Mathematics

Evaluation of the Use of Numerical Tools in Teaching Calculus Concepts

This study evaluated the use of numerical and graphing tools in teaching calculus concepts. Students taught with tool-assisted activities were compared with those taught conventionally using a pre-test and post-test design and questionnaires. The findings revealed that tool integration improved conceptual understanding and engagement, with greater gains on visual and applied items. The study observed that tool misuse could distract without structured activities. It recommends structured integration of computational tools in calculus instruction.

2025 — Undergraduate

Assessment of Classroom Factors Influencing Students' Achievement in Mathematics

This study examined classroom factors influencing students' achievement in mathematics. A descriptive survey was conducted with secondary school students and teachers using a structured questionnaire, and achievement records were analysed. The findings revealed that instructional quality, class size, and resource availability significantly influenced achievement, while attitudes and practice habits also mattered. The study observed variability across schools. It recommends improved instructional support, smaller effective groups, and enhanced learning resources.

2025 — Undergraduate

Mathematical Modelling of Resource Allocation and Optimisation Problems

This study developed mathematical models for resource allocation and optimisation problems. Allocation problems were formulated as constrained optimisation models and solved using structured methods, with shadow prices and constraints interpreted. The findings revealed that the models produced feasible optimal allocations and identified binding constraints, while sensitivity analysis showed how solutions shifted with parameter changes. The study observed that model formulation quality determined solution usefulness. It recommends optimisation modelling for budgeting and resource planning.

2025 — Undergraduate

Development of Mathematical Models for Disease Spread and Control

This study developed mathematical models for the spread and control of infectious disease. Compartmental models were formulated, analysed for threshold behaviour, and used to examine the effect of intervention parameters on outbreak size. The findings revealed that model thresholds governed whether outbreaks grew or died out, while control parameters such as contact reduction substantially reduced projected cases. The study observed sensitivity to model assumptions. It recommends calibrated compartmental models for public health scenario planning.

2025 — Undergraduate

Application of Graph Theory to Network and Routing Problems

This study applied graph theory to network and routing problems. Road and communication networks were modelled as weighted graphs, and shortest-path and connectivity analyses were performed. The findings revealed that graph algorithms identified optimal routes and critical links efficiently, while network robustness was expressed through connectivity measures. The study observed that edge weights materially affected recommendations. It recommends graph-based modelling as a foundational tool for network design and logistics.

2025 — Undergraduate

Combinatorial Counting Techniques in Scheduling and Allocation Problems

This study examined combinatorial counting techniques in scheduling and allocation problems. Representative problems involving permutations, combinations, and pigeonhole reasoning were formulated and solved, and the underlying combinatorial structures were analysed. The findings revealed that systematic counting produced correct enumerations and exposed feasibility constraints in allocation scenarios. The study observed that logical bookkeeping reduced counting errors. It recommends explicit combinatorial reasoning in operations planning.

2025 — Undergraduate

Solution Methods for Linear Differential Equations with Engineering Applications

This study examined solution methods for linear differential equations arising in engineering problems. First- and second-order equations were solved using integrating factors, characteristic equations, and variation of parameters, and solutions were interpreted physically. The findings revealed that structured methods produced complete and verifiable solutions, with initial conditions determining particular responses. The study observed that physical interpretation aided identification of modelling errors. It recommends linking differential equation courses to engineering applications.

2025 — Undergraduate

Application of First-Order Differential Equations to Population Growth Models

This study applied first-order differential equations to the modelling of population growth. Exponential and logistic models were formulated, solved, and calibrated to observed growth data, and qualitative behaviour was interpreted. The findings revealed that the logistic model described growth with limiting capacity more realistically than the exponential model at longer horizons. The study observed that parameter estimation strongly influenced predictions. It recommends calibrated differential-equation models for population and resource planning.

2025 — Undergraduate

Application of Stochastic Models to Queueing and Service Systems

This study applied stochastic models to the analysis of queueing and service systems. Arrival and service data from a selected service point were fitted to standard queueing models, and performance measures such as waiting time and queue length were derived. The findings revealed that model-derived measures closely matched observed behaviour, while variation arose from time-of-day effects. The study observed that capacity changes influenced queue performance systematically. It recommends queueing models for planning and capacity decisions.

2025 — Undergraduate

Numerical Solution of Ordinary Differential Equations with Error Analysis

This study examined numerical methods for the solution of ordinary differential equations and their associated errors. Euler, improved Euler, and Runge-Kutta style methods were applied to representative initial-value problems, and accuracy was assessed against exact solutions. The findings revealed that higher-order methods achieved greater accuracy at comparable step sizes, while error grew predictably with step size. The study observed stability limitations for stiff problems. It recommends combined use of order and step-size control in practice.

