Mathematics of Machine Learning: Master linear algebra, calculus, and probability for machine learning

“As a professor teaching AI, I’m always looking for resources that combine mathematical rigor with practical relevance—and Mathematics of Machine Learning delivers. I plan to assign several chapters as required readings in my AI course, especially those on linear algebra and multivariable calculus. Tivadar Danka does an excellent job connecting core mathematical concepts to real-world AI applications, with clear Python examples that make the material approachable. I also highly recommend this book to professionals looking to strengthen their mathematical foundation for AI through self-study—it’s both structured and accessible.”

Prof. Tom Yeh, University of Colorado Boulder, Host of AI by Hand

“Often, the biggest obstacle to real-world machine learning success is mastering the fundamental math. Tivadar Danka’s Mathematics of Machine Learning removes that roadblock by means of exact explanations and practical exercises. Designed around useful case studies, ranging from vector spaces to the geometric interpretation of gradients, this book not only provides theorems but also prepares you to immediately apply them in production projects.”

Etibar Aliyev, Team Lead (AI) at Google

“Most books that claim to teach the math behind machine learning either oversimplify or drown you in abstraction. This one does neither. It’s precise where it matters, informal when it helps, and never loses sight of why the math exists in the first place.

No fluff, no cringe analogies -  just clear thinking and beautifully structured exposition. You can tell the author has done the proofs and written the code.

Highly recommend it for anyone serious about understanding, not just using, ML.”

Mike Erlihson, PhD, Head of AI at Stealth Startup

“As someone who approached machine learning with a strong commitment to understanding the underlying mathematics, I quickly discovered how fragmented and inaccessible many resources were. Mathematics for Machine Learning stands out as a comprehensive, well-structured guide that brings together all the essential topics — from linear algebra and calculus to probability and optimization — in a clear and coherent manner. The material is presented with both rigor and clarity, and the accompanying Python code bridges the gap between theory and practice. This book is an indispensable resource for anyone looking to build a solid mathematical foundation in the field.”

Prashant Kulkarni, Lead AI Security Research Engineer at Google Cloud

“This book provides a carefully constructed guide on mathematics for your machine learning projects. It gives you exactly what you need to know at just the right level! It includes principles, illustrations, and code examples to bring the concepts to life. I highly recommend it to anyone who takes their career seriously!”

T. Scott Clendaniel, AI co-instructor at the University of Pennsylvania

“Danka’s work serves as a foundational text, bridging the often-intimidating gap between abstract mathematics and its tangible application in data science. This book is an indispensable resource for aspiring machine learning engineers and data scientists who are committed to mastering the theoretical bedrock of their discipline.

 

 The section on Linear Algebra is particularly noteworthy for its clarity and the part dedicated to Functions and Calculus is well executed. The inclusion of multivariate calculus is a testament to the book’s comprehensive nature, preparing the reader for the high-dimensional data prevalent in real-world machine learning problems. The book’s treatment of sequences, limits, continuity, and differentiation is both thorough and contextually relevant. This section empowers the reader to grasp the mechanics of model training at a much deeper level. The author successfully demystifies the calculus that underpins so much of machine learning, making it accessible to a broad audience.

Finally, the book’s inclusion of Probability Theory completes the triad of mathematical pillars essential for machine learning. The author’s overall approach encourages a mode of critical thinking that is often absent in more perfunctory texts. Readers are actively encouraged to engage with the material, to question assumptions, and even to attempt their own proofs of the theorems presented. […] In conclusion, “Mathematics of Machine Learning” is a must-have text that excels in its clarity, its practical relevance, and its ability to inspire a genuine appreciation for the mathematical elegance of machine learning.”

Antonio Gulli, Sr. Director, Distinguished Engineer, Google

Tivadar Danka is a mathematician by training, a machine learning engineer by profession, and an educator by passion. After finishing his PhD in 2016 (about the arcane subject of orthogonal polynomials), he switched career paths and has been working in machine learning ever since. His work includes applying deep learning to cell microscopy images to identify and phenotype cells, creating one of the most popular open source Python packages for active learning, building a full machine learning library from scratch, and collecting about a total of 100k followers on social media, all by posting high-quality educational content.