科学与数学cis.upenn.edu编辑精选
计算机科学与机器学习数学基础（PDF）
Math Basics for Computer Science and Machine Learning [pdf]
2017 — 2019，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
这是宾夕法尼亚大学 Jean Gallier 教授编写的数学讲义 PDF，面向计算机科学与机器学习方向，系统梳理群、环、域、向量空间等代数结构，以及线性代数的核心概念（子空间、线性无关、对偶空间、超平面、转置映射等），并涵盖概率等其他数学主题。它不是零基础入门书，更像一部体系完整、强调严格性的参考教材。
为什么经久不衰：作者是治学严谨的数学家，讲义免费公开且内容自洽深入，多年来一直是进入 ML 数学前值得备在手边反复查阅的经典资料。
HN 评论精选
作者极为严谨，此书属于"学通之后回看"的类型，入门宜先读 Strang。
作者 Jean Gallier 是我在宾大修高等线性代数时的老师，人非常风趣。想搞机器学习的人要记住：他是一位严肃的数学家，最看重严格性和深入理解，很多三星作业题基本做不出来。他写书首先是为了自己想明白问题。数学书分两种：你不懂时读的第一本，和全都懂了之后读的那本——链接里这本属于后者。线性代数入门可以看 Gilbert Strang 那本。
xiaolingxiao查看英文原文
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've had, and all math professors are characters. 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 he can understand things better. In math books, there's the book you first read when you don't understand something, then the book you read when you understand everything. This is book in the link. for linear algebra, this:https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/0980232775/ref=asc_df_0980232775/?tag=hyprod-20&linkCode=df0&hvadid=312152840806&hvpos=1o1&hvnetw=g&hvrand=13794249926302782300&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9015292&hvtargid=pla-454800779501&psc=1&tag=&ref=&adgrpid=61316181319&hvpone=&hvptwo=&hvadid=312152840806&hvpos=1o1&hvnetw=g&hvrand=13794249926302782300&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9015292&hvtargid=pla-454800779501)
讲义起点不低；零基础读者可先用图形学 3D 数学书补线性代数。
第二章开头说明：接下来四章会复习基本代数结构（群、环、域、向量空间），重点在向量空间，并回顾子空间、线性组合、线性无关、对偶空间、超平面、线性映射的转置等基本概念。如果有人需要比这更早的起点，我觉得《3D Math Basics for Graphics and Game Development》是真正适合入门的线性代数读物，即便你的兴趣不在图形学也适用；开头有些游戏梗略显幼稚，但正文没有这种风格。我自学计算机，正规数学只到高中，为了读《Real-Time Collision Detection》拿它复习，收获很大。可惜号称"入门"的数学书里，真正适合零基础的少得可怜。这不是在批评这份讲义，教授愿意免费公开资料我非常感激。
Gene_Parmesan查看英文原文
From the start of Chapter 2: "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." If anyone needs to start even earlier than this, I've actually found "3D Math Basics for Graphics and Game Development" 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/game dev. Some of the text in that book's intro is a little cringey with its reliance on kind of juvenile game references, but I didn't find that sort of writing continuing during the actual text. So just push past that stuff. I got a copy of it to act as a refresher before diving into Real-Time Collision Detection since it's been quite a long time since formal math for me (as in, high school, because I'm self-taught in CS). I've managed to make up a lot of ground by working hard and finding classes to audit online (Strang's linear alg course on OCW is a good one), but I have found that depressingly few math texts which claim to be "introductory" are actually truly introductory. This isn't a slight against the linked work, I absolutely love when profs make resources such as this freely available. "How to Prove It" and "Book of Proof" are also great intros to formal math, if less immediately practical.
标题有误导性：无需通读，本书定位是参考书。
"Math Basics"这个标题其实相当误导，容易让人以为要学完这本书的全部内容才能做好 CS 或 ML。把书里每个定义和定理都背下来，对这个目标既不必要也不充分。要记住，真正吃透这样一本数学书的某一页，可能需要一小时甚至更久（可以自己算算）。它更像一本参考书。
jointpdf查看英文原文
“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. Keep in mind it can take an hour, and sometimes way more, to really absorb a single page of a math book like this (do the math). This is more of a reference text.
内容实为约三年本科数学课程，与 CS 的直接关联被夸大。
标题里不该出现 CS。把这些笔记全部学完，差不多相当于一个标准的三年本科数学课程。所以它与 CS 的唯一关系就是：本科数学本来就能用于 CS，这在意料之中。
llamaz查看英文原文
CS shouldn't be in the title. If you learn everything in this set of notes you will have learned something close to a standard 3 year undergraduate math curriculum. So the only way it's related to CS is that undergraduate math is applicable to CS, as expected.
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