Sharmila Sivalingam, M.Sc., M.Phil. M.C.A, EdD
Assistant professor of Mathematics, Maryville University of St. Louis, Missouri, USA
Abstract: The key to any course development, either tradition, hybrid or online is to ensure that students should benefit from the design. Online course development is no exception from that. This paper discusses some of the strategies that the author used in online math course development and taught. This article discusses various features in the design and development including course content, web design, student engagement, student support and teacher’s presence. The author provides a critical review of the course design that help student to be motivated and learn in a student-centered environment. Recommendations for online course development are outlined.
Keywords: Online Math, course design, student engagement, communication, discussion, Instructor presence.
Pages: 145 – 158 | Full PDF Paper
Universidade Federal do Reconcavo da Bahia Cruz das Almas, BAHIA, Brazil.
Abstract: The lifting of the facet is a technique used to generate polyhedral facet for the integer optimization problem. For groups, semigroups, and abelian additive systems master problems, homomorphism and sub-morphism can be used for lifting the facets. Another known methodology is the sequential lifting, which provides a new facet from a facet an element which not considered by facet, thus considering a new element. For abelian groups, there exist results for the sequential lifting of facets to consider the algebraic aspect and not the geometric aspect of the polyhedron. In this case of semigroups or additive systems master problems, the subadditive cone is important to the lifting facet. These results do not use the polyhedron polarity to lifting facet, in this paper we used the polarity polyhedra results to define sequential lifting facets of non-master associative, abelian, and b-complementary. The results presented here extend the known theorems of the sequential lifting for groups and semigroups. The sequential lifting of facets theorems for non-master problems doesn’t consider the polarity of the polyhedron to characterize facets, as far as we know, this is the first result that establishes sequential lifting for associative, abelian and b-complementary additive system non-master problems.
Keywords: additive system, polyhedra-polarity, sequential lifting.
Pages: 159 – 169 | Full PDF Paper