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Mathematics Dissertation Titles

Info: 724 words(1 pages)Mathematics Dissertation Titles
Published: 19th August 2025 in Mathematics Dissertation Titles

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Introduction

Mathematics is often considered the universal language, a discipline that continues to expand and evolve both as a pure and applied discipline, confronting foundational theoretical questions and leading research and change in science, technology, engineering, economics, and data science. Mathematics encompasses pure mathematics, applied mathematics, computational modelling, statistics, cryptography, and mathematical biology. Relatedly, this thesis collection presents a range of research areas across mathematics from abstract theory to practical experience, all noting how mathematical thinking contributes underpinning problem solving in other disciplines.

Mathematics Dissertation Titles

1. Graph Theory Applications in Optimising Urban Transport Systems

Focus: This thesis will develop applications of graph theory to help design and implement efficient transport systems, decrease congestion, and improve journey times in major urban centres.

2. Mathematical Modelling of the Spread of Infectious Disease: The Case of COVID-19

Focus: This research will use differential equations and stochastic modelling to study the spread of COVID-19, explore interventions, and ultimately provide guidance on which interventions work, when they are most effective and, if possible, how to increase their efficacy.

3. The Influence of Number Theory in Modern Cryptography

Focus: This research will detail how the underlying principles of number theory, such as prime factorization and modular arithmetic, form the basis of encryption algorithms and secure communications.

4. Chaos Theory and its Applications for Climate Forecasting

Focus: This project will explore how chaos theory can model complex, nonlinear climate processes and, if implemented into forecasting models, may improve long term weather forecasts and climate data.

5. Optimisation Techniques in Machine Learning Algorithms

Focus: The thesis will consider mathematical optimisations methods e.g. gradient descent and convex optimisation and how they compares in terms of model accuracy and efficiency in machine learning using a mathematical perspective.

6. Topology and Its Importance in Contemporary Physics

Focus: This research document will review the relationship of topology with theoretical physics, specifically in regards to its role in quantum field theory and its applications in condensed matter physics.

7. Fractal Geometry for Modeling Natural Phenomena

Focus: This dissertation will explore the potential of fractal geometry to either model or analyze natural formations, by focussing on features of nature such as coastlines, mountain ranges and plant growth.

8. Financial Mathematics: Using Stochastic Calculus in the Pricing of Options

Focus: This study will evaluate the application of stochastic calculus within financial models (such as the Black-Scholes model) for pricing derivatives and risk management in finance.

9. The foundations of computational complexity theory and the P versus NP Problem

Focus: This dissertation will provide qualitative evaluations of the foundations of computational complexity theory with an emphasis on the P versus NP problem and its ramifications within the field of computer science.

10. Wavelet Processing for Signal Analysis

Focus: This study will explore the application of wavelet transforms (also known as wavelet analysis) to the processing and compression of signals, specifically in the areas of image compression and noise suppression.

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References:

  1. Syzdykbayeva, B., Raimbekov, Z., Baiburiev, R., & Dulatbekova, Z. (2025). Improving the Transport and Logistic Infrastructure of a City Using the Graph Theory Method: The Case of Astana, Kazakhstan. Sustainability, 17(6), 2486. https://www.mdpi.com/2071-1050/17/6/2486
  2. Kaur, R., Prabhanshi, Jhamb, I., & Verma, P. (2025). Transmission Dynamics of COVID-19 Across a Region: A Mathematical Model. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 1-16. https://link.springer.com/article/10.1007/s40010-025-00929-8
  3. Ahmed, M., Sulaiman, M. H., Hassan, M. M., & Bhuiyan, T. (2025). Predicting the classification of heart failure patients using optimized machine learning algorithms. IEEE Access. 
  4. Keçeci, M. (2025). Scalable Complexity in Fractal Geometry: The Keçeci Fractal Approach. Authorea Preprints. https://www.authorea.com/doi/full/10.22541/au.175131225.56823239
  5. Tunçel, L., Vavasis, S. A., & Xu, J. (2025). Computational complexity of decomposing a symmetric matrix as a sum of positive semidefinite and diagonal matrices. Foundations of Computational Mathematics, 25(1), 223-269. https://link.springer.com/article/10.1007/s10208-023-09637-4

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