The UK higher education has been one of the top destinations for international students over the last few decades, and it is beneficial to the UK local and national economy. However, recent changes of the governmental policies on the way UK universities are funded and the recession that still affects economies around the world have left many universities around the UK at financial survival risk. With relatively limited access to reduced research funds, student recruitment has a vital importance for most universities. It has been well established in the literature that academic reputation and the level of services have the most significant impact on national and international students. Thus, universities, to maintain their market share, must spend much energy and resources to improve the level of services offered to their students. The recently introduced National Student Survey (NSS) has become one of the most important metrics to assess student satisfaction that influences directly the university league tables and the Teaching Excellence Framework (TEF), which in turn effects international and national student recruitment. It is not surprising that underpinning student satisfaction has become the major target of UK universities. Therefore, a research investigation has been carried out to identify the most influential factors that comprise to the decision of overall satisfaction for the students studying Science, Technology, Engineering and Mathematics (STEM) subjects. On this purpose, a detailed statistical analysis was carried out on the NSS results and it was concluded that there is strong evidence, that “teaching” and “organisation and management” are the vital influential factors on the overall satisfaction of students.

The integration of digital technologies in mathematics is becoming increasingly significant, particularly in promoting conceptual understanding and student engagement. This study systematically reviews the literature on applications of Computer Algebra Systems, Artificial Intelligence, Visualisation Tools, augmented-reality technologies, Statistical Software, game-based learning and cloud-based learning in higher education mathematics. This meta-analysis synthesises findings from 88 empirical studies conducted between 1990 and 2025 to evaluate the impact of these technologies. The included studies encompass diverse geographical regions, providing a comprehensive global perspective on the integration of digital technologies in higher mathematics education. Using the PRISMA framework and quantitative effect size calculations, the results indicate that all interventions had a statistically significant impact on student performance. Among them, Visualisation Tools demonstrated the highest average percentage improvement in academic performance (39%), whereas cloud-based learning and game-based approaches, while beneficial, showed comparatively modest gains. The findings highlight the effectiveness of an interactive environment in fostering a deeper understanding of mathematical concepts. This study provides insights for educators and policymakers seeking to improve the quality and equity of mathematics education in the digital era.

Motivated by the nonlinear dynamics of mathematical models encountered in power systems, an investigation into the dynamical behaviour of the swing equation is carried out. This paper examines analytically and numerically the development of oscillatory periodic solutions, whereby increases of the control parameter, lead to a cascade of period doubling bifurcations, before eventually loss in stability is exhibited and effective forerunners to chaos revealed. Gaining an understanding on the dynamical behaviour of the system can help to produce a deeper insight of the bifurcations entailed, with the appearance of the triggered sequence of the first period doubling’s acting as precursors of imminent danger and difficult operations of a practical system.

A research investigation is undertaken to gain a more comprehensive understanding of the primary and subharmonic resonances exhibited by the swing equation. The occurrence of the primary resonance is characterised by amplified oscillatory reactions, voltage instability, and the possibility for system failure. The phenomenon of subharmonic resonance arises when the frequency of disturbance is a whole-number fraction of the natural frequency. This results in the occurrence of low-frequency oscillations and the potential for detrimental effects on equipment. The objective of this study is to expand upon the current literature regarding the impacts of primary resonance and enhance comprehension of subharmonic resonance in relation to the stability of a specific power system model. The analytical and numerical tools are utilised to investigate the fundamental principles of this resonant-related problem, aiming to provide an effective control solution. This choice is driven by the model’s complex nonlinear dynamical behaviour, which offers valuable insights for further analysis. This analysis includes the Floquet Method, the Method of strained parameters, and the concept of tangent instability in order to provide an extension to existing literature relating to primary and subharmonic resonances, taking into account the dynamic and bifurcation characteristics of the swing equation. This objective will be achieved through the utilisation of both analytical and numerical methods, enabling the identification of specific indicators of chaos that can contribute to the safe operation of real-world scenarios.

It is vital to study the stability of power systems under small perturbations to prevent blackouts. This study presents a load-shedding strategy that has been incorporated within the swing equation to reduce instability and delay the onset of chaotic dynamics. The objective of this study was to identify the minimal load reductions required after disturbances to maintain the frequency above a critical value. Analytical techniques such as eigenvalue analysis and perturbation methods can also be supported with numerical simulations using bifurcation diagrams, Lyapunov exponents, and the Simulink model. When compared to the conventional stepwise load-shedding method, the proposed approach allows for dynamic adjustments and presents a 49% increase in stable regions and a 45% reduction in recovery time. Performance was also analysed under different damping, inertia, and load scenarios. These results suggest that the strategy demonstrated in this research provides a robust and computationally practical solution for modern power system applications.

A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of the swing equation. The primary resonance, which can result in increased oscillatory responses, voltage instability, and potential system collapse, happens when the external disturbance frequency coincides with the natural frequency of the system. Subharmonic resonance occurs when the disturbance frequency is an integer fraction of the natural frequency, leading to low-frequency oscillations and possible equipment damage. The purpose of this study is to provide an extension of the existing literature of the effects of primary resonance and further provide a thorough understanding of subharmonic resonance on the stability of a certain power system paradigm. Motivated by the rich nonlinear dynamical behaviour exhibited by this evergreen model, analytical and numerical techniques are employed to examine the underlying principles, creating an efficient control solution for this resonant-related problem. The main objective of this research is to provide a comprehensive understanding of the primary and subharmonic resonances considering the dynamical and bifurcational behaviour of the underlying swing equation, whereby both analytical and numerical techniques are employed, allowing for an identification of certain precursors to chaos that may lead and cater for the safe operation of practical problems.