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Mathematics for Machine Learning 1st Edition
Purchase options and add-ons
- ISBN-10110845514X
- ISBN-13978-1108455145
- Edition1st
- PublisherCambridge University Press
- Publication dateApril 23, 2020
- LanguageEnglish
- Dimensions7 x 0.88 x 10 inches
- Print length398 pages
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From the Publisher
Editorial Reviews
Review
‘The field of machine learning has grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This comprehensive text covers the key mathematical concepts that underpin modern machine learning, with a focus on linear algebra, calculus, and probability theory. It will prove valuable both as a tutorial for newcomers to the field, and as a reference text for machine learning researchers and engineers.' Christopher Bishop, Microsoft Research Cambridge
'This book provides a beautiful exposition of the mathematics underpinning modern machine learning. Highly recommended for anyone wanting a one-stop-shop to acquire a deep understanding of machine learning foundations.' Pieter Abbeel, University of California, Berkeley
‘Really successful are the numerous explanatory illustrations, which help to explain even difficult concepts in a catchy way. Each chapter concludes with many instructive exercises. An outstanding feature of this book is the additional material presented on the website …’ Volker H. Schulz, SIAM Review
‘A solid and affordable resource for building foundational skills in machine learning.’ Ruwan Karunanayaka, University of the Fraser Valley
‘This is an excellent book on the mathematical foundations of machine learning. The colourful figures and even some equations make the content both engaging and easy to follow. I will definitely be recommending this book to my students.’ Hom Nath Gharti, Queen's University
Book Description
About the Author
A. Aldo Faisal leads the Brain and Behaviour Lab at Imperial College London, where he is faculty at the Departments of Bioengineering and Computing and a Fellow of the Data Science Institute. He is the director of the 20Mio£ UKRI Center for Doctoral Training in AI for Healthcare. Faisal studied Computer Science and Physics at the Universität Bielefeld (Germany). He obtained a Ph.D. in Computational Neuroscience at the University of Cambridge and became Junior Research Fellow in the Computational and Biological Learning Lab. His research is at the interface of neuroscience and machine learning to understand and reverse engineer brains and behavior.
Cheng Soon Ong is Principal Research Scientist at the Machine Learning Research Group, Data61, Commonwealth Scientific and Industrial Research Organisation, Canberra (CSIRO). He is also Adjunct Associate Professor at Australian National University. His research focuses on enabling scientific discovery by extending statistical machine learning methods. Ong received his Ph.D. in Computer Science at Australian National University in 2005. He was a postdoc at Max Planck Institute of Biological Cybernetics and Friedrich Miescher Laboratory. From 2008 to 2011, he was a lecturer in the Department of Computer Science at Eidgenössische Technische Hochschule (ETH) Zürich, and in 2012 and 2013 he worked in the Diagnostic Genomics Team at NICTA in Melbourne.
Product details
- Publisher : Cambridge University Press
- Publication date : April 23, 2020
- Edition : 1st
- Language : English
- Print length : 398 pages
- ISBN-10 : 110845514X
- ISBN-13 : 978-1108455145
- Item Weight : 1.76 pounds
- Dimensions : 7 x 0.88 x 10 inches
- Part of series : Studies in Natural Language Processing
- Best Sellers Rank: #44,197 in Books (See Top 100 in Books)
- Customer Reviews:
About the authors

Discover more of the author’s books, see similar authors, read book recommendations and more.

Professor Dr Aldo Faisal (@AnalogAldo) is Professor of Artificial Intelligence & Neuroscience at Imperial College London where is lab is based (https://FaisalLab.org). He was awarded a prestigious UKRI Turing AI Fellowship and is since 2019 the Founding Director of the UKRI Centre for Doctoral Training in AI for Healthcare (https://ai4health.io). Aldo works at the interface of AI and Biomedical Engineering to help people in disease and health. Core to his research approach is the virtuous cycle between using data-driven/AI methods to understand, model and predict from human beahviour, neuroscientific and biomedical problems, and in turn use the scientific discoveries gained from studying these problems to drive novel Machine Learning methods. He holds honorary posts at the Gatsby Computational Neuroscience Unit (UCL, London), at the MRC London Institute of Medical Sciences, or as Honorary Senior Fellow at the Nuffield Department of Clinical Neuroscience at the University of Oxford. He received a series of research prizes and distinctions such as being elected to the Global Futures Council of the World Economic Forum and winning the Toyota Mobility Foundation $50,000 Research Discovery Prize in 2018. He co-authored the Cambridge University Press textbook "Mathematics for Machine Learning" which was inspired from his experiences in pioneering courses on Machine Learning for computer science, natural sciences and engineering students long before it became popular.
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Top reviews from the United States
- 5 out of 5 stars
Wonderfully illustrated, welll laid out, great website and extra content
Reviewed in the United States on January 20, 2025If you already have a background with linear algebra, calculus, statistics, then this will be a nice refresher applied to the subject in question, machine learning. In that regard, it serves perfectly as a way to organize your study to get into AI/ML in a deeper way. Certainly deeper than from a purely user perspective.
