Lecture notes on high-dimensional data

These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random vectors in high dimensions; random projections; separation/disentangling of Gaussian data. A revised version has been published as part of the textbook [Mathematical Introduction to Data Science, Springer, Berlin, Heidelberg, 2024, https://link.springer.com/book/10.1007/978-3-662-69426-8].