College of Science, Engineering & Technologyhttp://hdl.handle.net/10500/1282014-07-30T15:36:06Z2014-07-30T15:36:06ZAn investigation of the use of computers in the teaching and learning of hyperbolic graphs in grades 10 to 12 mathematicsMavhungu, Lavhelani Emilyhttp://hdl.handle.net/10500/136942014-07-26T22:01:40Z2013-11-01T00:00:00ZAn investigation of the use of computers in the teaching and learning of hyperbolic graphs in grades 10 to 12 mathematics
Mavhungu, Lavhelani Emily
In this investigation an attempt was made to determine how learners and teachers use
computers in the teaching and learning of hyperbolic graphs in Mathematics. A
comprehensive literature study showed that there are many benefits in using computers
to study Mathematics. The investigation was done in two phases. In the first phase, a
questionnaire was given to learners. The second phase involved interviewing learners
and teachers. Findings indicate that learners and teachers enjoy using computers in the
teaching and learning of Mathematics. Analysis of the results shows that the use of
computers in teaching and learning of Mathematics, in particular the teaching and
learning of hyperbolic graphs is beneficial.
2013-11-01T00:00:00ZThe use of ALICE, a visual environment for teaching and learning object-oriented programmingDwarika, Jeralinehttp://hdl.handle.net/10500/133692014-04-23T15:22:00Z2014-04-23T00:00:00ZThe use of ALICE, a visual environment for teaching and learning object-oriented programming
Dwarika, Jeraline
University students learning object-oriented programming (OOP) encounter many complexities. This study undertook empirical research aimed at analysing learners’ interactions with the Alice visual programming environment, which seeks to engage and motivate learners to grasp concepts of OOP, whilst creating animated movies and video games.
A mixed-methods approach was employed, using questionnaire surveys and interviews to investigate learners’ experiences with Alice and their understanding of OOP. Findings indicated that learners lacked problem-solving abilities; were unable to grasp programming concepts on an abstract level and spent insufficient time practicing programming exercises. Alice proved to be an effective tool in helping to address these challenges and in improving learners’ grasp of OOP. Learners found Alice to have good usability.
Furthermore, test and exam results revealed a statistically significant difference between performances of learners who had been taught Alice in comparison to similar learners who were not exposed to the Alice intervention.
2014-04-23T00:00:00ZPricing European and American bond options under the Hull-White extended Vasicek ModelMpanda, Marc Mukendihttp://hdl.handle.net/10500/133462014-04-23T15:24:03Z2013-01-01T00:00:00ZPricing European and American bond options under the Hull-White extended Vasicek Model
Mpanda, Marc Mukendi
In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option.
2013-01-01T00:00:00ZConcerning ideals of pointfree function ringsIghedo, Oghenetegahttp://hdl.handle.net/10500/133422014-04-23T15:20:27Z2013-11-01T00:00:00ZConcerning ideals of pointfree function rings
Ighedo, Oghenetega
We study ideals of pointfree function rings. In particular, we study the lattices of z-ideals
and d-ideals of the ring RL of continuous real-valued functions on a completely regular
frame L. We show that the lattice of z-ideals is a coherently normal Yosida frame; and
the lattice of d-ideals is a coherently normal frame. The lattice of z-ideals is demonstrated
to be
atly projectable if and only if the ring RL is feebly Baer. On the other hand, the
frame of d-ideals is projectable precisely when the frame is cozero-complemented.
These ideals give rise to two functors as follows: Sending a frame to the lattice of
these ideals is a functorial assignment. We construct a natural transformation between the
functors that arise from these assignments. We show that, for a certain collection of frame
maps, the functor associated with z-ideals preserves and re
ects the property of having a
left adjoint.
A ring is called a UMP-ring if every maximal ideal in it is the union of the minimal
prime ideals it contains. In the penultimate chapter we give several characterisations for
the ring RL to be a UMP-ring. We observe, in passing, that if a UMP ring is a Q-algebra,
then each of its ideals when viewed as a ring in its own right is a UMP-ring. An example
is provided to show that the converse fails.
Finally, piggybacking on results in classical rings of continuous functions, we show that,
exactly as in C(X), nth roots exist in RL. This is a consequence of an earlier proposition
that every reduced f-ring with bounded inversion is the ring of fractions of its bounded
part relative to those elements in the bounded part which are units in the bigger ring. We
close with a result showing that the frame of open sets of the structure space of RL is isomorphic to L.
2013-11-01T00:00:00Z