Mathematical Methods in Data Science: Bridging Theory and Applications with Python

by Sébastien Roch

Overview

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.

Product Details

ISBN-13:	9781009509459
Publisher:	Cambridge University Press
Publication date:	10/31/2025
Series:	Cambridge Mathematical Textbooks
Pages:	499
Product dimensions:	0.00(w) x 10.00(h) x 0.00(d)

About the Author

Sébastien Roch is a Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin, Madison. At UW-Madison, he helped establish the Data Science Major and has developed several courses on the mathematics of data. He is the author of Modern Discrete Probability: An Essential Toolkit (2023).

Table of Contents

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.

Editorial Reviews

‘Mathematical Methods in Data Science provides a clear and accessible primer on key concepts central to data science and machine learning. Through engaging examples from neural networks, recommender systems, and data visualization, Roch illuminates myriad foundational topics and methods. Designed for readers from a broad range of backgrounds, this text is an indispensable resource for students and professionals.’ Rebecca Willett, University of Chicago

‘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

From the Publisher