If you don't have a background with linear algebra, calculus, statistics, it'll still provide a well organized studies plan for you to dive deeper.
It cannot, of course, be a textbook for these areas, it would take hundreds, thousands of pages to do so, and that's clearly not feasible.
What it does is introduce you to some concepts, refresh them, or refer you to further studies where there is a need to dive deeper in certain topics.
The book is clearly organized, well illustrated. For that alone I'm thankful, for many mathematics textbooks, even the ones targeting the professional mathematician, make the fatal mistake of assuming the reader finds images insulting.
They're not. Images help you organize thoughts visually, geometrically, providing important insights. For that alone, the content and organization, I would give the book 5 stars.
The examples are well laid out, the cases well illustrated, giving room for the reader to breathe without being crushed by a dense monolith of rendered equations.
Where it exceeds and stands above others is that the companion website provides, freely, the PDF of the book, an errata, instructor solutions to the exercises, and Jupyter Lab notebooks.
While other publishers would try to rob the customer blind by offering each of these as a separate product, for a hefty sum naturally, this publisher thought it would best serve the reader to have access to all this content for free.
Naturally, in this day and era, seeing someone focused on spreading knowledge for the sake of science and knowledge is commendable, and I cannot give me more than 5 stars sadly, for I would.
If you read it this far, this is a no-brainer. Visit the website, take a look at the PDF, buy it, so that you can have the version with you for your daily studies, and the PDF for that morning reading on the tablet.
The Jupyter notebooks make exploration fun and interesting, even if you're not experienced in the field.
It does not assume you are an expert in these areas, though naturally, it would benefit you greatly if you have experience or if at least you have some textbooks on linear algebra and some knowledge of differential, integral calculus.
To the authors, congratulations, and to the publisher, may you have a thousand years of prosperity and good fortune for making the auxiliary content freely available and in such a open and honest manner.
Bravo.
Highly recommended.
16 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Incredible Resource
Reviewed in the United States on September 3, 2022I had been looking for a book to bridge the gap between implementing machine learning code on the granular level and understanding it from a theoretical perspective and the search wasn't going well. Lots of other books that I tried before finding this one promised to help programmers become better mathematicians (or at least show them the math they need to learn in order to achieve that goal) but would almost always just provide code without context, or run through some incredibly basic, introductory level math without explaining at all how it connects to the various machine learning algorithms you'll be implementing as a programmer.
This book, however, takes the math seriously, and is incredibly direct and efficient in the introduction of new, relevant topics in calculus, linear algebra, and probability and statistics that you'll need to know if you want to truly understand the libraries you're using. I find myself reading a section in the book, going back to a "dedicated" textbook on the subject at hand - linear algebra or calculus or probability and statistics - and further studying the material, and then going back to Mathematics for Machine Learning to make sure I understand the topic better. This is the exact learning flow that I wanted, and the book delivers. Can't recommend enough!
54 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Brilliant and Precise
Reviewed in the United States on April 29, 2020The book is the missing piece between books like Artificial Intelligence: A Modern Approach and the mathematics you require to take such an undertaking. The authors do assume very little prior knowledge from the reader, but it t is recommended that you've had exposure to some of the mathematical topics prior to reading the book. But don't let that stop you if you're a beginner: you'll have to make a few detours to grasp some terms and such. Having said that, a course on single variable calculus ought to be under your belt. That's basically the only prerequisite.
The explanations are clear, and the book is designed to bring clarity and lucidity onto the topics, not send the student on an endless pit of proofs and rigor.
59 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 4 out of 5 stars
A Book Struggling with its Identity
Reviewed in the United States on July 14, 2023Don't get me wrong, this is a really good book. But this is a book that's stuck somewhere between a Mathematics book and a Computer Science book.
Having studied the mathematics in ML during college, I'm already familiar with the topic discussed in the book. I'm mainly reading it as a refresher of linear algebra and calculus that I haven't used in years.
It does a good job laying out necessary mathematical concepts, but it doesn't do as good of a job at providing proofs/explanations to a lot of the properties and extensions. For example, the book gives a good algebraic definition of orthogonality in terms of vectors and subspaces (inner product of the vectors/subspaces in question equal 0). However, in the next section about function orthogonality, the book just says "functions can be seen as vectors" and provides a definition in terms of a definite integral. The book didn't provide reasoning for such a jump from inner product to integral, nor did it provide explanations or intuitions for the upper and lower bounds of the integral. There are many more examples where the book doesn't provide proofs/explanations and hurries on to introduce new concepts.
The first few chapters alone is definitely enough for you to understand the concepts of the later chapters, but you WILL need to read dedicated mathematics textbooks (like the ones they pointed out in the "further readings" sections at the end of each chapter) if you want to form a sound mathematical foundation.
