科学与数学cis.upenn.edu编辑精选
面向计算机科学与机器学习的代数、拓扑、微分学与优化理论
Algebra, Topology, Differential Calculus, and Optimization Theory for CS and ML [pdf]
2019 — 2025，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
宾夕法尼亚大学 Jean Gallier 撰写的约 2000 页数学专著（PDF），系统覆盖计算机科学与机器学习所需的代数、拓扑、微分学与优化理论。它以数学家的严谨风格罗列定义与定理，追求详尽而非入门友好。
为什么经久不衰：它把 CS/ML 所需的数学基础汇编成一部罕见的完整参考，多年反复登上 HN 首页，适合作为需要严格数学定义时的查阅手册。
HN 评论精选
这类巨型个人笔记更像作者的思想日记，不适合作为学习教材
这种庞大宽泛的个人笔记集对作者很过瘾，对读者却未必。很多人问该怎么读，答案是不该读。这类文档更像日记而非教科书，展示的是别人技术思维的脚手架，而不是教你搭建自己的。最好的教科书总是聚焦且经过教学打磨的。
knzhou查看英文原文
Giant, broad sets of notes like these are very satisfying for the writer -- not so much for the reader. I should know, since I have a similar 1500 page work on the foundations of physics, and nobody's ever found it comprehensible. [1] I think a lot of academics have these personal tomes lying around, though most haven't bothered to type them up. I see a lot of comments asking how one should read these things, but the answer is that one shouldn't. These documents are more like diaries than textbooks. They'll show you the scaffolding of somebody else's technical mind, not how to build your own. The best textbooks are always focused, and honed by teaching experience. 1: https://knzhou.github.io/#lectures
该书面向数学家而非计算机科学家，对普通 CS 背景读者不友好
既然提到 CS，批评是公平的：我有 CMU 的 CS 学位，这份材料对我来说完全看不懂。它不仅从数学视角写就，而且面向的是数学家而非计算机科学家。既对 CS 人员即时有用又易于上手的数学书少之又少。多数数学书的毛病是堆砌定义却不说明它在实践中的用处，我吸收抽象结构的能力有限，大脑会判定它们无用而清空。
armitron查看英文原文
Since it mentions CS I feel criticism is fair: I have a CS degree from CMU and this material is simply incomprehensible to me. It's not only written from a mathematical perspective but also aimed at mathematicians, and not computer scientists. Unfortunately, math textbooks that are both immediately useful and instantly accessible to computer scientists are few and far between. Why doesn't anyone strive to cover that gap? I find that the major point of contention with most math textbooks is their tendency to pile one definition after another without showing me how that definition is useful in practice. I have a limit in how many abstract mathematical structures and theorems I can absorb before my brain simply wipes them out since it deems them to be useless. For that reason, the best math textbooks for me have been grounded in practicality (and are not really math textbooks). I learned calculus from Spivak, abstract algebra from Antoine Joux and analysis from Sussman.
总结此前讨论：内容密集严谨，适合有数学背景者，作者以严谨著称
此前讨论的要点：内容非常密集；没有数学训练很难读懂；它不是入门书，除非你有背景知识。作者 Gallier 是一位极严肃的数学家兼计算机科学家，重视严谨、不用含糊的说法掩盖任何东西，因此这本书在所选主题上极其详尽（可能因此牺牲了覆盖面）。
abhisuri97查看英文原文
Previous discussion: https://news.ycombinator.com/item?id=20570025 Tl;dr: * This is dense * This is hard to understand if you don't have an education in mathematics * This is not really meant to be an "introduction to X" book unless you have the background knowledge * Gallier (who imo is an awesome professor) really values rigor and not hiding anything behind hand-wavy statements. He is an incredibly serious mathematician + computer scientist (https://en.wikipedia.org/wiki/Jean_Gallier). Accordingly, this book (work in progress) tries to be incredibly detailed on the topics it chooses to cover (and may miss out on some areas of CS + ML solely bc it chooses detail over comprehensiveness).
希望有依赖关系图方便按需规划学习路径
第一章在哪？如果这类巨型教科书能附带详细的依赖关系图就好了，这样读者可以按模块序列逐步学习，最终到达自己感兴趣的主题。
calf查看英文原文
Where's Chapter 1? And wouldn't it be great if huge textbooks like these had a detailed dependency graph, so you could easily build up through a sequence of topic modules to reach something that interests you.
历次讨论
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