-The aim of this study is to investigate of solution approaches of elementary mathematics prospective teachers in order to solve analytical problems on the lines and the circles which are presented visual and algebraic forms. 63 third-grade prospective teachers who were studying in the Department of Elementary Mathematics Teaching, Education Faculty participated in the study. Solution approaches of the prospective teachers were determined by analyzing the solutions of four problems which included visual and algebraic analytic problems on lines and circles. When the answers of prospective teachers were examined, it was found that most of the participants adopted geometric approaches in order to solve the analytic problems on both lines and circles and the problems in visual and algebraic forms. So, as geometric approach is not enough for solution of every problem, the study recommends that students should learn different solution approaches and raise awareness of necessity of various approaches.
The existence of saddle point of the Lagrange function for a convex programming problem in Banach spaces ordered by a cone with empty interior is established under a strong simultaneity condition. As a consequence, the Kuhn-Tucker conditions are derived. It is shown that the Slater and the strong simultaneity condition are equivalent if the cone determining the partial order has an interior.
C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 6 2 , N u m b e r 2 , P a g e s 1 1 -1 5 (2 0 1 3 ) IS S N 1 3 0 3 -5 9 9 1
CALCULATION METHOD FOR QUADRATIC PROGRAMMING PROBLEM IN HILBERT SPACES, PARTIALLY ORDERED BY CONE WITH EMPTY INTERIOR
FEYZULLAH AHMETO ¼ GLUAbstract. In the article, a numerical method for convex programming problem (with linear inequality) in Hilbert spaces is given. Firstly, by Khun-Tucker conditions problem is reduced to minimize a convex funtional under nonnegative variables. Then, last problem is solved by coordinate descent method.
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