Prime numbers play an integral part in many upper level mathematics courses, most notably in Number Theory. Can a course or section on prime numbers be introduced at the secondary (high school) level? This report outlines a possible course in a manner suitable for grade level instruction. These topics include: an extended section on the complete number system, a brief history of primes, their cardinality, and both the Fundamental Theorem of Arithmetic and Prime Number Theorem, the applications of primes, and the impact of primes within perfect numbers will all be explored. A brief discussion on questions that still remain relating to prime numbers will conclude this report. / text

In a world where technology advances, it is important that the human-computer interface follows in the same pace, to maximize the user experience. This means that when the machines become more powerful and the services become more comprehensive, it is important that they still are adapted to the users.In the web browsing world, a concept called infinite-scroll has become popular when trying to maximise the user experience. This technique uses JavaScript to dynamically load more content to a webpage whilst the user is scrolling without ever reloading the page, to achieve a more fluid experience. This technique is used widely in social media websites such as Facebook and Twitter among others.However, this technique have been used very rarely on other types of websites. Why this could be the case and how infinite-scroll performs on an intranet will be described in this report. A quantitative study on how the user behaviour differs between a website with pagination and infinite-scroll has been conducted and analysed by gathering statistics through Google Analytics about how users interacts with the website in question. The study indicates that infinite-scroll can be useful on an intranet when adapted according to usability guidelines.

This thesis consists of seven chapters. Chapter 1 is an introduction to the infinite products. Here we provide a proof for representing sine function as an infinite product. This chapter also describes the notation used throughout the thesis as well as the method used to prove the identities. Each of the other chapters may be read independently, however some chapters assume familiarity with the Jacobi triple product identity. Chapter 2 is about the Jacobi triple product identity as well as several implications of this identity. In Chapter 3 the quintuple product identity and some of its special cases are derived. Even though there are many known proofs of this identity since 1916 when it was first discovered, the proof presented in this chapter is new. Some beautiful formulas in number theory are derived at the end of this chapter. The simplest two dimensional example of the Macdonald identity, A2, is investigated in full detail in Chapter 4. Ian Macdonald first outlined the proof for this identity in 1972 but omitted many of the details hence making his work hard to follow. In Chapters 5 and 6 we somewhat deviate from the method which uses the two specializations to evaluate the constant term and prove Winquist's identity and Macdonald's identity for G2. Some of the work involved in proving G2 identity is new. Finally in Chapter 7 we discuss the work presented with some concluding remarks as well as underlining the possibilities for the future research. Throughout the thesis we point to the relevant papers in this area which might provide different strategies for proving above identities.

MSc (Mathematics) / Department of Mathematcs and Applied Mathematics / Magnetohydrodynamics ows have gained signi cant attention due to their importance in engineering applications. In this study, we numerically analysed the Dufour and Soret e ects on an unsteady MHD mixed convection ow past an in nite vertical plate with viscous dissipation. The governing non-linear partial di erential equations (PDEs) are transformed into a system of ordinary di erential equations (ODEs) by the suitable similarity transformations. The resulting equations consist of the momentum, energy and mass di usion equations. These resulting equations are solved using the Spectral Local Linearization Method (SLLM). Results obtained by the SLLM are in good agreement with the bvp4c technique. The e ects of di erent physical parameters entering into the problem are displayed graphically. The values of the Skin-friction (f0(0)), Nusselt number (􀀀 0(0)) and Sherwood number (􀀀 0(0)) are shown in tabular form for di erent values of the parameters. From the results, it is noted that the Soret number (Sr) and the Dufour number (Du) have negligible e ects on temperature pro le, whereas the decrease in the Soret number (Sr) leads to a decrease in both velocity and concentration of the uid, and the increase in Dufour number (Du) reduces the velocity and also has negligilbe e ect on the concentration pro le. / NRF