Mathematical Methods in Data Science
Bridging Theory and Applications with Python

Explore the mathematics of data science with this advanced undergraduate and graduate text integrating theory with applications in Python.

Sébastien Roch (Author)

9781009509459, Cambridge University Press

Hardback, published 30 October 2025

582 pages
25.4 x 17.8 x 3.2 cm, 1.345 kg

'This book is an outstanding introduction to the fundamentals of data science by an expert educator and researcher in the area. Its choice of topics, its use of Python, its plentiful examples and exercises, and its battle-testing in the classroom make it a top choice for students and educators seeking a mathematically rigorous yet practical entrée into data science.' Stephen J. Wright, University of Wisconsin

Bridge the gap between theoretical concepts and their practical applications with this rigorous introduction to the mathematics underpinning data science. It covers essential topics in linear algebra, calculus and optimization, and probability and statistics, demonstrating their relevance in the context of data analysis. Key application topics include clustering, regression, classification, dimensionality reduction, network analysis, and neural networks. What sets this text apart is its focus on hands-on learning. Each chapter combines mathematical insights with practical examples, using Python to implement algorithms and solve problems. Self-assessment quizzes, warm-up exercises and theoretical problems foster both mathematical understanding and computational skills. Designed for advanced undergraduate students and beginning graduate students, this textbook serves as both an invitation to data science for mathematics majors and as a deeper excursion into mathematics for data science students.

1. Introduction: a first data science problem
2. Least squares: geometric, algebraic, and numerical aspects
3. Optimization theory and algorithms
4. Singular value decomposition
5. Spectral graph theory
6. Probabilistic models: from simple to complex
7. Random walks on graphs and Markov chains
8. Neural networks, backpropagation and stochastic gradient descent.

Subject Areas: Numerical analysis [PBKS]