrieved from ERIC database. (ED478408).
CR  - Hill C., H., Rowon, B., & Ball D., L. (2005). The effects of teachers mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
CR  - Kryazhovskikh, G. V. (1983). Generating and defining relations of subalgebras of Lie algebras. Sibirsk. Mat. Zh. 24(6), 80–86.
CR  - Reutenauer, C. (1983). Free lie algebras, Oxford University Press.
CR  - Shirshov, A. I. (1953). Subalgebras of free Lie algebras. Mat. Sbornik N. S., 33(75), 441–452.
CR  - Shirshov, A. I. (1958). On free lie rings. Mat. Sbornik N. S., 45(87), 113–122.
CR  - Shulman, L., S. (1986). Those who understand knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
UR  - https://doi.org/10.17152/gefd.98884
L1  - https://dergipark.org.tr/en/download/article-file/76893
ER  -