Math Basics for Computer Science and Machine Learning [pdf]

The professor who wrote this is Jean Gallier, and I had him for advanced linear algebra at Penn. I am also pretty close to him in so far as a student can be close to a professor. On a personal note, he is one of the funniest professor I&#x27;ve had, and all math professors are characters.<p>For the people who are interested in ML, the thing to remember here is that he is a Serious mathematician, and he values rigor and in-depth understanding above all. A lot of his three star homework problems were basically impossible. He writes books first and foremost so <i>he</i> can understand things better. In math books, there&#x27;s the book you first read when you don&#x27;t understand something<i>, then the book you read when you understand everything. This is book in the link.<p></i>for linear algebra, this:<a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Introduction-Linear-Algebra-Gilbert-Strang&#x2F;dp&#x2F;0980232775&#x2F;ref=asc_df_0980232775&#x2F;?tag=hyprod-20&amp;linkCode=df0&amp;hvadid=312152840806&amp;hvpos=1o1&amp;hvnetw=g&amp;hvrand=13794249926302782300&amp;hvpone=&amp;hvptwo=&amp;hvqmt=&amp;hvdev=c&amp;hvdvcmdl=&amp;hvlocint=&amp;hvlocphy=9015292&amp;hvtargid=pla-454800779501&amp;psc=1&amp;tag=&amp;ref=&amp;adgrpid=61316181319&amp;hvpone=&amp;hvptwo=&amp;hvadid=312152840806&amp;hvpos=1o1&amp;hvnetw=g&amp;hvrand=13794249926302782300&amp;hvqmt=&amp;hvdev=c&amp;hvdvcmdl=&amp;hvlocint=&amp;hvlocphy=9015292&amp;hvtargid=pla-454800779501" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Introduction-Linear-Algebra-Gilbert-S...</a>)

From the start of Chapter 2:<p>&quot;In the following four chapters, the basic algebraic structures (groups, rings, fields, vectorspaces) are reviewed, with a major emphasis on vector spaces. Basic notions of linear algebra such as vector spaces, subspaces, linear combinations, linear independence, [...], dual spaces,hyperplanes, transpose of a linear maps, are reviewed.&quot;<p>If anyone needs to start even earlier than this, I&#x27;ve actually found &quot;3D Math Basics for Graphics and Game Development&quot; to be a good true intro for linear algebra-related stuff. I think this would probably hold even if your primary interest is something other than graphics&#x2F;game dev. Some of the text in that book&#x27;s intro is a little cringey with its reliance on kind of juvenile game references, but I didn&#x27;t find that sort of writing continuing during the actual text. So just push past that stuff.<p>I got a copy of it to act as a refresher before diving into Real-Time Collision Detection since it&#x27;s been quite a long time since formal math for me (as in, high school, because I&#x27;m self-taught in CS). I&#x27;ve managed to make up a lot of ground by working hard and finding classes to audit online (Strang&#x27;s linear alg course on OCW is a good one), but I have found that depressingly few math texts which claim to be &quot;introductory&quot; are actually truly introductory.<p>This isn&#x27;t a slight against the linked work, I absolutely love when profs make resources such as this freely available.<p>&quot;How to Prove It&quot; and &quot;Book of Proof&quot; are also great intros to formal math, if less immediately practical.

“Math Basics” is quite the misnomer—it gives the impression that one would need to study all of the contents of this book to be an effective practitioner in CS or ML. Memorizing every definition and theorem in this book would be neither necessary nor sufficient for that purpose.<p>Keep in mind it can take an hour, and sometimes way more, to <i>really</i> absorb a single page of a math book like this (do the math). This is more of a reference text.

Great book.<p>I think it&#x27;s a good time to mention a couple of nice books (related)<p>1. Elementary intro to math of machine learning [0]. Its style is a bit less austere than that of OP&#x27;s. It also has a chapter on probability. It could possible serve as a great prequel to the book linked in the OP.<p>2. The book on probability related topics of general data science: high-dimensional geometry, random walks, Markov chains, random graphs, various related algorithms etc [1]<p>3. Support for people who&#x27;d like to read books like the one linked in the OP, but never seen any kind of higher math before [2]. This book has a cover that screams trashy book extremely skimpy on actual info (anyone who reads a lot of tech books knows what I am talking about), but surprisingly,it contains everything it says it does and in great detail. Not even actual math textbooks (say, Springer) are usually written with this much detail. Author likes to add bullet point style elaboration to almost every definition and theorem which is (almost) never the case with gazillions of books usually titled &quot;Abstract Algebra&quot;, &quot;Real Analysis&quot;, &quot;Complex Analysis&quot; etc. Some such books sometimes attach words like &quot;friendly&quot; to their title (say, &quot;Friendly Measure Theory For Idiots&quot;) and still do not rise to the occasion. Worse yet, a ton (if not most) of these books are exact clones of each other with different author names attached. The linked book doesn&#x27;t suffer from any of these problems.<p>[0] Mathematics For Machine Learning by Deisentoth, Faisal, Ong<p><a href="https:&#x2F;&#x2F;mml-book.github.io&#x2F;book&#x2F;mml-book.pdf" rel="nofollow">https:&#x2F;&#x2F;mml-book.github.io&#x2F;book&#x2F;mml-book.pdf</a><p>[1] Foundations Of Data Science By Blum, Hopcroft, Kannan<p><a href="http:&#x2F;&#x2F;www.cs.cornell.edu&#x2F;jeh&#x2F;book%20no%20so;utions%20March%202019.pdf" rel="nofollow">http:&#x2F;&#x2F;www.cs.cornell.edu&#x2F;jeh&#x2F;book%20no%20so;utions%20March%...</a><p>2] Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra by Steve Warner<p><a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Pure-Mathematics-Beginners-Rigorous-Introduction&#x2F;dp&#x2F;0999811754" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Pure-Mathematics-Beginners-Rigorous-I...</a>

Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand.<p>So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.