On the other hand, it did a decent job introducing many important algorithms in ML and the mathematics behind them, but it also lacks many key ideas important to ML. One would expect a book focusing on the mathematical side would be fairly theoretical on the subject of learning, but it doesn't cover fundamental theories in learning such as PAC learning, VC dimensions, No Free Lunch theorem, etc. I think the "Understanding Machine Learning: From Theory to Algorithms" book by Shai Shalev-Shwartz and Shai Ben-David is a much better read on those subjects.
Overall, it's a good book to have, especially when you need to a quick refresher on the mathematics or needs some help understanding the mathematical intuitions behind popular ML algorithms. What the book is not, is a beginner-friendly machine learning textbook for those who don't already know some linear algebra.
33 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Excellent book for reviewing math materials
Reviewed in the United States on November 11, 2021This book is excellent for brushing up your mathematics knowledge required for ML. It is very concise while still providing enough details to help readers determine important parts. This is my go-to if I need to review some concepts or brush up on my knowledge in general.
I wouldn't recommend this book if you have absolutely no prior math experience though as it can be hard to digest and sometimes they would skip parts here and there in proofs and examples. Especially for the probability section, the concepts will be very hard to grasp without prior knowledge
16 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Awesome book but it can scare the beginners :)
Reviewed in the United States on February 27, 2022Great book who wants to understand the maths behind the ML models, but some parts are rocket science :). I would definitely recommend this book to people in academia or to whom who has enough time to dive deep into theoretical aspect of the ML.
8 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Great book for beginners!
Reviewed in the United States on September 13, 2020Even though I can get a free e-copy, I still like the paperback version because I flip through it occasionally. This book sketches a clear big picture of the knowledge tree for ML and provides necessary build blocks to help you build solid foundations in preparation for practical ML.
You have to be aware this paperback version doesn't come with solutions. One of my reason to buy this is for the solutions. It turned out that only instructors can request solutions from the press company.
16 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Great Reference and Refresher Book
Reviewed in the United States on February 22, 2021Fits my needs pretty well. A well-curated collection of the essential math for AI and ML. I purchased the physical copy, despite having the free PDF, because I enjoyed it a lot and plan to re-read it with more detailed note-taking and highlighting on the book itself. I did have to consult other sources just to clear up some parts but was expected in reading a math book. Highly recommended!
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Top reviews from other countries
Slacker5 out of 5 starsDies ist das BESTE Buch über die Mathematik des Machine Learnings
Reviewed in Germany on March 16, 2024Nachdem ich vor 25 Jahren Informatik studiert habe und dort bereits "Neuronale Netze" (feed-forward back-propagation) kennengelernt hatte, wollte ich, motiviert durch den Hype der aktuellen AI (insbesondere machine learning sowie deep learning) mehr darüber lesen.
Daher zunächst das "Standardwerk" (Titel "Deep Learning") gekauft. Die dort enthaltene Mathematik ist, meines Erachtens, so stark ver-klausuliert und auch von der Notation her schwer zu lesen, dass ich dieses Buch hier "Mathematics for Machine Learning" gekauft habe: Ich muss sagen/schreiben: Das ist die BESTE Darstellung der verschiedenen mathematischen Themenbereiche (Vektoren, Matrizen, Lineare Algebra, Wahrscheinlichkeitsrechnung, u.s.w.), die ich als Praktiker der Informatik je gesehen habe.
Sehr gut verständlich (mit dem math. Grundwissen eines Informatikers), sehr tolle praxis-bezogene Beispiele zu den mathematischen Verfahren.
Darüber hinaus in einem hervorragenden Englisch geschrieben, das wirklich Freude macht, es zu lesen.
Ich denke, dass jeder, der sich intensiv mit Machine Learning auseinandersetzen möchte, hier sowohl ein Lehrwerk als auch ein Nachschlagewerk erhält.
Übungen mit Lösungen (auf github) runden dieses Buch ab. Ich bin begeistert!!!
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Martha Sandoval5 out of 5 starsExcelente herramienta !!
Reviewed in Mexico on March 30, 2026Buen libro !
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Gabriella5 out of 5 starsGuardare le cose da un punto di vista diverso
Reviewed in Italy on January 30, 2024Le basi matematiche di questo libro non sono da super specialisti. Ma anche per chi è un ricercatore, questo libro offre un approccio diverso su molti temi standard, facendoti guardare a cose che conosci bene da un punto di vista inaspettato
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FPAGL5 out of 5 starsUne référence pour commencer dans ce domaine
Reviewed in France on August 25, 2022Les bases mathématiques et analyse numériques de niveau Master1 (Bac+4).
Agréable à avoir en format papier.
+ accès au site web pour suivre les quelques coquilles.
Simple regret : impossible d'accéder aux corrections des nombreux exercices sans être un enseignant dans une faculté.
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Shantanu Das5 out of 5 starsGreat building block
Reviewed in India on October 11, 2025This is a very structured approach to gain a strong grasp of the mathematical fundamentals required for machine learning. If you pair this up with "Understanding Machile Learning: From Theory to Algorithms" by Shai Ben-David and Shai Shalev Shwartz, then that's a clear winner combo for ML theory.
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