科学与数学courses.csail.mit.edu编辑精选
计算机科学中的数学
Mathematics for Computer Science [pdf]
2017 — 2020，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
MIT 6.042《计算机科学中的数学》的免费 PDF 教材，涵盖证明、离散数学、图论、概率等计算机科学所需的数学基础。全书 900 多页，语言直观易读，多次登上 HN 首页。
为什么经久不衰：它是完全免费开源的优质教材，比动辄数百美元的商业教科书更易读，多年后仍是学习 CS 数学基础的经典选择。
HN 评论精选
一线教师用它替代昂贵的商业教材，认为开源可自行补充内容是巨大优势
今年秋天我要在南卡罗来纳大学给约五十名学生上必修的离散数学课。之前用的 Epp 教材很出色，但售价高达 280 美元，很多学生靠打最低工资的工维持生计，我不想让他们花这么多钱。幸运的是我看到了这本！唯一的顾虑是我们的学生数学基础比 MIT 学生弱，比如我们花几周专门练归纳证明，而这本教材的例子似乎不够。我打算采用它并按需补充，而且它是开源的，我可以直接往里写补充材料并公开我的版本。
impendia查看英文原文
This fall I will be teaching the required "Discrete Math for CS course" to about fifty students at the University of South Carolina. Previously I used Epp's book [1] which in my opinion is an outstanding book but regrettably is $280.44. Many of our students are working minimum wage jobs to make ends meet, and I don't want to make them pay so much if I can at all help it. Lucky I saw this!! I do have one reservation though -- many of our students come in with a weaker mathematical background than MIT students; for example we spent several weeks doing proofs by induction (and no other kinds of proofs) and this text doesn't seem to feature a couple of weeks worth of examples. I think I'll probably go with this and supplement as needed. Really it looks quite wonderful. (And hell, the book seems to be open source which would mean that I could potentially write supplmentary material directly into the book and make my version available publicly as well.) This thread seems like a particularly good place to solicit advice: experiences with this book or others, what you wished you'd learned in your own undergraduate course on this subject, etc. I've taught this course once before -- I feel I did quite well but I still have room to improve. Thanks! [1] https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_1?ie=UTF8&qid=1488775608&sr=8-1&keywords=epp+discrete+mathematics
易读性和概率章节是突出优点
这本书是基础内容的非常易读的入门读物，比很多一味追求严格性而不注重直觉讲解的教科书好读得多。这是普林斯顿 CS 理论入门课的教材之一，概率部分尤其出色。
beisner查看英文原文
This book is a really accessible primer on the basics. Much more readable than a lot of other textbooks, which kind of go all-out in terms of rigor rather than present things intuitively. This was one of the textbooks we used in Princeton's introductory CS theory class (COS 340: Reasoning About Computation). The probability section is especially good.
质疑普通程序员是否真需要这么多数学，尤其是证明
这份文档超过 900 页，读完并理解要花多久？真的都有必要吗？表面上看这是个收益存疑的艰巨任务。我编程六年了，包括手动实现 RSA 加密，只需要基本数学知识。这份材料从证明讲起——我从未在学校学过证明，它在我看来只属于科学论文而非计算机从业者的实际生活。我不是批评它，只是真心想知道这 900 页能带给我什么。
lucb1e查看英文原文
This document is over 900 pages. How long are you supposed to take to read and understand all of this? And is this really all necessary? On the surface this looks like an insurmountable task with questionable benefits. Don't get me wrong, but in the past 6 years of casual and professional programming, I've needed only a basic understanding of math, the most difficult thing being collision detection in games, and that includes doing RSA cryptography by hand. This paper starts off with proofs, something I've never had in school and which always seemed to me as if they only belong in scientific math papers, not practical life of someone doing computer science. I don't mean to criticize the document or math in general, I would genuinely like to understand what 900 pages of this is going to bring me, especially when it starts with something I've never needed or seen outside of theoretical math discussions.
作者背景不凡，是 Akamai 的联合创始人兼 CEO
第二作者 F Thomson Leighton 不只是在 Akamai Technologies 工作，他是联合创始人兼 CEO。
fred256查看英文原文
The second author, F Thomson Leighton, doesn't just work at Akamai Technologies, he's the co-founder and CEO.
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