Machine Learning Tutorials For Pure Mathematics And Theoretical Physics

This book offers a focused collection of lectures and tutorials on applying machine learning techniques to research in theoretical physics and pure mathematics. Machine learning continues to transform the scientific landscape, providing powerful tools capable of driving significant advances across these disciplines. Through clear conceptual explanations and practical examples, this text equips students and researchers with the knowledge and skills needed to integrate these methods into their own work.

The book begins with an introduction to the core principles of machine learning, including neural networks and transformer architectures. It then explores advanced optimization and search strategies, with an in-depth look at genetic algorithms, quantum annealing, and reinforcement learning. In the final chapters, these techniques are applied to contemporary problems in string theory and knot theory, illustrating their potential in cutting-edge research contexts. Throughout, the material is reinforced with worked examples and accompanied by code implementations to support hands-on learning.

Designed for graduate students and researchers in physics and mathematics, this book serves as an accessible yet rigorous introduction to the practical use of machine learning in modern scientific research.

Professor Andrei Constantin is a Royal Society Dorothy Hodgkin Fellow and Supernumerary Fellow in Mathematics and Physics at Mansfield College, University of Oxford, UK. He obtained an undergraduate degree in Physics from the University of Bremen and an MSc in Theoretical and Mathematical Physics from LMU Munich, Germany. After completing his doctoral studies at the University of Oxford, he held postdoctoral positions at Oxford and Uppsala University, Sweden. His research focuses on the development of mathematical and computational tools to investigate string theory and its implications for particle physics, cosmology, and quantum gravity.

Professor Yang-Hui He is a Fellow of the London Institute for Mathematical Sciences, a lecturer in mathematics at Merton College, University of Oxford, and a visiting professor at City St George's, University of London, and Nankai University, China. He obtained his BA at Princeton University, USA (summa cum laude, Shenstone Prize and Kusaka Prize), his MA at the University of Cambridge, UK (Distinction, Tripos), and his PhD at the Massachusetts Institute of Technology, USA. After a postdoc at the University of Pennsylvania, he joined the University of Oxford as FitzJames Fellow and an STFC Advanced Fellow. He works at the interface of string theory, algebraic and combinatorial geometry, and machine learning.