Here are some textbooks I find useful for my work.
Math of data science
High-dimensional probability
- High-Dimensional Probability (Vershynin, 2018)
Statistical inference
- Statistical Learning with Sparsity (Hastie–Tibshirani–Wainwright, 2015)
- Scalable Monte Carlo for Bayesian Learning (Fearnhead–Nemeth–Oates–Sherlock, 2024)
Computation of data science
Deep learning
- Deep Learning: Foundations and Concepts (Bishop, 2024)
- Understanding Deep Learning (Prince, 2023)
Optimization
- Convex Optimization (Vandenberghe, 2004)
- First-Order Methods in Optimization (Beck, 2017)
Applied topology
- Computational Topology for Data Analysis (Wang, 2021)
- Persistence Theory: From Quiver Representations to Data Analysis (Oudot, 2015)
Metric embeddings
- Lecture notes on metric embeddings (Matoušek, 2013)
- Minimum-Distortion Embedding (Agrawal–Ali–Boyd, 2021)
- Advances on Metric Embeddings (FOCS 2022 Workshop) (Various authors, 2022)
Theory
- Math and Computation (Wigderson, 2019)
- The Nature Of Computation (Mertens, 2011)
Physics of data science
Statistical mechanics
- Information Theory, Inference, and Learning Algorithms (MacKay, 2003)
Pure math
Algebraic topology
- Algebraic Topology (Hatcher, 2002)
- Topology Through Inquiry (Su, 2019)
Homological algebra
- An Introduction to Homological Algebra (Rotman, 2009)
- An introduction to homological algebra (Weibel, 1994)
Thanks to Lee Lady’s blurbs, I also like Jans, Rings and Homology (1964) and Sharpe and Vamos, Injective Modules (1975), both of which are out of print.
Category theory
- Category Theory in Context (Riehl, 2016)
- Basic Category Theory (Leinster, 2014)
Differential geometry
- Visual Differential Geometry and Forms (Needham, 2021)
- Differential Topology (Pollack, 1974)