Papers by Georgiana Velicu
In our contemporary times-the era of the fast developments of all area, the claim that we cannot ... more In our contemporary times-the era of the fast developments of all area, the claim that we cannot live without mathematics is justified. The culture of Math is the basic element of the culture of modern people. Thus, learning Math is not reduced to the mere assimilation of knowledge, it aims to the formation of a certain way of thinking through permanent mind training. The " taste " for Mathematics is formed in the first years of school, the lessons and complementary activities are essential for the acquisition of a mathematical thinking. The teacher, in the primary grades, has the task to put the foundations of elementary mathematical notions and has the role to make pupils to get the core mathematical concepts and, also, to insist that their thinking to be stimulated in a wonderful way. The teacher must arouse the interest and love for the study of this beautiful matter. So, what makes Math lessons more attractive? What are the factors that can increase the quality of learning mathematics? To these questions we will try to answer in this paper. We talk about some factors that influence the quality of the lessons containing Math activities, like planning of Math lessons using modern strategies of learning. So we discuss about the use of active-participative methods and also we talk about interdisciplinary approaches, illustrating the strengths and weaknesses of those strategies. Finally, we present the importance of introducing specific methods and techniques of compounding and solving problems.
In this paper we construct a new morphism of matrix coalgebras, than we prove that it is an epimo... more In this paper we construct a new morphism of matrix coalgebras, than we prove that it is an epimorphism and also that its kernel is a coideal in the matrix coalgebra. Finally we give a generalization on this type of morphism between two matrix coalgebras.
Scopul acestei lucrări este acela de a studia diverse proprietăţi, în special condiţii de finitud... more Scopul acestei lucrări este acela de a studia diverse proprietăţi, în special condiţii de finitudine, ale unor clase de coalgebre, mai exact coalgebrele de incidenţă. Coalgebrele de incidenţă au fost definite de Sweedler [29] în 1969 şi au fost explicate de Joni şi Rota [17] în 1979, mai ales, cum aceste coalgebre oferă posibilitatea de a interpreta probleme combinatoriale în termeni de coalgebre. Coalgebrele şi comodulele se obţin prin dualizarea algebrelor şi a modulelor. Teoria coalgebrelor peste corpuri şi a comodulelor este bine ilustrată în lucrări de specialitate cum ar fi: M.E.Sweedler [29], E.Abe [1], S.Montgomery [18], S.Dăscălescu, C.Năstăsescu şi Ş.Raianu [23]. Intuitiv o coalgebră peste un corp poate fi înţeleasă ca o noţiune duală celei de algebră peste un corp.
In this paper I present some causes of backwardness in mathematics. These causes are: somatosenso... more In this paper I present some causes of backwardness in mathematics. These causes are: somatosensory data causes, personality problems, school immaturity and anxiety. Also, I presented how family climate influence learning, and this was from the point of view of mobilization processes. Finnaly I have given some ideas in order to prevent backwardness in mathematics: frontal activity, individual activity and group and team activity. Also, I discussed about how homeworks influence learning of mathematics.
This article is a collection of a few interesting applications on finite groups and morphisms of ... more This article is a collection of a few interesting applications on finite groups and morphisms of groups, applications which already have been given to undergraduate’s international and national contests, some of them using only basic ideas of modern and abstract algebra.
Let C = IC(X) be the incidence coalgebra of an intervally finite partially ordered set X over a f... more Let C = IC(X) be the incidence coalgebra of an intervally finite partially ordered set X over a field. We investigate finiteness properties of C.
In this paper we construct the coradical filtration for incidence coalgebra and path coalgebra. W... more In this paper we construct the coradical filtration for incidence coalgebra and path coalgebra. We introduce the length filtration for incidence coalgebra and we prove that these two filtrations coincide.
Let P be a partially ordered set (poset) locally finite and kQ the path coalgebra over a field k ... more Let P be a partially ordered set (poset) locally finite and kQ the path coalgebra over a field k associated to P. In this paper we investigate finiteness properties of this coalgebra by using an injective morphism of coalgebras from incidence coalgebra kS of P to the path coalgebra kQ. We deduce that kQ is left semiperfect only if kS have the same property, and that kQ is cosemisimple when the order relation on P is the equality. Finally we characterize the coradical filtration of the path coalgebra.
In this paper we determine all grouplike elements of some some classes of coalgebras over a field... more In this paper we determine all grouplike elements of some some classes of coalgebras over a field k, as well as: trigonometric coalgebras and hyperbolic coalgebras. Also we prove that matrix coalgebra ) , 2 ( k M C doesn't have any grouplike element.
The basic ideas and ways of thought of algebra permeate nearly every part of mathematics. Moreove... more The basic ideas and ways of thought of algebra permeate nearly every part of mathematics. Moreover, modern algebra cultivates the ability to handle abstract ideas. From the most basic ideas of the modern and abstract algebra, the notions of group and subgroup are fundamental. We all know that a group G is an algebraic structure, more precisely a nonempty set endowed with an operation which combines between them two elements from G, obtaining in this way new and spectacular results and properties for the elements and also, for the subsets of G. In this article, we present how a subgroup of a group can receive interesting properties by using nonempty subsets of the main group and a positive integer previously fixed. Also, in this paper we give a few applications which are related to the new construction, namely the radical of a subgroup of a group.
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Papers by Georgiana Velicu