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  • Mathematics for Machine Learning

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Mathematics for Machine Learning 1st Edition

4.6 out of 5 stars (1,021)

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The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

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From the Publisher

Mathematics for Machine Learning, Cambridge University Press, linear algebra

Editorial Reviews

Review

‘This book provides great coverage of all the basic mathematical concepts for machine learning. I'm looking forward to sharing it with students, colleagues, and anyone interested in building a solid understanding of the fundamentals.' Joelle Pineau, McGill University, Montreal

‘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

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

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:
    4.6 out of 5 stars (1,021)

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Customer reviews

4.6 out of 5 stars
1,021 global ratings

Customers say

Customers find the book provides a well-curated collection of essential math for machine learning and serves as a great reference. The clarity of explanations receives mixed feedback, with some finding it clear while others say it lacks explanations. Moreover, customers disagree on the book's suitability for beginners, with some noting it's not a book for learning.
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20 customers mention mathematics, 17 positive, 3 negative
Customers appreciate the book's mathematics content, describing it as a well-curated collection of essential concepts that goes great with any math methods book.
...Then, moves quickly into intermediate level with practical and relevant information....Read more
...This book, however, takes the math seriously, and is incredibly direct and efficient in the introduction of new, relevant topics in calculus, linear...Read more
...machine learning and neural networks, and also have a basic intuition behind the math, and want to combine this intuition with a formal mathematical...Read more
...material you need to know in a very compact format, allowing you to proceed with studying ML (which is probably your goal) - it is very dense....Read more
13 customers mention content, 11 positive, 2 negative
Customers find the content of the book awesome, with one customer specifically mentioning the Jupyter Lab notebooks.
This is an awesome book but you need some basic experience on linear algebra and calculus to put in context and make it easier going through the...Read more
Best book if you are looking to study math of machine learning! Author has given references where to do further studies....Read more
Don't get me wrong, this is a really good book....Read more
Just an unbelievable book. It may be a bit difficult to follow but complemented by a couple of online resources for when you're stuck it's awesome....Read more
8 customers mention reference content, 6 positive, 2 negative
Customers find the book serves as a great reference, with one customer noting its handy paperback format and another mentioning its comprehensive topic catalogs.
...years of prosperity and good fortune for making the auxiliary content freely available and in such a open and honest manner. Bravo....Read more
...It's going to be a good fundamental reference text you'll refer over and over, but a very poor textbook to study math beyond ML.Read more
...more difficult math, this book is a disappointment - it references a lot of other texts when the math gets interesting - i.e. instead of covering...Read more
...I can agree that it presents catalogs of topics and glow for ML but not a “Don’t look any further” text which I was expecting.Read more
12 customers mention clarity of explanations, 7 positive, 5 negative
Customers have mixed opinions about the clarity of the book's explanations, with some finding them clear and starting with basics using examples, while others find them lacking.
...That's basically the only prerequisite. The explanations are clear, and the book is designed to bring clarity and lucidity onto the topics...Read more
This is an awesome book but you need some basic experience on linear algebra and calculus to put in context and make it easier going through the...Read more
...Definitions are precise. Explanations are succinct. It is not intended to be, but is a masterpiece that brings out the beauty of mathematics.Read more
...There are many more examples where the book doesn't provide proofs/explanations and hurries on to introduce new concepts....Read more
8 customers mention suitable for beginners, 4 positive, 4 negative
Customers have mixed opinions about the book's suitability for beginners, with some finding it unsuitable as a learning resource.
...- definition, theorem, example - make this book very accessible to all STEM undergraduates....Read more
...This is NOT a book for learning. It is a detailed and expanded table of contents that can be used to identify any topics that you are missing....Read more
Great book for beginners!Read more
...NOT a FIRST book for working professional....Read more

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, 2025
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    If 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 helpful
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  • 5 out of 5 stars
    Incredible Resource
    Reviewed in the United States on September 3, 2022
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    I 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 helpful
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  • 5 out of 5 stars
    Brilliant and Precise
    Reviewed in the United States on April 29, 2020
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    The 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 helpful
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  • 4 out of 5 stars
    A Book Struggling with its Identity
    Reviewed in the United States on July 14, 2023
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    Don'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 helpful
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  • 5 out of 5 stars
    Excellent book for reviewing math materials
    Reviewed in the United States on November 11, 2021
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    This 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 helpful
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  • 5 out of 5 stars
    Awesome book but it can scare the beginners :)
    Reviewed in the United States on February 27, 2022
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    Great 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 helpful
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  • 5 out of 5 stars
    Great book for beginners!
    Reviewed in the United States on September 13, 2020
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    Even 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 helpful
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  • 5 out of 5 stars
    Great Reference and Refresher Book
    Reviewed in the United States on February 22, 2021
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    Fits 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

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  • 5 out of 5 stars
    Dies ist das BESTE Buch über die Mathematik des Machine Learnings
    Reviewed in Germany on March 16, 2024
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    Nachdem 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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  • 5 out of 5 stars
    Excelente herramienta !!
    Reviewed in Mexico on March 30, 2026
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    Buen libro !

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  • 5 out of 5 stars
    Guardare le cose da un punto di vista diverso
    Reviewed in Italy on January 30, 2024
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    Le 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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  • 5 out of 5 stars
    Une référence pour commencer dans ce domaine
    Reviewed in France on August 25, 2022
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    Les 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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  • 5 out of 5 stars
    Great building block
    Reviewed in India on October 11, 2025
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    This 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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