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Cover of Mathematics of Data Science

Mathematics of Data Science

Written by Daniela Calvetti,Erkki Somersalo

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200 pages, about 4 hours of reading

Mathematics

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About this book

This textbook provides a solid mathematical basis for understanding popular data science algorithms for clustering and classification and shows that an in-depth understanding of the mathematics powering these algorithms gives insight into the underlying data. It presents a step-by-step derivation of these algorithms, outlining their implementation from scratch in a computationally sound way. Mathematics of Data Science: A Computational Approach to Clustering and Classification proposes different ways of visualizing high-dimensional data to unveil hidden internal structures, and nearly every chapter includes graphical explanations and computed examples using publicly available data sets to highlight similarities and differences among the algorithms. This self-contained book is geared toward advanced undergraduate and beginning graduate students in the mathematical sciences, engineering, and computer science and can be used as the main text in a semester course. Researchers in any application area where data science methods are used will also find the book of interest. No advanced mathematical or statistical background is assumed.

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Reading guide

Themes, characters and key ideas in Mathematics of Data Science, written by Chaptra AI.

  • about 100 hours
  • advanced
  • instructive
  • rigorous
  • analytical

Mathematics of Data Science by Calvetti and Somersalo serves as a foundational textbook, meticulously detailing the essential mathematical concepts underpinning modern data science. It systematically covers key areas such as linear algebra, calculus, probability theory, optimization, and numerical methods, presenting them with rigor and clarity. The book aims to equip readers with a deep theoretical understanding necessary to comprehend, develop, and apply data science algorithms effectively. It bridges the gap between abstract mathematical theory and its practical applications in data analysis, machine learning, and statistical inference, making complex topics accessible to advanced students and researchers.

“"Data science is not just about algorithms; it is fundamentally about understanding the underlying mathematical principles that govern those algorithms."”

Key themes

Mathematical Rigor as Foundation
This theme emphasizes that a deep, principled understanding of data science necessitates a strong grasp of its underlying mathematical theories. The book consistently reinforces the idea that true mastery comes from comprehending 'why' algorithms work, not just 'how' to apply them, advocating for a rigorous analytical approach over heuristic methods.
Interconnectedness of Mathematical Disciplines
The book masterfully demonstrates how seemingly disparate mathematical fields—linear algebra, calculus, probability, and optimization—are deeply intertwined and collectively essential for data science. It highlights how tools from one area often provide insights or solutions in another, fostering a holistic understanding.
Quantifying Uncertainty and Inference
A core theme is the mathematical framework for dealing with uncertainty inherent in data. This involves a thorough exploration of probability theory, statistical inference, and Bayesian methods to model randomness, make predictions, and draw conclusions from noisy or incomplete data.

Worth discussing

How does a deep understanding of linear algebra (e.g., SVD, eigenvectors) fundamentally change one's approach to dimensionality reduction compared to a purely algorithmic understanding?

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