ABSTRACT The concept of cycle index was first discovered by Howard Redfield in 1927. The cycle index formulas of various group actions have been computed since then by various authors. The formulas have been used to count graphs in mathematics and chemical compounds in chemistry. Therefore cycle index is a very useful tool in enumeration. It is widely applied in other fields of study like biology and jewelry industry. The cycle index of the symmetric group acting on ordered pairs, tripl...

ABSTRACT GeoGebra is a free computer application software that provides an algebra view, geometry view, spreadsheet view and an input bar. This study looked at if and how this resource can be used to enhance the teaching of Geometry in secondary schools in Kajiado County in Kenya. The objectives of this study were to assess the applicability of GeoGebra in the teaching of mathematics in secondary schools in Kenya. The relationship in performance of students taught with the help of this ...

ABSTRACTThis study assesses the performance of three numerical turbulence models; k -e ,k -w and k -w - SST in predicting heat transfer due to natural convection inside anair filled cavity. The heat transfer due to natural convection inside a rectangularclosed cavity should be modeled to include the effect of turbulence for Rayleighnumber greater than or equal to 9 10 .The non-linear terms i j u u and qi u in theaveraged momentum and energy equations respectively were modele...

ABSTRACTThis study models natural turbulent convection in a rectangular enclosure with localized heating and cooling. The equations used in modeling the flow are the equation of continuity, momentum equation and the energy equation. These equations are decomposed using the Reynolds decomposition then the decomposed equations are non – dimensionalised and reduced using the Boussinesq assumptions. The model that is considered is a rectangular enclosure with one side wall being heated and the ...

ABSTRACT Magnetohydrodynamic boundary layer flow involving a fluid of varying viscosity subject to thermal radiation and Newtonian heating has various applications in industry and engineering some of the applications include designing of cooling systems used in electronic devices, cooling of nuclear reactors, harvesting of solar energy, thermal insulation, heat exchangers and in geothermal reservoirs. Heat transfer by thermal radiation is of significance to engineering processes that oc...

ABSTRACTThe purpose of this study was to explore the various challenges and opportunities influencing integration of ICT in teaching and learning Mathematics in secondary schools in Nairobi County. The study sought to: Determine the levels of ICT integration in teaching and learning Mathematics; identify the challenges and opportunities of ICT use in teaching and learning Mathematics; and identify best pedagogical practices used in teaching Mathematics using ICT. The study adopted Rogers’s ...

ABSTRACTThere have been many investigations on the combinatorial structures and invariants over the group actions on the subsets of its elements. Studies on Group Theory have yielded varied and important results in the advancement of Algebra. Several studies have also been made on Graph Theory. Some Mathematicians have studied the concept of automorphisms on graphs thereby yielding important results. Automorphism groups from graphs containing the cyclic and dihedral groups, Cn and Dn respecti...

ABSTRACT The Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the polynomials that give rise to them via the Galois groups came to be called Galois Theory in honor of Everiste Galois who first discovered them in 1830. In this project we find the extensions of whose Galois group is isomorphic to, , and the quaternion group . In each case we identify the extensio...

AbstractThe concept of the cycle index formulas of a permutation group was discovered inthe year 1937. Since then cycle index formulas of several groups have been studiedby di_erent scholars. For instance the cycle index of the dihedral group Dn acting onthe set of vertices of a regular ngon is known and has been applied in enumerationof di_erent mathematical structures. In this study the relationship between the cycleindex formula of a semidirect product group and the cycle index ...

ABSTRACTTrigonometry topics are very important in mathematics education as trigonometric functions have many applications in fields such as adverse physics, mechanical and electrical engineering, music, astronomy and biology. Any challenges encountered by students in learning affect overall performance in the subject. The purpose of the study was to determine the pedagogical factors affecting learning of the topic in secondary schools and recommendation made. The objectives of the study were:...

AbstractPlatonic solids are 3-dimensional regular, convex polyhedrons. Each of the faces are equidistant and equiangular to each other in any of the solids. They derive their name from the ancient Greek philosopher, Plato who wrote about them in his dialogue, the Timaeus as reported by Cornford (2014). The solids features have fascinated mathematicians for decades including the renown geometer, Euclid: In his Book XIII of the Elements, as rewrote by Heath et al. (1956...

AbstractThe action of the symmetric group S5 on the cosets of its non-maximal subgroups is an aspect that seems to have received less attention for sometime. Most studies have infact looked on the action of symmetric group S5 on the cosets of its maximal subgroups leaving many properties about its action on non-maximal subgroups unknown. This project has therefore looked at the action of the symmetric group S5, on the cosets of some of its non-maximal subgroups. ...

ABSTRACT The action of and on the cosets of their subgroups is a very active area in enumerative combinatorics. Most researchers have concentrated on the action of these groups on the cosets of their maximal subgroups. For instance Tchuda computed the subdegrees of the primitive permutation representations of . Kamuti determined the subdegrees of primitive permutation representations of . He also constructed suborbital graphs corresponding to the action of on the cosets of However ma...

ABSTRACTIn this study the effects of applying variable pressure gradient to a MHD fluid flowing between two plates in an inclined magnetic field was carried out. It involved an unsteady hydromagnetic fluid flowing through two plates where the upper plate was porous and moving with a constant velocity in a direction that is contrary to fluid flow direction. The lower plate was non-porous and stationary. In the past years, research studies relating to MHD fluid flow through plates have been don...