2025 — Undergraduate

Modelling of Random Phenomena Using Probability Distributions

This study modelled random phenomena using probability distributions and assessed goodness of fit. Observations from selected random processes were summarised and fitted to discrete and continuous distributions, and fitted models were compared. The findings revealed that distributional models captured central tendencies and variability effectively, while model adequacy varied with the underlying process. The study observed that choice of distribution improved inference. It recommends distribution fitting as a standard step in stochastic analysis.

2025 — Undergraduate

Performance Evaluation of Root-Finding Methods for Nonlinear Equations

This study evaluated the performance of root-finding methods for nonlinear equations. Bisection, regula falsi, secant, and Newton-type methods were implemented for representative equations, and convergence speed, accuracy, and robustness were compared. The findings revealed that derivative-based methods converged fastest for smooth roots, while bracket methods remained robust where derivatives were problematic. The study observed trade-offs between speed and reliability. It recommends method selection informed by function behaviour and starting conditions.

2025 — Undergraduate

Eigenvalue Decomposition and Its Application to Markov Chain Analysis

This study examined eigenvalue decomposition and applied it to the analysis of Markov chains. Transition matrices were decomposed, steady-state vectors were derived from dominant eigenspaces, and convergence rates were interpreted. The findings revealed that eigenvalue analysis determined long-run behaviour of the chains accurately, with the dominant eigenvalue governing stability. The study observed that spectral properties explained mixing behaviour. It recommends teaching eigenvalue methods as a bridge between abstract algebra and applied stochastic modelling.

2025 — Undergraduate

Application of Matrices to the Solution of Systems of Linear Equations

This study applied matrix methods to the solution of systems of linear equations arising in applied contexts. Systems were solved using Gaussian elimination, matrix inversion, and determinant-based approaches, and results were verified by substitution. The findings revealed that matrix methods handled small and medium systems efficiently and exposed existence and uniqueness conditions clearly. The study observed that pivoting improved numerical stability. It recommends routine use of matrix formalism in solving and analysing linear systems.

2025 — Undergraduate

Continuity and Limits with Applications to Economic Functions

This study examined concepts of continuity and limits and their application to economic functions. Representative demand, cost, and growth functions were analysed for continuity, limiting behaviour, and endpoint properties. The findings revealed that continuity assumptions permitted reliable use of marginal and equilibrium analyses, while discontinuities corresponded to economically significant thresholds. The study observed that limit-based reasoning clarified asymptotic behaviour. It recommends grounding economic modelling in rigorous analysis of continuity and limits.

2025 — Undergraduate

Numerical Approximation of Definite Integrals and Convergence Behaviour

This study examined the numerical approximation of definite integrals and the convergence behaviour of common quadrature rules. Representative integrals were approximated by rectangular, trapezoidal, and Simpson-like rules at increasing partitions, and errors were analysed. The findings revealed that all methods converged to the true integral as partitions increased, with higher-order methods converging faster, while error magnitudes depended on function smoothness. The study observed predictable error patterns. It recommends selecting quadrature rules based on required accuracy and function properties.

2025 — Undergraduate

A Study of Sequences and Series with Applications to Financial Models

This study investigated the convergence of sequences and series and applied the results to financial models involving compounding and annuities. Theoretical tests for convergence were applied to representative series, and convergent cases were used to compute limiting values relevant to finance. The findings revealed that convergence tests identified behaviour reliably, while geometric-series results underpinned accurate valuation formulas. The study observed that divergence of series corresponded to unbounded model behaviour. It recommends explicit links between analysis and applied finance in instruction.

2025 — Undergraduate

Application of Differential Calculus to Rate Problems in Real-World Systems

This study applied differential calculus to rate and optimisation problems drawn from real-world systems. Representative problems involving rates of change, related rates, and extreme values were formulated and solved analytically, with results interpreted in context. The findings revealed that calculus-based methods determined optimal and critical points accurately, while sensitivity to parameter changes was tractable through derivatives. The study observed improved problem interpretation when solutions were checked against physical context. It recommends embedding application-based problems in calculus instruction.

2025 — Undergraduate

Application of Group Theory to the Analysis of Symmetry Problems

This study examined the application of group theory to the analysis of symmetry problems. Symmetry groups were constructed for selected geometric and physical configurations and analysed using group axioms, subgroups, and cosets. The findings revealed that group-theoretic descriptions captured the structure of symmetries compactly and supported classification of configurations by symmetry type. The study observed that the group framework simplified analysis of combined transformations. It recommends the continued application of group methods in geometry, crystallography, and physics.

2025 — Undergraduate

Assessment of Algebraic Structure Methods in the Solution of Congruence Problems

This study assessed algebraic structure methods for solving congruence problems. Linear and quadratic congruences were solved using modular arithmetic techniques, and solutions were verified and compared across methods. The findings revealed that structured methods, including the Chinese remainder approach, produced correct and efficient solutions, with systematic handling of non-unique cases. The study observed that understanding modular structures reduced computation time. It recommends emphasising structural approaches in teaching number-theoretic problem solving.

2025 — Undergraduate