This programme aims to engage enthusiastic and motivated Mathematics students in innovative research, both in pure Mathematics and its applications in Computer Science. It is designed for students with a strong background in Mathematics or closely related disciplines. In particular, the programme serves as a valuable stepping stone for students intending to pursue PhD studies or research roles at universities and research institutes. Some research projects within the programme will explore new directions in neural networks and artificial intelligence (AI), with potential applications in industry. The importance of interdisciplinary research is highlighted in the UK’s Research and Development Roadmap, which encourages innovative collaborations between mathematical sciences, biomedical research, and computing technologies.