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

(University of Wisconsin, Madison)
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A hands-on textbook for advanced undergraduates and beginning graduate students in data science, offering an accessible introduction to the essential mathematics behind modern data analysis. With practical Python examples and hundreds of exercises and problems, it's an invaluable resource for students and educators alike.

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.

Arvustused

'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

Muu info

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