I love that they have problems you can solve as well at the end of (almost) every chapter.<p>This IS a lot of math (1,962 pages) and it’s missing a preface&#x2F;introduction which would have been helpful to understand if I need to go linear or if a la carte is okay. At the moment I’d assume each major section is independent.<p>Awesome find! Wonder how It’s used. (One of) the author(s) seems pretty prolific too - <a href="http:&#x2F;&#x2F;www.cis.upenn.edu&#x2F;~jean&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.cis.upenn.edu&#x2F;~jean&#x2F;</a>

Whoah, this covers a lot. I was expecting some linear algebra, calculus, and discrete math, but there&#x27;s actually some stuff in there I don&#x27;t know after doing a masters in math.

I love professor gallier! He&#x27;s an incredible person.<p>That being said, this is faaaaaar beyond basics. It&#x27;d be more appropriate to call this an incomplete (aiming to be comprehensive) guide to almost everything you need to know in computer science (related to math).

That&#x27;s almost 2,000 pages of math...I don&#x27;t know why and how, but somehow I forgot most of the Statistics knowledge I obtained as a graduate student (in Stat) 10 years ago.<p>I remembered that I took an advanced course about Bayesian Inference, and one course about Multivariate Statistics (PCA, Factor analysis, these kind of things), and my project is about Bernstein Polynomial. That&#x27;s it...

In basic calculus one can burn countless hours memorizing mechanical rules to derive and integrate different function forms, or one can just plug the function into something like wolfram-alpha and get, for a lot of useful cases, a symbolic answer, or at least some approximate answer for a point or interval.<p>The point is, understanding integrals and derivatives doesn&#x27;t require one to memorize all the mechanical rules. Using software to compute those functions can be a huge time saver. No one should go with pen an paper double checking if that polynomial integral is correct or not!<p>With a book almost 2000 pages long, I wonder if this books leans more heavily on the mechanical-rules side of math. In my mind, is the difference between writing a book such that you can <i>write your own wolfram alpha</i>, or writing a book so you can just <i>use it</i>.

Haha 1900 pages on &quot;basics&quot;?<p>I suspect there are better resources for each topic covered (e.g Gilbert Strang books and OCW lectures for Linear Algebra), but it is definitely interesting to peruse and get a sense of relevant topics.

&quot;Math Basics&quot;<p>It&#x27;s 2000 pages long....

Even if you were ambitious and manage to read 5 pages per day everyday this would take you more than one year to read this from start to finish.

Nice to see wavelets in here - but it&#x27;s a shame that he seems to be encouraging people to actually use Haar wavelets. They&#x27;re fine for teaching - but there are usually better choices in real life. Daubechies are a good default

The writing style of this book i.e. rigorous math notation and proposition&#x2F;proof presentation is going to put off the great majority of potential CS and ML readers. At almost 2000 pages it sure makes a great door-stop though.

Me: Oh, good! I&#x27;ve always been pretty good at math but I want to learn how to make sense of the math I encounter in CS and ML.<p>[Reads the first paragraph of the 2nd chapter]<p>Me: I don&#x27;t know anything about math. At all.

Basics should be concepts that get you to 80% and tell you where to look for the rest 20%. This book tries to get you directly to 95% and is best treated as a reference book.

Strangely, probability theory is completely omitted.

I really can&#x27;t figure out who the target audience for this book is, if it has a target audience at all.

403 forbidden. Can someone host this?

I look at this and profoundly thank the people who make ml libraries for us the rest of us.

This is more like courses a talented undergrad math major would take through 4 years.

Okay, so this looks potentially awesome. But given that it is a reference work rather than some introductory &quot;basic&quot; little quick read-through, I&#x27;d prefer to have it in paper form.<p>Any hope of that happening?

this is an incredible reference for a machine learning researcher who wants to fill in some gaps in their existing mathematical knowledge.<p>But I would be shocked if this would be of any use for someone trying to learn a little linear algebra in order to play with neural networks. For that I think you still want Strang.<p>I think &quot;foundations&quot; might have been a better word than &quot;basics&quot; here. &quot;Basics&quot; in any case is not in the printed title, only in the filename.

403 forbidden, can someone help us out?

Can someone recommend me a book on Linear Algebra, Statistics and Probability?

That’s... quite a lot of math

This book looks great, I&#x27;ve been looking for a resource like that.

Great to see Prof. Gallier featured on here!

Math &quot;Basics&quot; in nearly 2k pages!

Q: Is this all necessary for ML?

is Linear Algebra something you need to work with machine learning?

This is a good book

This is nice.

Wow!